IFTA Journal 2013 Edition A Professional Journal Published by The International Federation of Technical Analysts

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1 IFTA Journal 2013 Edition A Professional Journal Published by The International Federation of Technical Analysts 13 Inside this Issue 6 The Implied Volatility Projection Range (IVPR); Extending the Statistical and Visual Capability of the VIX 13 Psychological Barriers in Asian Equity Markets 20 Regime-Switching Trading Bands Using A Historical Simulation Approach In the business world, the rearview mirror is always clearer than the windshield. Warren Buffett

2 The Future of Technical Analysis has arrived. Discover a whole new world of possibilities at

3 Letter From the Editor By Rolf Wetzer, Ph.D...5 EDITORIAL Rolf Wetzer, Ph.D. (SAMT) Editor, and Chair of the Editorial Committee Aurélia Gerber (SAMT) Editor Ralf Böckel, CFA (VTAD) Editor Michael Samerski Editor Mark Brownlow, CFTe (ATAA) Editor Send your queries about advertising information and rates to Articles The Implied Volatility Projection Range (IVPR); Extending the Statistical and Visual Capability of the VIX By Mohamed El Saiid, CFTe, MFTA... 6 Psychological Barriers in Asian Equity Markets By Shawn Lim, CFTe, MSTA, and Bryan Lim MFTA Papers Regime-Switching Trading Bands Using A Historical Simulation Approach By Ka Ying Timothy Fong, CFTe, MFTA Using a Volatility Adjusted Stop Loss (VASL) to Enhance Trading Returns By Edward Rowson, CFTe, MFTA Momentum Indicators: An Empirical Analysis of the Concept of Divergences By Stephan Belser, CFTe, MFTA...35 Wagner Award Paper Momentum Success Factors By Gary Antonacci...45 Educational Heikin-Ashi: A Better Technique to Trends in Noisy Markets By Dan Valcu, CFTe...54 About cover photo: Abstract Waves Photo by piccerella Book Review Mastering Market Timing, Using the Works of L.M. Lowry and R.D. Wyckoff to Identify Key Market Turning Points By Richard A. Dickson and Tracy L. Knudsen Reviewed by Regina Meani, CFTe Author Profiles...61 IFTA Board of Directors IFTA Journal is published yearly by The International Association of Technical Analysts Key West Avenue, Suite 100, Rockville, MD USA The International Federation of Technical Analysts. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying for public or private use, or by any information storage or retrieval system, without prior permission of the publisher. IFTA.ORG PAGE 3

4 IFTA TH ANNUAL CONFERENCE San Francisco Check the website for updates:

5 Letter From the Editor By Rolf Wetzer, Ph.D. Dear IFTA Colleagues and Friends: In all our writings and teaching on technical analysis, we never forget to quote our mantra history repeats itself. If we go back 100 years and look at the Dow Jones Industrial Index, it seems that this is a good assumption. In 1912, the first quarter started with an upsurge. In Spring, the market went sideways, spiced with good volatility. In Summer, the market rose to a new high. Does this sound familiar? The International Federation of Technical Analysts (IFTA) Journal is traditionally international, both in its contributions and techniques described. This year, the Journal has four separate sections. In the first section, two articles were submitted by IFTA colleagues from the Egyptian Society of Technical Analysts (ESTA) and the Society of Technical Analysts (STA). ESTA s contribution covers volatility bands based on the VIX Index. STA offers information on a strict testing procedure for psychological barriers in Asian stock markets; as our 2012 Annual Conference will be in Singapore, this article might offer additional insight into some of the Conference topics. In the second section, there are three papers from our Master of Financial Technical Analysis (MFTA) program. One of the authors, Stephan Belser, MFTA, was awarded the John Brooks Memorial Award for Congratulations! This year, aside from our own MFTA material, we are happy to publish a paper from another organisation. With the permission of the National Association of Active Investment Managers (NAAIM), we have included a paper by Gary Antonacci, winner of the NAAIM Wagner Award We hope that you find this paper informative. We conclude with contributions from two of IFTA s current Board members. Dan Valcu, CFTe, IFTA s Membership Director and Vice President of Europe, has written an article on a Japanese charting technique. IFTA s former Journal Editor and Director, Regina Meani, CFTe, contributed a book review. Again, like IFTA itself, the Journal is truly international. I would like to thank the authors for their contributions. And, not only do Journal articles come from all over the globe, our editors do too. I would like to thank Aurélia Gerber, Ralf Böckel, Michael Samerski and Mark Brownlow for their help in editing this Journal. Last but not least, I would like to thank Linda Bernetich and Jon Benjamin for the layout and their effort in putting the Journal together. We are now in the fifth year of a financial crisis. In 1912, the year ended with a drawdown. Hopefully, as good market technicians, we should be prepared this time. In all our writings and teaching on technical analysis, we never forget to quote our mantra history repeats itself. IFTA.ORG PAGE 5

6 The Implied Volatility Projection Range (IVPR); Extending the Statistical and Visual Capability of the VIX By Mohamed El Saiid, CFTe, MFTA 1. Abstract This paper proposes a new method for extending the statistical and visual capability of the Chicago Board Options Exchange (CBOE) market volatility index (VIX) over the S&P 500 (SPX). The paper subsequently provides several visual examples of the proposed method and discusses its implications and uses over the chart from a technical standpoint. Finally, the paper discusses implementing the same methodology on other implied volatility-based indices over their corresponding/underlying equity market indices. The methodology proposed in this paper will be referred to hence forth as the Implied Volatility Projection Range or IVPR. 2. Introduction 2.1 The VIX definition The Chicago Board Options Exchange (CBOE) market volatility index (VIX) is a forward-looking index of the expected return volatility of the S&P 500 index (SPX) over the next 30 days. This forward-looking feature is implied from the atthe-money SPX option prices. As such, the VIX measures the volatility that investors expect to see, rather than what has been recently realized. 1 The VIX estimates the expected volatility by averaging the weighted prices of the SPX puts and calls over a wide range of strike prices. 2 In that respect and as opposed to equity market indices which are comprised of stocks, the VIX index is comprised of options, where each option price is intended to reflect the market s expectation of future volatility. 3 The VIX was initially developed by Prof. Robert E. Whaley in 1993 and is a registered trademark of the CBOE. Since then, several modifications were introduced in its calculations The VIX implications (indications) over the SPX In his writings, Whaley discussed that while volatility implies unexpected market moves regardless of direction, the VIX is dubbed as the investor fear gauge. He justified this to be on the back of the current domination of the SPX option market by the hedgers. Hedgers demand on puts tends to increase when there is a concern for a potential decline in the stock market. Once that concern manifests, the VIX values tend to increase. Whaley coined this feature as portfolio insurance. As such, the VIX indicator tends to reflect the price of portfolio insurance. 5 Attempting to prove his argument, Whaley s tests established the following: 6 Small SPX daily changes result in negligible VIX changes. Volatility tends to follow a mean-reverting process. There is an inverse, yet asymmetric relationship between the SPX and the VIX movements. According to Whaley, the latter feature is brought about by portfolio insurance. To support Whaley s argument, we have performed a series of linear correlation tests between the SPX and the VIX over 5,520 daily closing values (from January 1990 to December 2011). The first correlation test performed was conditional exclusively on positive SPX returns. The second test was conditional only on negative SPX returns. The third to seventh tests were conditional on achieving returns greater than +/-0.50%, +/-1.00%, +/-2.00%, +/-3.00% and +/-4.00% in the SPX. The outcomes of these tests were then compared to a final nonconditional correlation test between the SPX and the VIX and the results are shown in table 1. Table 1: Non-conditional vs. conditional correlation results between the SPX and the VIX Correlation test Correlation. Coefficient (R) Non-conditional correlation Conditional Correlation Tests Positive SPX returns correl Negative SPX returns correl Greater than +/-0.5% SPX returns correl Greater than +/-1% SPX returns correl Greater than +/-2% SPX returns correl Greater than +/-3% SPX returns correl Greater than +/-4% SPX returns correl From the results presented above we can make the following deductions: A negative correlation does exist between the SPX and the VIX regardless of the correlation conditions. The negative correlation appears stronger at (R) conditional to negative SPX returns (-0.6) than at (R) conditional to positive SPX returns (-0.46). This reflects the asymmetry of movements of both indices as a result of portfolio insurance. Negative correlation increases or becomes more significant as the SPX returns become more volatile. In other words, the VIX values become more significant as the SPX daily returns surge and/or plunge. 2.3 How the VIX is currently being used The VIX generally exhibits two strong characteristics. One being a consistent negative correlation with the SPX, while the PAGE 6 IFTA.ORG

7 other is the strong tendency for the VIX to revert to its long term mean, thus reflecting the absence of deterministic growth in volatility (unlike stocks). 7 According to these two features, the common interpretations of the VIX values (as a standalone index) include the following: Abnormally high VIX readings imply a potential bottom, or the occurrence of a counter-trend rally in the SPX. The opposite is true at relatively low VIX readings. On the other hand, an up trending VIX implies a potentially sustainable downtrend in the SPX and vice versa. Figure 1 visually depicts both features of the VIX; the tendency to revert in an oscillatory-type motion despite experiencing trending phases in the process, as well as the negative correlation with the SPX. This is evident by the VIX peaks and valleys that coincide with key SPX lows and highs, respectively. In this chart we have indicated relatively high and low VIX readings with reference to the 30% and 16% levels, respectively, based on visual inspection over the period presented. A common strategy among traders when using the VIX is to go long on equities when the VIX rebounds from key highs and sell (or short) equities when the VIX rebounds from key lows. 3. Statistical interpretation and inferences of the VIX values 3.1 Statistical interpretation The VIX calculation produces a probability-based interpretation with respect to the estimated range of the SPX rates of returns over the next 30 days. 8 Example: Assume that the SPX closed at 1, and the VIX closed at today. Since the VIX values are annualized standard deviation values multiplied by 100, to transform the value back to represent the 30 days (or 1 month) sigma, we divide 25 by 100 and then divide the outcome by the square root of In this example the result was 7.22%. According to the statistical Empirical Rule, this is interpreted as follows: there is a probability of 68.2% (approximately) that the expected range of the SPX returns over the next 30 days will lie within +/-7.22%, or within the range of (1, ,393.82). 3.2 Statistical inferences Testing the VIX interpretation according to the Empirical Rule and using historical daily closing values for the VIX from January 1990 to December 2011, we present the outcomes in table 2. Figure 1: Upper window: The SPX index Daily values Candlestick chart Normal scale Lower window: The VIX index Daily values Candlestick chart Semi-logarithmic scale Periods marked in red indicate key highs on the SPX which coincided with VIX lows as identified by the 16% level Periods marked in blue indicate key lows on the SPX which coincided with VIX highs as identified by the 30% level ul Aug Sep Oct Nov Dec 2008 Mar Apr May Jun Jul Aug Sep Oct Nov Dec 2009 Mar Apr May Jun Jul Aug Sep Oct Nov Dec 2010 Mar Apr May Jun Jul Aug Sep Oct Nov Dec 2011 Mar Apr May Jun Jul Aug Sep Oct IFTA.ORG PAGE 7

8 Table 2: Statistical results Standard Deviation Inside VIX range 2,417 4,177 5,111 5,395 5,472 5, % 75.7% 92.6% 97.7% 99.1% 99.6% Outside VIX range 3,104 1, % 24.3% 7.4% 2.3% 0.9% 0.4% Outside lower VIX range 1, % 8.9% 4.0% 2.0% 0.9% 0.4% Outside upper VIX range 2, % 15.4% 3.4% 0.3% 0.0% 0.0% Total observed data 5,521 5,521 5,521 5,521 5,521 5,521 Empirical Rule 38.20% 68.20% 86.60% 95.40% 98.80% 99.80% As observed from table 2, the VIX estimates managed to contain the SPX action quite well over the period (5,521 days) under study. Accordingly, this paper proposes extending the statistical and visual capability of the VIX by representing the statistical interpretation of the VIX values over the SPX in the form of a projection range that moves dynamically as the SPX progresses forward in time. 4. Introducing the Implied Volatility Projection Range (IVPR) In this section, we introduce the IVPR and convey the means to visually plot it over the SPX. With reference to the interpretation previously presented, we regress the results over time (shown in table 3) and plot the resulting SPX range(s) over the SPX values on the chart (visualized by figure 2). Figure 2: Upper window: The SPX index vs. the IVPR Daily values Candlestick chart Normal scale. Lower window: The VIX index Daily values Candlestick chart Normal scale 7 March April May June July August Upper SPX VIX range shifted forward by 30-days Lower SPX VIX range shifted forward by 30-days September October November December February Ma Table Figure 3: Calculating 2 introduces the SPX the IVPR projection when range visually based plotted on the VIX over values the Date SPX Close VIX close VIX adj to 30 days Volatility Lower IVPR Upper IVPR 05/25/2010 1, % 05/26/2010 1, % 05/27/2010 1, % 05/28/2010 1, % 06/01/2010 1, % 06/02/2010 1, % 06/03/2010 1, % 06/04/2010 1, % 06/07/2010 1, % 06/08/2010 1, % 06/09/2010 1, % 06/10/2010 1, % Results are plotted 06/11/2010 1, % 30 days forward as 06/14/2010 1, % implied 06/15/2010 1, % 06/16/2010 1, % 06/17/2010 1, % 06/18/2010 1, % 06/21/2010 1, % 06/22/2010 1, % 06/23/2010 1, % 06/24/2010 1, % 06/25/2010 1, % 06/28/2010 1, % 06/29/2010 1, % 06/30/2010 1, % 07/01/2010 1, % 07/02/2010 1, % 07/06/2010 1, % 07/07/2010 1, % 07/08/2010 1, % , /09/2010 1, % , /12/2010 1, % 1, , /13/2010 1, % , /14/2010 1, % , /15/2010 1, % 1, , /16/2010 1, % 1, , /19/2010 1, % , /20/2010 1, % , /21/2010 1, % , PAGE 8 IFTA.ORG

9 Figure 3: The SPX index vs. the IVPR Daily values Candlestick chart Normal scale April May Lower low outside lower IVPR June W-shape formation Lower low failed to break below lower IVPR July Subsequent rally August Figure 4: The SPX index vs. the IVPR Daily values Candlestick chart Normal scale Higher high outside higher IVPR M-shape formations Higher high failed to break above upper IVPR Subsequent decline Higher high outside higher IVPR Higher high failed to break above upper IVPR Subsequent decline September October November December February March April May June July August 2 IFTA.ORG PAGE 9

10 Figure 2 introduces the IVPR when visually plotted over the SPX (upper window) and depicts the VIX (lower window). As a result of the visualization process, the IVPR boundaries are plotted 30-days forward as implied by the VIX calculation. Accordingly, the VIX implies a probability of 68.2% (approximately) that the expected range of the SPX returns over the next 30 days will lie within terminus points of the IVPR. 5. Technical interpretations of the IVPR Additional to the common uses/applications of the VIX previously stated, we introduce further interpretations by using the IVPR. 5.1 During the SPX trending phases During up-trending phases, volatility (the VIX) trends down. Meanwhile the SPX trends close to the upper IVPR and occasionally trends above it for a relatively short period. As the SPX forms higher highs, the SPX exceeds the projected estimation of the upper IVPR. However, in specifically observed cases, failing to reach the upper IVPR during uptrends implies weakness in the trend and suggests a countertrend correction. This can sometimes lead to a change in the overall SPX trend direction, especially if the VIX itself reverses direction. We recommend adopting the technique associated with the M-shape formations as a trading pattern that aims at highlighting such weaknesses. The M (& W) shape formations were proposed by Bollinger through his works on the Bollinger Bands (B-Bands) as two useful techniques to identify weaknesses in the underlying trends. 10 Moreover during up-trends, the SPX rarely makes any attempts towards the lower IVPR. In fact, all the SPX attempts towards the lower IVPR during a structurally-maintained uptrend and excluding trend reversal events are considered key lows in that up-trend. These dips are regarded as buying opportunities in the market. The opposite holds true during down-trending phases. The VIX trends up, while the SPX trends close to/and occasionally exceeds the projected estimation of the lower IVPR, as it registers lower lows. In certain cases, failing to reach the lower IVPR during down-trends implies weakness in the trend and suggests a counter-trend correction. This can sometimes lead to a change in the overall SPX trend direction, especially if the VIX itself reverses direction. Similarly, we propose the trading technique associated with the Bollinger W-shape formations as an appropriate tactic to be used during such events. On the other hand, during down-trends, rare attempts for the SPX towards the upper IVPR are observed and are considered key highs/selling opportunities in the market. Figure 3 shows the IVPR plotted over the SPX. Unlike the May/June low, the lower low created in July failed to move below the lower IVPR, implying that the market failed to exceed its prior 30-day volatility expectations and implied lesser volatility going forward. This was followed by a counter-trend rally that sustained till August. This trading pattern is comparable to a W-shaped B-Band pattern. Figure 4 shows the IVPR plotted over the SPX. The chart suggests two cases of M-shaped B-Band formations and their subsequent countertrend declines. 5.2 During the SPX trendless phases and trend reversals: Trendless phases During trendless or sideways phases in the SPX, the buying and selling power in the market are generally not sufficient to build-up or sustain a structured trend (up or down). It was observed that all price excursions from both IVPR boundaries were unsustainable. We propose using both IVPR boundaries during such phases as overbought (OB) and oversold (OS) levels for the SPX. As such, reaching or breaking the upper boundary, followed by a pullback inside, is regarded as a selling (trading) opportunity and vice versa for the lower IVPR. This tactic is similar to that used with moving average-based envelopes during sideways trends. 11 Figure 5: The SPX index vs. the IVPR Daily values Candlestick chart Normal scale IVPR aids in identifying OB/OS conditions during SPX sideways or trendless phases April May June July August September October November December 1992 February March April May June July August September October Figure 5 shows how the IVPR boundaries can be used to help identify OB and OS levels once a sideways phase has been identified over the SPX Trend reversals A trend reversal phase may be viewed as a temporary sideways or trendless condition in which an exchange in power between the buyers and sellers occur. This causes an existing trend structure (up-trend or down-trend) to reverse to the opposite trend structure. We have observed that during structural trend reversals in the SPX, volatility of the SPX also tends to change in behavior. During reversals from down trends, the following occurs: The undergoing rise in volatility (up trending VIX) begins to reverse from high levels (above 30%) at the same time or prior to the actual reversal of the SPX. The SPX begins to fall short of moving below the lower IVPR boundary, or at least makes brief attempts at the lower IVPR when compared to previous lows in that same bear trend. The SPX performs successful attempts to reach the upper IVPR, signaling new strength in buying power PAGE 10 IFTA.ORG

11 The IVPR boundaries fail to mark lower lows indicating that volatility is receding. The trend reversal is confirmed when the SPX successfully moves and sustains outside the upper IVPR following an initial structural trendreversal pattern. Figure 6, shows the bottoming phase which occurred on the SPX following the bear trend. Additional to the classic reversal structure which consisted of a higher low (in March 2003), followed by a higher high (in May/June), we have highlighted the behavior of the SPX with the IVPR. The last registered lower high of the SPX (November 2002) managed to breach above the IVPR on the near term frame. This was followed in March 2003 by a relatively brief breach below the IVPR and a higher SPX low was created during that same month. This higher SPX low was confirmed by a higher IVPR low. Finally, the higher SPX high which occurred later in May/June 2003 was associated with a breach of the upper boundary of the IVPR. Figure 7 shows the topping phase which occurred on the SPX prior to the bear trend. A lower high (in September 2000), followed by a lower low (in December 2000) constituted a trend reversal pattern. Confirming this reversal, the last registered SPX peak during this period (March 2000) was accompanied by a breach above the upper IVPR. The following (lower high), however, failed to move outside the upper IVPR (a confirmed weakness). This was followed by a lower low in December that succeeded to move below the lower IVPR to confirm the market reversal. Conclusion Without any doubt, the VIX is an invaluable market indicator that provides essential market clues and expresses the SPX trend conditions from the volatility standpoint. In this paper, we have recognized the virtues of the VIX as a standalone index and proposed a new method that aims at extending the statistical and visual capability of the VIX, namely, the IVPR. The IVPR transforms the stationary/statistical Figure 6: The SPX index vs. the IVPR Daily values Candlestick chart Normal scale This SPX high was associated with a breach of the upper IVPR; an event unseen in this 2-year bear trend except during May A higher SPX high (reversal confirmation) accompanied by a breach of the upper IVPR A higher SPX low May June July August September October November December 2003 February March April May June July August September Figure 7: The SPX index vs. the IVPR Daily values Candlestick chart Normal scale A lower SPX high A lower SPX low A lower SPX low (reversal confirmation) accompanied by a breach of the lower IVPR This SPX high failed to breach the upper IVPR ber Novem ber December 2000 February March April May June July August September October November December 2001 February March April Figure 8: The NASDAQ 100 index vs. the IVPR Daily values Candlestick chart Normal scale June July August September October November December February March April May June IFTA.ORG PAGE 11

12 interpretation of the VIX values into dynamic boundaries that project the SPX expectations in the future, derived from a statistical standpoint. The IVPR is yet still not without limitations. Although the IVPR managed to contain the SPX data according to predetermined statistical probabilities, the SPX will often exceed the IVPR boundaries and sustain over the NT horizon. We attribute this to a TA-based premise stating that markets move in defined trend structures. 12 In part, this is evident when the SPX values track one of the IVPR boundaries during a trending phase and not the other. Nevertheless, the IVPR offers a more comprehensive statistical and visual capability when compared to the VIX index (on a standalone basis). This advantage is especially valuable when trying to understand the relationship between the VIX and the SPX, and ultimately aids to some extent in forecasting the expected moves of the SPX in the future. References [1, 2] Chicago Board Options Exchange (CBOE), VIX White Paper, Pages: 1 and 4 respectively. [3, 4, 5, 6, 7] Whaley, Robert E., Understanding the VIX, The Journal of Portfolio Management, Spring Pages: 98, 99, 100 and 101 respectively. [8, 9] Rhoads, Russel, Trading VIX Derivatives: Trading and Hedging Strategies Using VIX Futures, Options, and Exchange Traded Notes, Wiley, Page Bollinger, John A., Bollinger on Bollinger Bands, McGraw-Hill, Page 94. [11, 12] Murphy, John J., Technical Analysis of the Financial Markets, New York Institute of Finance, Pages: 207 and 3 respectively. Figure 9: The Russell 2000 index vs. the IVPR Daily values Candlestick chart Normal scale August September October November December 2009 February March April May June July August Sep August September October November December 2009 February March April May June July August Sep Figure 10: The SPX index vs. the 2 standard deviations Daily values Candlestick chart Normal scale IVPR at 2 standard deviation IVPR will contain at 2 standard more of deviation the SPX action will contain more of the SPX action ly August September October November December 2008 February March April May June July August September October November December 2009 February March 300 ly August September October November December 2008 February March April May June July August September October November December 2009 February March Bibliography Bollinger, John A., Bollinger on Bollinger Bands, McGraw-Hill, Chicago Board Options Exchange (CBOE), VIX White Paper, Hull, John C., Options, Futures, and Other Derivatives, Prentice Hall, Mason, Robert D., Marchal, William G., Lind, Douglas A., Statistical Techniques in Business & Economics, McGraw-Hill/Irwin, Murphy, John J., Technical Analysis of the Financial Markets, New York Institute of Finance, Pring, Martin J., Technical Analysis Explained: The Successful Investor s Guide to Spotting Investment Trends and Turning Points, McGraw-Hill, Rhoads, Russell, Trading VIX Derivatives: Trading and Hedging Strategies Using VIX Futures, Options, and Exchange Traded Notes, Wiley, Whaley, Robert E., Understanding the VIX, The Journal of Portfolio Management, Spring Software and data Data courtesy of Bloomberg and Reuters. Charting software courtesy of Equis International MetaStock v.9.1. PAGE 12 IFTA.ORG

13 Psychological Barriers in Asian Equity Markets By Shawn Lim, CFTe, MSTA, and Bryan Lim In this study, we investigate the presence of psychological barriers in the equity indexes of 10 Asian Markets over a 10 year period from This investigation was conducted through the use of uniformity tests, barrier proximity tests and tests on the predictability of stock returns. We have found evidence for barriers at the 1000 level for 6 of these markets (JKSE, KLSE, N225, STI, KS11, TWII) and at the 100 level for 4 of these markets (AORD, JKSE, KLSE, STI). However, while there may be evidence of psychological barriers, there is little evidence for the predictability of stock returns induced by the presence of these psychological barriers. Introduction Hang Seng Index: Investors hope for support at 19,000, Nikkei rebounds after slipping below 8,500, KOSPI may test support at 1,900 points, and the list goes on. This is just a small snapshot of news headlines taken in May 2012, but the underlying theme is a distinctively familiar one. Regions of round numbers have often been regarded with special significance in the financial press, with the approach or penetration of these levels often taken by financial commentators to be of particular importance and is hence often used as a barometer of market sentiment. However, while the evidence that people (or at least the press) view levels around round numbers as important is indisputable, is the added attention truly warranted? Empirical studies applied to US markets have found some evidence of psychological barriers (Donaldson and Kim 1993) while evidence for return predictability has been weak (Koedijk and Stork 1994). While there has been substantial empirical research on the presence of these effects in Western markets, there has been considerably less research focused on Asian markets and this study attempts to supplement this growing body of knowledge by testing for the presence of psychological barriers around round numbers in Asian Equity Indices. There are 3 ways that tests for psychological significance are often conducted; tests on the distribution of digits, tests on the frequency of digits, and the behaviour of returns around presupposed barriers. This study tests for barriers using these 3 categories of tests as applied to the 10 selected Asian Equity Indices. Psychological barriers refer to regions of support or resistance around round numbers, hence at the 11300, 11400, 11500, etc levels for barriers at the 100 level and at 12000, 13000, 14000, etc for barriers at the 1000 level. As there is no fundamental reason for these levels to be of particular importance, the presence of regions of support or resistance around these levels have been attributed to behavioural biases, hence the term psychological barriers. Some explanations that have been offered for these round number effects include psychological preferences for round numbers (Ziemba et al 1986), coordination on limited price set (Harris 1991), convenience (Mitchell 2001), odd pricing (Schindler and Kirby 1997), bounded rationality and aspiration levels (Sonnemans 2006). Data This study uses closing prices for the following 10 Asian Equity Indices for the 10-year period from 1 Jan 2001 to 31 Dec 2011 as obtained from Yahoo Finance. Table 1 provides a summary of the indices used and their range over the test period. Table 1: Summary of the 10 Asian Equity Indices and their range from 1 Jan 01 to 31 Dec 11 Symbol Name Market High Low AORD All Ordinaries Australia SSEC Shanghai Composite China HSI Hang Seng Index Hong Kong BSESN BSE 30 India JKSE Jakarta Composite Indonesia KLSE KLSE Composite Malaysia N225 Nikkei 225 Japan STI Straits Times Index Singapore KS11 KOSPI Composite Index Korea TWII Taiwan Weighted Taiwan M-Values In order to test for the presence of psychological barriers, it is first necessary to introduce the concept of M-values as is often used in empirical tests for barriers. M-values are two digit numbers, ranging from 00 to 99 and represent a point, with 00 representing the region around a round number. We use 2 sets of M-values for each index, M 1000 for M-values to test the presence of barriers at the 1000 level and M 100 for M-values to test the presence of barriers at the 100 level. These are defined as follows: mod 100. Where P t is the integer part of P t. For example, if prices are and , M 100 are 98 and 38 respectively. ( ) mod 100. IFTA.ORG PAGE 13

14 For example, if prices are and , M 1000 are 99 and 73 respectively. When examining barriers at the 100 level, we would expect to see the index closing less frequently at the xx00.xx level if the barriers existed, and for the 1000 level we would expect to see the index closing less frequently at the x00x.xx level. This is what the respective M-values represent and is the rationale for using them in the tests specified throughout the rest of this paper. Frequency Distribution The following charts show the distribution of the M-values for the 10 markets: PAGE 14 IFTA.ORG

15 Presence of Psychological Barriers Uniformity Test To investigate the presence of psychological barriers, we conduct tests for positional and transgressional effects at the M 1000 and M 100 levels by carrying out a chi-square test using 3 different set ups and the resulting test statistics are reported in Table 2 and Table 4. We regard the thousand and hundred levels as potential psychological barriers and hence test the M-values at the corresponding levels. If there are no particular areas with any significance, we would then expect the M-values to follow a uniform distribution, i.e. there would be no particular reason for an index to close at, for example, (M 1000 = 90, M 100 = 00) more frequently than (M 1000 = 87, M 100 = 70) over the 10 year period investigated and hence we would expect to see the index closing at approximately an equal number of times at the 99 M-value as at the 45 M-value and so forth. If there IFTA.ORG PAGE 15

16 are regions of resistance or support close to round numbers, however, we would then expect to see less M-values close to the 00 region and for the distribution of all the M-values to not follow a uniform distribution. Hence, the first test ( Absolute Test ) tests the distribution of all the M-values against a uniform distribution with the hypothesis h 0 : the 100 M-values follow a uniform distribution against h 1 : the 100 M-Values do not follow a uniform distribution. The Chi-Squared Test static for each index is computed as follows: ( ) Where O i stands for the number of observations in each category i (i = 0 99 for Absolute Test, i=1 10 for Barrier Test and i = 1,2 for Remainder Test ) and E i stands for the number of observations expected ( ) ( ). The number of degrees of freedom for each test is computed as df = n-1. The second test ( Barrier Test ) follows the methodology adopted by Koedijk and Stork (1993) and splits the M-values into 10 disjunct categories of equal size, i.e , 16-25,, We register the number of times the index closes with an M-Value in these categories and perform a chi-square test with 10 categories in the manner described above. This test for uniformity is similar to the Absolute Test but widens the range of the potential areas of significance and is consistent with the conventional wisdom of areas of support and resistance being price bands and not absolute price levels. While the first and second tests pick up whether the distribution of M-values follows a uniform distribution, they say little about the location of these deviations and whether they are indeed around regions of round numbers, as per the purpose of the investigation. For example, if the index closes much less frequently in the M-value region but is uniformly distributed over the remaining values, the null hypothesis would be rejected in the first two tests but this would not be the effect we are trying to test for. Hence, a third test ( Remainder Test ) is introduced that attempts to separate this effect by splitting the M-values into 2 categories (96-05, 06-95) and a chisquared-goodness-of-fit test with the expected number in each category based on the expected number if it followed a uniform distribution has also been conducted and the results reported below. The barrier tests and remainder tests have also been conducted for a wider 20 point band (90-09,etc) but the results were qualitatively similar to the tests for the 10 point band and hence have been omitted in the presentation below. Barrier Proximity Test One major limitation of the uniformity tests is the lack of information on directionality, in that while it may present evidence for a non-uniform distribution due to unexpected deviations in our region of interest, it fails to show if that is because the index closes more frequently in those regions (price clustering) or because the index closes less frequently (evidence of barriers). This information is picked up in our second test, the barrier proximity test, as described by Donaldson and Kim (1993). We employ a variant of the methodology that yields more interpretable information in line with that adopted by Koedijk and Stork (1994). We test by means of a OLS regression test whether the distribution of M-values is linked to the presence of psychological barriers. A vector P(M) with length 100 is created, which registers the relative frequency of each M-value occurring along with 3 dummy variables, D 1, D 2 and D 3 and which equal 1 if the M-value of the index at closing is in one of the following ranges: 98, 99, 00, 01, 02 for D 1 ; 93,, 97 or 3,, 7 for D 2 ; 85,, 92 or 8,, 15 for D 3. We then regress the P(M) vector against these 3 variables: ( ) If there are no psychological barriers and the M-values follow a uniform distribution, what we would expect is an intercept of C = 1 and, and β 1, β 2 and β 3 = 0. If the β values are significant and not equal to zero, what this implies is that the relative frequency of M-values at the respective levels is greater (lower) than 1 if the β values are positive (negative). For example, if C = 1 and β 1 = 0.2 and β 1 is statistically significant, what this suggests is that the relative frequency of occurrence of a M-value if it is in the 98, 99, 0, 1, 2 region is = 0.8, i.e. significantly less than we would expect if the M-values are uniformly distributed and supportive of the presence of psychological barriers at round numbers. The results of this regression are shown in Table 3 and Table 5 below. Positional Effects In this section we investigate if the indices close more or less frequently around round numbers by performing the uniformity tests and barrier proximity tests on the M-values of the closing prices across the 10 years from 1 Jan 2001 to 30 Dec Uniformity Tests From the uniformity tests, we see strong evidence against a uniform distribution of M-values at the level for 8 out of 10 of the indices in the absolute test (AORD, SSEC, BSESN, JKSE, KLSE, STI, KS11, TWII), with the results confirmed in the barrier tests and in 5 out of 8 of these indices in the remainder tests (SSEC, JKSE, KLSE, STI, KS11). For the AORD, BSESN and TWII indices that show evidence for non-uniformity in the absolute and barrier but not remainder test, this could be indicative of non-uniformity in this distribution of M-values, not due to significantly less (or more) values in the region of interest, but outside the round number region. For the 100 level we find some evidence against uniformity in the barrier tests for 2 out of 10 of the indices (N225, STI). Barrier Proximity Tests From the regression, we see evidence of psychological barriers at the 1000 level in 6 out of 10 of the indices (SSEC, JKSE, KLSE, N225, STI, KS11) consistent with the results from the uniformity test, as well as evidence of barriers at the 100 level in the 3 out of 10 of the indices (JKSE, KLSE, TWII). We also find evidence of clustering around the 93-97, 3-7 levels as indicated by the positive and significant β 2 values in the AORD and TWII M 1000 regressions, which could be an explanation for the results they exhibited in the remainder tests. PAGE 16 IFTA.ORG

17 Table 2: Chi-squared test statistics from the uniformity tests on closing prices Index Absolute Tests Barrier Tests Remainder Tests M 1000 M 100 M 1000 M 100 M 1000 M 100 AORD SSEC HSI BSESN JKSE KLSE N STI KS TWII Results significant at the 95% confidence level are in yellow Table 3: Regression parameters for the barrier proximity tests on closing prices Index c P c β 1 P β 1 β 2 P β 2 β 3 P β 3 M AORD M M SSEC M M HSI M M BSESN M M JKSE M M KLSE M M N225 M M STI M M KS11 M M TWII M Results significant at the 90% confidence level are in yellow. P A represents the P-value of the t-test run with the hypothesis: h0: A = 0, H1: A 0 Table 4: Chi-squared test statistics for the uniformity tests on M-value transgressions Index Absolute Tests Barrier Tests Remainder Tests M 1000 M 100 M 1000 M 100 M 1000 M 100 AORD SSEC HSI BSESN JKSE KLSE N STI KS TWII Results significant at the 95% confidence level are in yellow Transgressional Effects In this section we test for the presence of psychological barriers by investigating if the regions around round numbers have been transgressed less frequently than other regions. For instance, if the index jumps from 1420 to 1532, the M 1000 values from 43 to 53 are transgressed and the M 100 values from 21 to 32 are transgressed. We conduct chi-squared tests for uniformity and perform the barrier proximity tests using the same specifications as above on the distribution of M-values that have been transgressed for each index and the results are presented in an identical format to Tables 2 and 3 in Tables 4 and 5. Uniformity Test For the uniformity tests, we see evidence against a uniform distribution of M-values in all the indices at the 1000 level and for 8 out of 10 indices at the 100 level (AORD, SSEC, HSI, BSESN, JKSE, KLSE, N225, STI) in the barrier tests. This is confirmed in 7 out of 10 indices at the 1000 level (AORD, HSI, JKSE, KLSE, N225, STI, KS11) in the remainder tests and in 6 out of 10 indices in the absolute tests (AORD, JKSE, KLSE, STI, KS11, TWII). At the 100 level, this is confirmed in 6 out of 8 indices in the remainder tests (AORD, HSI, BSESN, JKSE, KLSE, STI) and in 2 out of 8 indices in the absolute tests (KLSE, STI). The stark difference in the number of indices that demonstrate evidence against a uniform distribution in the absolute test compared to in the barrier and in the remainder tests particularly at the 100 level suggests that for some of these indices the individual M-values may be approximately uniformly distributed, but when grouped into categories around the barrier levels there is evidence against a uniform distribution, which can be seen as evidence for the presence of psychological barriers in the region around round numbers but not at the exact round number level, consistent with the conventional wisdom of support and resistance existing as regions around a level instead of at a single fixed level. IFTA.ORG PAGE 17

18 Barrier Proximity Test For the barrier proximity tests, we see evidence supporting the presence of psychological barriers in 5 out of 10 of the indices at the 1000 level (JKSE, KLSE, N225, STI, TWII) and evidence of price clustering around round numbers in 2 out of 10 of the indices at the 1000 level (AORD, HSI) with the remaining indices with intercepts that are not statistically significant, suggesting the absence of psychological barriers. At the 100 level, we see evidence supporting the presence of psychological barriers in 6 out of the 10 indices (AORD, JKSE, KLSE, STI, KS11, N225 (with weak evidence)) and evidence supporting price clustering in 2 out of 10 indices (HSI, BSESN) with the remaining indices with intercepts that are not statistically significant. Return Predictability Having examined the presence of psychological barriers, we proceed to investigate if these levels can be used to predict stock returns. We employ the methodology of Koedijk and Stork (1994) and test the following specification over the sample: Where ( ) ( ) ( ) ( ) Table 5: Regression parameters for the barrier proximity tests on M-value transgressions Index c P c β 1 P β 1 β 2 P β 2 β 3 P β 3 M AORD M M SSEC M M HSI M M BSESN M M JKSE M M KLSE M M N225 STI KS11 TWII M M M M M M M Results significant at the 90% confidence level are in yellow. P A represents the P-value of the t-test run with the hypothesis: h0: A = 0, H1: A 0 And where r t stands for the stock return, s t for the index at time t, D t (1) stands for the value of the first dummy variable at time t, D t (2) stands for the value of the second dummy variable at time and t and D t (3) stands for the value of the third dummy variable at time t. The dummy variables are specified in the same way as the regression that was run for the barrier proximity test. From the regression, we find little evidence to support return Table 6: Regression parameters for the test on return predictability Index c M AORD M M SSEC M M HSI M M BSESN M M JKSE M M KLSE M M N225 M M STI M M KS11 M M TWII M Results significant at the 90% confidence level are in yellow. represents the P-value of the t-test run with the hypothesis: h0: A = 0, H1: A 0 PAGE 18 IFTA.ORG

19 predictability for most of the indices with most of the parameter estimates for the dummies of the psychological barriers not statistically significant. Only in the BSESN at the 100 level, KLSE at the 1000 and 100 level, the KS11 at the 100 level and the TWII at the 1000 level is there some evidence of the predictability of stock returns induced by the presence of psychological barriers. Discussion Table 7 summarizes the results from all the tests with a final conclusion on whether there is sufficient evidence for positional effects, transgressional effects and psychological barriers. When there were conflicts in the results within each section, they were resolved in the following manner: If there was evidence of a non-uniform distribution but no evidence of barriers in the regression test, it was concluded that there was no evidence for that section. If there was evidence of barriers in the regression test but no evidence of non-uniformity in all the 3 tests, it was concluded that there was no evidence for the section. If there was evidence of barriers in the regression test and evidence of non-uniformity in only one of the 3 tests, if that non-uniformity test was the barrier test, then it was concluded that there was no evidence for the section; but if the non-uniformity test was the remainder test then it was concluded that there was evidence for the section. For conflicting results between the section for transgressional effects and positional effects, they were resolved in the following manner: If there was evidence of transgressional effects but not positional effects, it was concluded that there was evidence of psychological barriers. If there was evidence of positional effects but not trangressional effects it was concluded that there was no evidence of psychological barriers. This is because the data set for the testing of transgressional effects is larger and hence the evidence would have to be stronger for there to be evidence of barriers. In addition, the test for transgressional effects specifically looks at movements from one day to the next and hence would capture the presence of barriers in a more compelling manner than the test for positional effects. Conclusion In this study, we have examined the presence of psychological barriers in the equity indexes of 10 Asian Markets over a 10 year period from We have found evidence for barriers at the 1000 level for 6 of these markets (JKSE, KLSE, N225, STI, KS11, TWII) and at the 100 level for 4 of these markets (AORD, JKSE, KLSE, STI). However, while there may be evidence of psychological barriers, there is little evidence for the predictability of stock returns induced by the presence of these psychological barriers. References Aggarwal, R., & Lucey, B. M. (2007). Psychological barriers in gold prices? Review of Financial Economics, Chen, M. H., & Tai, V. W. (2011). Psychological barriers and prices behaviour of taifex futures International Conference of Taiwan Finance Association Donaldson, R. G., & Kim, H. Y. (1993). Price barriers in the dow jones industrial average. Journal of Financial and Quantitative Analysis, 28(3), Dorfleitner, G., & Klein, C. (2009). Psychological barriers in European stock markets: Where are they? Global Finance Journal, Harris, L. (1991). Stock price clustering and discreteness. Review of Financial Studies 4, Johnson, E., Johnson, N. B., & Shanthkumar, D. (2008). Round numbers and security returns. Koedijk, K. G., & Stork, P. A. (1994). Should we care? Psychological barriers in stock markets. Economics Letters, Schindler, R.M. and Kirby, P.N. (1997). Patterns of rightmost digits used in advertised prices: implications for nine-ending effects. Journal of Consumer Research 24, Ley, E. & Varian, H.R. (1994). Are there psychological barriers in the Dow-Jones index? Applied Financial Economics, 4, Mitchell, J. (2001) Clustering and Psychological Barriers: The Importance of Numbers. The Journal of Futures Markets, 21, Sonnemans, J. (2006). Price clustering and natural resistance points in the dutch stock market: a natural experiment. European Economic Review, Ziemba, W.T., Brumelle, S.L., Gautier, A. and Schwartz, S. L. (1986). Dr. Z s 6/49 lotto guidebook. Vancouver, Canada: Dr. Z Investments. Table 7: Summary of results for the various tests IFTA.ORG PAGE 19

20 Regime-Switching Trading Bands Using A Historical Simulation Approach By Ka Ying Timothy Fong, CFTe, MFTA Abstract Bollinger Bands have been one of the greatest tools developed for technical analysis. In statistical terms, Bollinger Bands involve the construction of a 95% confidence interval around the moving average of a stock s price and they capture the mean plus and minus two standard deviations. Having said that, Bollinger Bands are subject to a number of limitations including the assumption that prices are normally distributed and ambiguity in terms of generating explicit trading decisions when prices move in trends. The key objective of this research paper is to develop the next-generation trading bands that not only use empirical price distributions without making a normality assumption but also include the use of autocorrelation to determine whether prices are moving in a trending or oscillating regime so that a better buy or sell decision can be made. The regime-switching trading bands using historical simulation will be applied to different test cases and the performance of these next-generation trading bands will be summarized in this paper. 1. Introduction Buying low and selling high is one of the most fundamental strategies in trading. Trading bands are intuitive and easy-touse tools that can help traders in determining entry and exit points for their investments. The most popular and well-known trading bands are the Bollinger Bands, and Section 2 provides a fulsome review of Bollinger Bands and other trading bands that currently exist. Bollinger Bands were developed by John Bollinger in the 1980s. Given the relatively limited computing power and technology during that period of time, it would be logical to develop a tool that is easy to calculate. One of the implicit assumptions made in the use and interpretation of Bollinger Bands is the normality of the distribution of stock prices. Interestingly, there is a great deal of empirical evidence that suggests that asset prices, such as equity prices, are better characterized by skewed and fat-tailed distributions rather than normal distributions. Therefore, it would be useful if we could develop trading bands that could capture the empirical behavior without making any simplifying assumptions about the shape of the distribution. No single technical analysis tool is perfect and it is logical to complement an existing tool (i.e. Bollinger Bands in this case) with other metrics that could potentially fine-tune trading signals. The Directional Movement Indicator (DMI) developed by Welles Wilder is an interesting trading tool as it not only has an indicator component but also a metric called Average Directional Index (ADX) that determines whether or not prices move in trends, which in turn will determine whether the DMI indicator itself should be used for generating a reliable trading signal. The DMI tool offers us two key lessons to consider in developing a new technical analysis tool. The first key lesson learned is that a comprehensive technical analysis tool or trading system should have two key components. One component acts as a filter to help the trader determine whether or not the tool or indicator itself should be used. The other component, of course, is the main indicator itself. The second key lesson learned is the importance of assessing whether the price is trending or oscillating in technical analysis. This paper will describe the development of the nextgeneration trading bands that not only capture the skewed and fat-tailed nature of stock price distributions but also use a statistical filter to determine whether the price is in the trending or oscillating regime, in the short, term so that traders can make better buy or sell decisions. 2. Review of the Use of Bollinger Bands and Other Trading Bands Bollinger Bands (BB) are one of the useful decision-making tools developed in technical analysis. They are typically calculated as the 20-day simple moving average of closing prices plus and minus two standard deviations over that 20- day period. The lower bound forms a support while the upper bound forms a resistance. It is important to highlight the linkage between Bollinger Bands and the concept of confidence intervals in statistics. In statistical terms, Bollinger Bands are basically 95% confidence interval around the moving average and they capture the mean plus and minus two standard deviations as long as the distribution is normally distributed. A buy signal is generated when prices are trending down and hit the lower band. Similarly, a sell signal is generated when prices are trending up and hit the upper band. One of the implicit assumptions used in the interpretation and application of Bollinger Bands is normality and a significant amount of empirical evidence suggesting that security prices such as stock prices are not normally distributed. Instead, they show skewed and fat-tailed distribution exhibiting various degrees of skewness and kurtosis. Therefore, symmetrical bands around the moving average such as Bollinger Bands may not capture the skewness and kurtosis of the price movements adequately. Bollinger Bands also make another implicit assumption that stock prices tend to be mean-reverting as a buy signal is generated when the price hits the lower band, while a sell signal is generated when the price hits the upper band. In other words, prices that go outside the bands are considered to be too extreme and therefore are expected to be pulled back to the PAGE 20 IFTA.ORG

21 moving average. A commonly identified limitation of Bollinger Bands is the lack of an appropriate signal when prices move in trends and in turn track along either the upper or lower band. Therefore, a statistical indicator or metric that could measure whether the prices are oscillating or reverting would be very useful for improving the accuracy of trading signals generated by these bands. Other trading bands that are typically covered in standard technical analysis textbooks are Moving Average Envelopes (ENV), Keltner s Channel (KC) and Donchian Channel (DC). Moving Average Envelopes can be obtained by adding or subtracting a pre-determined fixed percentage, e.g. 5% to a simple or exponential moving average. An obvious advantage of ENV is its computational simplicity. However, the selection of the fixed percentage is perhaps too arbitrary, and there is no intuitive statistical interpretation of the pre-defined percentage and the resulting envelope. Keltner s Channel is made up of two bands plotted around an Exponential Moving Average (EMA) of typical prices. For the upper band, the Average True Range (ATR) is calculated over 10 days, doubled and added to a 20-day EMA. A similar procedure can be used to calculate the lower band. There are two key differences between Bollinger Bands and Keltner s Channel. Firstly, Bollinger Bands use closing prices in the calculation while Keltner s Channel uses typical prices in the calculation. Secondly, Bollinger Bands use standard deviation to measure dispersion but Keltner s Channel uses ATR to measure variability. One should also observe that Keltner s Channel has attempted to measure dispersion or variability by using ATR (which could capture gaps in the price series) rather than standard deviation, but it does not have a mechanism to tell under what conditions the channels themselves should be used. Lastly, Donchian Channel (DC) is an indicator developed by Richard Donchian. It is formed by taking the highest high and the lowest low over the last n days. If the stock price is above its highest high for the last n days, then a buy signal is generated. On the other hand, if the stock price is below its lowest low for the last n days, then a sell signal is generated. The key difference between Donchian Channel and the other three trading bands (i.e. BB, ENV and KC) is that trading signals generated by Donchian Channel are based on breakout of the channels while trading signals from other trading bands are based on meanreversion away from the channels. One could see why Bollinger Bands are superior among these four trading bands as Bollinger Bands give rise to some intuitive interpretation in the context of normal distribution. If the underlying prices follow a normal distribution, the empirical rule could be used to interpret the results, i.e. 68% of the price data is within one standard deviation from the mean, 95% of the price data is within two standard deviations from the mean, etc. Therefore, prices going outside the bands are considered abnormal and are expected to revert to the mean. Table 1 below shows a summary of key features of the four commonly used and well-documented trading bands as well as the proposed regime-switching trading bands (or Fong s Bands, to keep it simple). A key observation from the review of four commonly used and well-documented trading bands described is that none of them can be considered as a comprehensive trading system (which is previously defined as a tool that has two key components). Therefore, this paper will introduce the following three specific new dimensions into our regime-switching trading bands: 1) historical simulation approach to generate the trading bands so that the empirical price distribution can be captured, 2) an autocorrelation filter to make the bands a trading system by indicating whether the price is trending or oscillating, and 3) a swing confirmation filter to deal with the situation where prices have a higher tendency to increase momentum rather than reverting to the mean. 3. The Significance of Historical Simulation, Autocorrelation and Swing Filter in Fine-Tuning the Decision-Making Process for the Use of Trading Bands Historical simulation is a non-parametric approach that is often used in the context of Value-at-Risk calculation for trading books at banks. This approach makes no parametric assumptions about the price distribution and also involves the use of percentiles in measuring risk. One of the key assumptions in historical simulation is that past history will repeat itself in the future. This assumption is consistent with one of the three key principles or foundations of technical analysis that history will repeat itself (i). For risk measurement purposes, banks focus on the tail or the lower percentile of the return distribution. In the context of this research paper, the 5 th percentile and the 95 th percentile of the closing prices for the last 20 days will form the upper and lower bands, and the dispersion Table 1 IFTA.ORG PAGE 21

22 of stock prices will be measured by the interpercentile range (i.e. the difference between the 5 th percentile and the 95 th percentile). We can also apply this concept to any percentile and for any historical look-up period. More importantly, depending on the skew and kurtosis of the price history, these bands that are generated by historical simulation capture the entire empirical distribution (including fat tails) and may be asymmetrical (unlike the Bollinger Bands). The second key principle of technical analysis is the belief or observation that prices move in trends (i). An objective method of measuring whether prices are moving in trends or oscillating is very important in technical analysis. For example, Welles Wilder s Average Directional Index (ADX) is a well-known indicator that measures the strength of the trend as part of the DMI trading system. Perhaps a more direct and intuitive way of measuring whether the price is trending or oscillating is to use the concept of autocorrelation. Autocorrelation is definitely a well-known concept for statisticians or econometricians in time series analysis. However, autocorrelation is somewhat underused in technical analysis. It is not a standard topic in technical analysis textbooks used for professional technical analysis designations, such as the CFTe program administrated by IFTA. Also, most technical indicators that are commonly available on popular websites such as Yahoo Finance or stockcharts.com do not take autocorrelation into consideration. A brief overview of autocorrelation would be definitely helpful in illustrating its usefulness in the trading system proposed in this paper. Autocorrelation, also known as serial correlation, measures the correlation of the data points over time. The following is the sample autocorrelation formula: where P is the closing price of a stock, h is the time lag, N is the number of observations and P is the average closing price over the respective period. In the context of measuring trends for daily prices over a short period of time, we are dealing with a time lag (h) of 1 specifically. It means that we are measuring whether an up-day is likely to be followed by another up-day and vice versa, where an up-day is defined as a day where the closing price is higher than the closing price on the previous day. The following two diagrams illustrate the key interpretation of autocorrelation in the context of technical analysis: Figure 1 Figure 2 Figure 1 shows a situation where prices move in a perfect uptrend and the autocorrelation for this case is +1. On the other hand, Figure 2 shows a situation where prices are oscillating in such a way that a daily price change in one direction is followed by a daily price change of equal size in the opposite direction. In this case, the sample autocorrelation will be -1. The sign of the sample autocorrelation tells the trader whether the prices move in trends or not. Positive autocorrelation implies that prices move in trends (i.e. trending regime) while negative autocorrelation implies that prices oscillate (i.e. oscillating regime). The magnitude of the sample autocorrelation gives an indication of the strength of a trend. In the context of identifying a change from a trending regime to an oscillating regime, if the autocorrelation changes from a positive sign to a negative sign, the direction of a price movement is more likely to reverse (more detailed explanation of the application of the bands can be found in Section 4) and therefore the use of historically simulated trading bands is more likely to identify optimal entry and exit points for a trade. One of the problems encountered through the use of the Bollinger Bands is that the price can track along the bands when prices show exceptional momentum. In other words, the price could touch the upper or lower band multiple times over a short period of time, resulting in a false or premature buy or sell signal. In this case, even the autocorrelation filter might not help us resolve the problem completely when prices show extremely strong momentum. In this situation, a swing filter, first introduced by Arthur Merrill in his book, Filtered Waves, in 1977, will be useful in generating a correct buy or sell signal. The swing filter is basically a pre-determined percentage of price movement and is generally considered as a breakout trading tool. In other words, prices are assumed to continue on its trend until prices reverse more than the pre-defined threshold or trigger. In the situation where prices hit the trading band with positive autocorrelation, it means that the price is breaking out to levels observed in the extreme tails of the historical price distribution. The swing filter serves as a means to confirm the price reversal so that those extra miles from the trend can be captured more fully in the use of the trading bands. Detailed description of test cases is provided in Section The Methodology for Regime- Switching Trading Bands using a Historical Simulation Approach (Putting them all together) Transitions between a rising and falling trend are often signaled by price patterns (ii). Many of these patterns involve the consolidation of prices manifested in the form of a zigzag or whipsaw. These consolidation movements generally show negative autocorrelation, as shown in Section 3. The use of autocorrelation eliminates a cognitive recognition or assessment of these price patterns by the traders and it measures objectively whether the price is trending or oscillating, i.e. whether the price is going through the transition signaling a potential turn or reversal. In other words, the autocorrelation is positive when prices are trending and the autocorrelation is negative when prices are oscillating (i.e. giving a reversal signal). In the context of our regimeswitching trading bands, if the autocorrelation is changing from positive to negative by crossing the zero line (when the price is hitting the lower band or upper band), it indicates that the price may be transitioning or consolidating and therefore it is more PAGE 22 IFTA.ORG

23 likely for the historically simulated trading bands to give the traders the optimal entry/exit points right before the reversal of the price. In the application of the regime-switching trading bands, when prices move in a downtrend towards or hit the lower band (for example), it will only trigger a buy signal when the price is in an oscillating regime (i.e. negative autocorrelation). Then, the swing filter rule of x% will be used to generate a buy signal, meaning that the prices need to revert to the upside for more than x% before a legitimate buy signal is generated. The following diagram (Figure 3) illustrates how autocorrelation could facilitate the decision-making process for buying with trading bands (and the converse for selling is true as well): A decision-tree generated from the regime-switching trading bands is outlined in Figure 4 below: In terms of the parameters and other assumptions for the bands, we will use the 5 th and the 95 th percentiles over the last 20 days as our trading bands, with an autocorrelation filter, using the last 10 days of closing price data in the application of the regime-switching trading bands, using a historical Figure 3 Stock Price positive autocorrelation when prices move in a downward trend negative autocorrelation when prices oscillate or consolidate during a transition period use the lower band as entry point to buy Lower Band If the price reverts to the upside for more than x%, it confirms that the price is breaking out from the consolidation pattern and a buy signal will be generated. Figure 4 Price hits or gets close to the lower band. Price hits or gets close to the upper band. If autocorr is positive (i.e. trending regime), then do nothing. If autocorr is non-positive (i.e. oscillating regime), then buy only when the price reverts up by more than x%. If autocorr is positive (i.e. trending regime), then do nothing. If autocorr is non-positive (i.e. oscillating regime), then sell only when the price reverts down by more than x%. IFTA.ORG PAGE 23

24 simulation approach. The detailed methodology of how the bands and the autocorrelation are calculated mathematically will be discussed below. As mentioned in previous sections of this paper, the generation of the bands will involve the use of percentiles. The value of the P th percentile of an ascending ordered price data series containing n data points with values such that v 1 v 2 v n is defined as v p. First of all, the rank for a given percentile P is calculated as follows: 9 9 pi pi+ 1 = 1 a = where i = 1 b = 9 and i 9. It is important to note that a and b represent the respective averages over slightly different time periods i.e. {R 1, R 2,, R 9 } for the calculation of a vs. {R 2, R 3,, R 10 } for the calculation of b. The application of the regime-switching trading bands using empirical data and the associated results on their performance will be discussed further in the next section. 5. Application of Regime-Switching Trading Bands and Empirical Results where rank is further broken down into an integer component i and a decimal component d such that the sum of the two components is equal to the rank. Then the value of the P th percentile (V P )will be calculated as follows: Given the above parameterization and methodology, the lower band (L) will be calculated as the 5 th percentile and the upper band (U) will be calculated as the 95 th percentile given the last 20 days of closing prices which are ranked in an ascending order such that p 1 p 2 p 20. By using the above percentile concept, the lower band and the upper band on a given day will be calculated as follows: Regarding the calculation of autocorrelation, only 10 out of 20 closing prices are used in order to make the autocorrelation value more sensitive to recent closing prices and preserve the principle of harmonicity developed by J.M. Hurst at the same time. Specifically, a time lag of 1 and the last 10 days of closing prices (i.e. R 1, R 2,, R 10 ) will be used to calculate the daily autocorrelation value for the regime-switching trading bands where p t is the closing price on the t th day looking backwards. The following formula shows how the daily autocorrelation value (r 1 )is calculated: Data from January 1, 2010 to December 31, 2010 is used in the following three empirical test cases: (a) the S&P 500 index; (b) a sector ETF (GLD); and (c) a single-name stock (Suncor). [Due to limited space we only show case a and b - the editor] We will apply both the regime-switching trading bands (i.e. Fong s Bands) and Bollinger Bands to each of the above three cases. In order to test the effectiveness of the regime-switching trading bands, we will benchmark their performance against the Bollinger Bands by calculating the total cumulative return for both approaches under the three different test cases by implementing the following trading strategies: 1) If a buy signal is generated using the bands, then we will put all the money to buy the equity product. 2) We will keep the long position until a legitimate sell signal is generated. 3) When a sell signal is generated, we will sell first to close an opening position and then establish a new short sell position with all the money in the account. 4) We will not cover our short position until a legitimate buy signal is generated. 5) Similarly, immediately right after the short is covered, we will use all the money to establish a long position in the equity product as a result of a new buy signal. In summary, we will be alternating net long and net short positions using the legitimate buy and sell signals generated by the bands. Regarding the exact generation of trading signals using Bollinger Bands, a buy signal is generated when the closing price on a particular day is less than or equal to the lower Bollinger Band, and the trader will initiate a long position at the opening price on the next day. Similarly, a sell signal is generated when the closing price on a particular day is greater than or equal to the upper Bollinger Band, and the trader will initiate a short position at the opening price on the next day. As outlined in the previous section, a buy signal using the regime-switching trading bands when the following conditions are met in sequence: 1) the closing price on a particular day is less than or equal to the lower band, 2) the autocorrelation estimate is negative or close to zero, 3) the x% swing filter is triggered when any percentage change on a single day, as well as any consecutive daily changes, exceeds the x% threshold, and 4) a legitimate buy signal is generated and the trader will initiate a long position at the opening price on the next day. Similarly, a sell signal using the regime-switching trading bands when the following conditions hold in sequence: 1) the closing price on a particular day is greater than or equal to the upper band, 2) the autocorrelation estimate is negative or close to zero, 3) the x% swing filter is triggered when any percentage change on a single day, as well as any consecutive daily changes, exceeds the x% PAGE 24 IFTA.ORG

25 threshold, and 4) a legitimate sell signal is generated and the trader will initiate a short position at the opening price on the next day. In terms of the parameters and other assumptions for the bands (as mentioned in Section 4), we will use the 5 th and the 95 th percentiles over the last 20 days as our trading bands with an autocorrelation filter using last 10 days of closing price data and a 2% swing confirmation filter for the regime-switching trading bands. The 2% swing filter is triggered when any percentage change on a single day, as well as any consecutive daily changes, exceeds the 2% threshold. As you will notice in Section 5c, Suncor showed a very secular trend and a strong tendency to oscillate. Graph S&P 500 Time Series with Fong's Bands As a result, it is appropriate to use a shorter time window (i.e. 5 days instead of 10 days) for calculating autocorrelation to fully capture the strong tendency to oscillate or mean-revert. On the other hand, Bollinger Bands with default setting (i.e. the simple moving average plus and minus two standard deviations using the last 20 days of closing prices) will be used as the benchmark for our comparison of performance. 5a) Equity index S&P 500 It is important to note that the index showed both trending and oscillating behavior during the time window used in this case study. A close examination of Graph 1 and Graph 2 reveals that the index was trending from the middle of February to end of April as well as from the beginning of September to end of October. On the other hand, the index was oscillating between early May and end of August. Table 2 and Table 3 summarize the trading results for the S&P 500 index using regime-switching trading bands and Bollinger Bands respectively. The use of regime-switching generated an annual cumulative return of 32.8% while the use of Bollinger Bands only generated 16.4%. The results are actually not surprising as we expect that the autocorrelation filter will be able to deal with both trending and oscillating behavior demonstrated by the index during 2010 effectively and explicitly. A minor technical point to note is that the closing prices were very close to the upper Bollinger Band during the first week of January but they did not hit the band according to our definition described earlier in this section (as the closing prices were not equal to or greater than the upper band). Table Jan Jan-10 1-Feb Feb-10 1-Mar Mar Mar Apr Apr May May-10 7-Jun Jun-10 5-Jul Jul-10 2-Aug Aug Aug Sep Sep Oct Oct-10 8-Nov Nov-10 6-Dec Dec-10 Autocorrelation of Lag 1 with 10-day Moving Window Table 3 4-Jan Jan-10 1-Feb Feb-10 1-Mar Mar Mar Apr Apr May May-10 7-Jun Jun-10 5-Jul Jul-10 2-Aug Aug Aug Sep Sep Oct Oct-10 8-Nov Nov-10 6-Dec Dec-10 Graph 2 S&P 500 Time Series with Bollinger's Bands Jan Jan-10 1-Feb Feb-10 1-Mar Mar Mar Apr Apr May May-10 7-Jun Jun-10 5-Jul Jul-10 2-Aug Aug Aug Sep Sep Oct Oct-10 8-Nov Nov-10 6-Dec Dec-10 5b) Exchange Traded Fund (ETF) GLD It is important to mention that GLD (i.e. gold ETF) showed an exceptional upward trend during the year of 2010 and it was overbought for a significant period of time. Graph 3 and Graph 4 illustrate that the prices of GLD were tracking along both the regimeswitching trading bands and Bollinger Bands from early April to mid-may as well as early August to mid-october due IFTA.ORG PAGE 25

26 to its extreme trending behavior. Table 4 and Table 5 summarize the trading results for GLD using regimeswitching trading bands and Bollinger Bands, respectively. The use of regimeswitching generated a reasonable cumulative return or profit of 17.4% while the use of Bollinger Bands resulted in disappointing negative return or loss of 6.3%. The use of Bollinger Bands generated premature trading signals as they cannot cope with trending behavior effectively. If you look at the first period of explicit uptrend from early April to mid-may more closely, the regimeswitching trading bands did not generate a sell signal until June 21 so that a significant portion of the strong uptrend could be captured. On the other hand, Bollinger Bands generated a premature signal on April 7 and therefore the strong uptrend was not captured by the trading strategies using Bollinger Bands. Similarly, during second period of explicit uptrend from early August to mid-october, the regime-switching trading bands capitalized on the trend and generated a sell signal towards the end of this trending period on October 19. However, Bollinger Bands generated an early sell signal on September 14 in the middle of the strong uptrend. A minor technical point to note is that the closing price on January 11 was very close to the upper Bollinger Band but did not hit the band according to our definition described earlier in this section (as the Table 4 closing price was not equal to or greater than the upper band). This test case is another great example demonstrating that the autocorrelation filter is an effective tool in dealing with extreme trending behavior. Based on the three test cases, regimeswitching trading bands generated consistent positive returns regardless of the underlying equity product (i.e. index vs. sector ETF versus single-name equity) for all cases. On the other hand, Bollinger Bands only generated positive returns for two of the three cases. In terms of dealing with trending vs. oscillating asset prices, we observe that GLD showed heavy trends in 2010 while Suncor Graph Jan-10 4-Jan Jan-10 1-Feb Jan-10 1-Feb Feb Feb-10 GLD Time Series with Fong's Bands showed very strong tendency to oscillate in a secular pattern. Regime-switching trading bands appeared to be able to cope with both trending and oscillating behavior quite effectively as they generated profits for strong trending and strong oscillating equity products. On the other hand, although the use of Bollinger Bands generated a higher positive return for the oscillating test case for Suncor than the use of regime-switching trading bands (i.e. 54.8% instead of 26.0%), Bollinger Bands cannot effectively deal with assets that are trending such as GLD, leading to a negative return of 6.3%. Our test cases demonstrated that the regime-switching trading bands can effectively resolve one of limitations of 1-Mar Mar Mar Apr Apr May May-10 7-Jun Jun-10 5-Jul Jul-10 2-Aug Aug Aug Sep Sep Oct Oct-10 8-Nov Nov-10 6-Dec Dec-10 Autocorrelation of Lag 1 with 10-day Moving Window 1-Mar Mar Mar Apr Apr May May-10 7-Jun Jun-10 5-Jul Jul-10 2-Aug Aug Aug Sep Sep Oct Oct-10 8-Nov Nov-10 6-Dec Dec-10 Graph 4 GLD Time Series with Bollinger's Bands 140 Table Jan Jan-10 1-Feb Feb-10 1-Mar Mar Mar Apr Apr May May-10 7-Jun Jun-10 5-Jul Jul-10 2-Aug Aug Aug Sep Sep Oct Oct-10 8-Nov Nov-10 6-Dec Dec-10 PAGE 26 IFTA.ORG

27 Bollinger Bands mentioned in Section 2 of our paper. It is also worth noting that two of the three test cases do not have fat-tails at all. In fact, the tails were even thinner than the ones in a normal distribution as their excess kurtosis were negative during 2010 (as indicated in Table 6). As a result, the historical simulation aspect of the regime-switching trading bands, which was designed to capture the fat-tails, did not contribute too much to the positive returns for GLD and Suncor. On the other hand, S&P 500 showed some excess kurtosis (i.e. fatter tails) and it is also interesting to observe at the same time that the regime-switching trading bands had the best absolute performance and relative performance for this particular test case. This evidence suggests that the historical simulation approach could add value to the regime-switching trading band for asset prices that show skewed and fat-tailed distributions. Table 6 Another interesting observation is that the autocorrelations are above the zero line (i.e. positive) most of the time for all the three cases. This observation could suggest that equity indices, equity ETFs and individual stocks tend to move in trends from day to day over a short period time as trends are statistically characterized by positive autocorrelation. This is great news to those who believe in technical analysis since our observation is actually consistent with one of the three key principles in technical analysis, i.e. prices move in trends! 6. Conclusion The proposed trading bands involve a non-parametric approach with the use of autocorrelation and swing filter to finetune trading decisions. Based on our empirical tests, our regimeswitching trading bands using historical simulation generated substantial positive returns for different types of equity products, and they improved trading performance for asset prices that have a strong tendency to move in trends relative to the Bollinger Bands. This research does not only highlight the significance of the use of autocorrelation in technical analysis but also outlines the next-generation trading bands for traders. References i. Murphy, JJ, Technical Analysis of the Financial Markets, New York Institute of Finance, New York, 1999, Chapter 1, p. 2. ii. Pring, MJ, Technical Analysis Explained: The Successful Investor s Guide to Spotting Investment Trends and Turning Points, McGraw Hill, New York, 2002, Chapter 5, p. 64. Bibliography Murphy, JJ, Technical Analysis of the Financial Markets, New York Institute of Finance, New York, Pring, MJ, Technical Analysis Explained: The Successful Investor s Guide to Spotting Investment Trends and Turning Points, McGraw Hill, New York, StockCharts.com, ChartSchool ( php?id=chart_school) TRADESIGNAL GET AHEAD OF THE MARKET. intalus.com The ultimate solution for Technical Analysis and algorithmic trading Design and back-test almost any trading strategy before you risk your money Scan thousands of securities according your own criteria or use some from hundreds of pre-installed indicators and strategies Supports Bloomberg, Thomson Reuters, Trayport, Morningstar, your own data and others Supports EasyLanguage Made in Germany ORDER YOUR FREE TRIAL TODAY GRE T PERFORMANCE. WORLDWIDE. MADE IN GERMANY. SINCE BERLIN. BREMEN. FRANKFURT. HONG KONG. LONDON. LUXEMBOURG. MOSCOW. PARIS. ZURICH. FOLLOW US INTALUS is a registered trademark of Intalus GmbH, Germany Tradesignal is a registered trademark of Tradesignal GmbH, Germany All other trademarks are the property of their respective owners. IFTA.ORG PAGE 27

28 Using a Volatility Adjusted Stop Loss (VASL) to Enhance Trading Returns By Edward Rowson, CFTe, MFTA Abstract How can two traders using the same technical trading strategy have such widely different investment returns? This is a question that has played on my mind ever since I started trading and using technical analysis. Within the discipline of technical analysis we are frequently presented with new and dynamic ways of interpreting charts to help spot trends or reversal patterns but little time is spent looking at the utilisation of these skills once acquired. There seems to be a disproportionate focus on the interpretation of price action over the implementation of a trade based on that interpretation. This paper will focus on the latter point, and more specifically on whether implementing VASL methodologies within several simple trading strategies can produce enhanced returns when compared to a variety of standard stop loss strategies. Further investigation will be carried out to investigate whether optimisation of a VASL strategy is possible. Hopefully this will illustrate the importance of employing a risk management strategy when trading. Introduction It is the intention of this paper to investigate whether a dynamic approach to stop loss calculation, by studying the historic volatility of the underlying security, performs better than the more traditionaly used stop loss strategies. Across the industry traders and portfolio managers employ a wide variety of stop loss methodologies and it would be impossible to test all of them in this paper so the investigation will concentrate on the most widely used stop loss strategy, specifically the Percentage Drawdown stop loss strategy. This strategy will act as the control to test the performance of the (VASL) methodology against. By back testing the different methodologies across a number of simple technical trading strategies it is intended to conclude whether there is any empirical evidence that supports the use of a more dynamic approach to stop loss calculation. It is important to note that we are not testing the success of the trading strategies in this paper but the success of the differing stop loss strategies to limit the losses on losing trades and thus maximise the overall return on capital used. The overall investigation being does the use of a VASL strategy enhance trading performance? For the sake of this paper volatility is quantified as the standard deviation of a specified sample of a security s historical closing prices. Let s expand on the concept behind the Volatility Adjust Stop Loss (VASL) methodology. The normal (Gaussian) distribution of a sample of data can be expressed as the probability of future price action and illustrates the proportion of samples that would fall between 0, 1, 2 and 3 standard deviations above and below the mean. About 68% of values drawn from a normal distribution are within one standard deviation σ away from the mean; about 95% of the values lie within two standard deviations; and about 99.7% are within three standard deviations. During the course of this investigation a range of standard deviations will be tested, and their ability to limit losses and increase profits will be compared. It is hard to judge before conducting the study what to expect as using a large standard deviation stop loss would allow positions to run for longer as the stop wouldn t be particularly tight to the price but at the same time this would result in being stopped out after large retracements from the high price thus giving back a lot of any potential gains. On the other hand, a very close stop loss created using a low standard deviation would result in being stopped out close to any high price and maximise the gains but at the same time mean that positions would be stopped out earlier as part of the market noise. The results of this investigation should shed light on which technique performs best. Previous MFTA papers published in the annual Journal have looked at stop loss calculation. Most recently David Linton introduced in his MFTA paper, which was published in the 2008 IFTA Journal, titled Optimisation of Trailing stop losses, the benefits of using trailing stop losses to optimise trading returns. The concept of trailing stop losses will be incorporated in this study both within the volatility adjusted stop loss strategy and within the control environment to which the results will be compared. The control environment will be, as mentioned previously, the Percentage Drawdown stop loss strategy which will be tested across a number of varying technical momentum trading strategies which will be outlined in the control environment section. There are two variations for calculating the trailing stop loss. Both will be tested to make sure the most profitable control is in place to judge the comparative performance of the VASL methodology. The first shall be referred to as the Dynamic approach, and is the one explained in David Linton s paper which can be summarised by the following formula: Dynamic control stop loss Initial stop loss = Price * (100-stop %) If (Price*(100-stop %)> SL) SL=Price*(100-stop %)-i.e. raise stop level If Price<SL then Exit Position. Using an example, a long position in SABIC was initiated on the 8 th of July 2009 at a closing price of SAR, a 10% stop loss was used, the initial stop loss was SAR (=90% of 56.00). As the closing price rose so did the trailing stop loss; when the price retreated the stop loss flat lined. The trade was closed on the 16 th of May 2010 at the closing price of , as PAGE 28 IFTA.ORG

29 this was the day that the price closed below the 10% trailing stop which, on the 16 th of May 2010, was SAR. The second variation for the calculating of a trailing stop loss can be described as the Static approach. This is where the Initial stop loss spread, described above, is calculated to give an absolute number in terms of the price change, this price change then acts as the trailing stop loss, in equal increments to any subsequent price rise. The Static stop loss can be summarised by the following formulas: Static control stop loss Initial stop spread = price*(% drawdown/100) For a long position the stop loss = Entry price Initial stop spread Subsequent stop loss = closing high price since position inception Initial stop spread The main drawback to using the Static technique is that if a security doubles in price then the absolute drawdown will only represent half the original move that the initial stop loss was based, this could increase the risk of being whipsawed as the stock price increases. Using another example: a long position in Marco Telecom was initiated on the 31 st of August 2010 at the closing price of MAD, a 7% stop loss was used giving a stop loss of MAD, thus the initial stop spread was equal to 10.2 MAD (the difference between the entry price and the stop loss). The highest close was on the 28 th of February 2011 at , the trailing stop flat lined at MAD (highest close initial stop spread). The stop loss was triggered on the 20 th of May 2011 when the price closed below the stop loss at Both techniques will be investigated to see if there is any empirical evidence to support either technique as the preferred benchmark. The Control Environment As previously mentioned, to test the theory that VASL can enhance trading profits, it is important to have a credible control to test the hypothesis against. Unfortunately it is not possible to test every stop loss strategy used by traders, so for the purpose of this paper, we will look at one of the most popular stop loss strategies: the Percentage Drawdown stop loss will be tested. As already discussed, there are two variations to the Percentage Drawdown stop loss, the Static and the Dynamic. Both variations will be initially tested to see if there is any marked difference. Whichever technique is most successful will be used as a benchmark to compare the volatility adjusted returns against. The control environment will consist of running a number of technical momentum strategies across the top nine stocks (by market capitalisation) in the MENA (Middle East and North African) region. Using the daily closing price the back test will be run from the 1 st of January 2006 to the 12 th of September 2011 inclusive. The prices will be converted to USD and will be the total return price since the beginning of the period (1 st January 2006) so that any dividend distribution is included; the following technical trading strategies were tested: Moving average crosses The technique of trading in the direction of the long-term trend can be implemented with two simple moving averages. The slower moving average, using a longer calculation period, identifies the primary trend. The faster moving average is used for timing. The following moving average cross indicators were used: 10/20 day simple moving average cross Buy when the 10 day moving average (fast trend line) crosses from below to above the 20 day (low trend line) moving average (MAV). 20/60 day simple moving average cross Buy when the 20 day crosses from below to above the 60 MAV. 60/200 day simple moving average cross Buy when the 60 day crosses from below to above the 200 MAV. Overbought/oversold RSI The Relative Strength Index (RSI) is a measurement that expresses the relative strength of the current price movement as increasing from 0 to 100. For this paper an RSI of 25 will indicate oversold and 75 overbought. Buy when the RSI rises above 25 from an oversold position Sell when the RSI falls below 75 from an overbought position Control environment parameters The control environment has a number of constants so that the results can be easily compared, these include: Each security will be back tested using the above trading strategies over the period commencing 1 st January 2006 to the 12 th of September 2011 inclusive. The trailing stop loss from 1% to 20% inclusive will be tested in increments of 1%, so 1%, 2%, 3% etc. The standardised position size of $500,000 rounded to the nearest share will be used. The total return of the securities will be calculated so the stop losses aren t triggered by the securities going ex-dividend. The moving averages will be calculated from the total return priced in USD not the underlying price. Only buy signals will be tested. No commission or slippage will be included (the use of the top nine stocks by market capitalisation and liquidity will be used to offer a realistic environment to open and close these trades). Closing prices will be used to open trades, mark the high for the trailing stop loss, and used to close the trade. This may result in the trade being closed well below the actual stop loss should there be a large move on that day. As all trades will be treated the same the results will still be comparable. Only trades that have been opened and subsequently closed will be included in this analysis; those trades that remained open as at the 12 th of September 2011 will not be included. Multiple trades can be opened if the technical buy signal is triggered while an existing trade is still open; each trade is treated independently. As the securities total return price is calculated daily in USD using the daily FX rate, the positions will have currency exposure. IFTA.ORG PAGE 29

30 The Results Interpretation of the control environment results When comparing the success of the two controls it is important to compare the relevant statistics, remembering that the fundamental aim of any stop loss strategy is to minimise losses, both on a total bases as well as the average loss. Secondly is how that stop loss strategy impacts the overall return on capital of the trading strategy. Key metrics to consider in the evaluation of the best control include 1) annualised return on capital 2) average winning P&L to average losing P&L 3) the number of trades that exceed two standard deviations on the negative side and 4) the average return to capital risk employed. The Table below summarises the results of the two strategies: Table 1: Summary of results Static SL Dynamic SL Total Notional $5,376,500,000 $5,277,000,000 Average Notional $500,000 $500,000 Total P&L $230,096,264 $253,849,884 Average P&L $21,398 $24,052 Average Return on Capital 4.3% 4.8% Average Annualised Return on Capital 23.6% 21.9% Total Return on Risk 4, , Average Return on Risk Total Number of Trades No of Winning Trades No of Losing Trades Hit Ratio 43.7% 42.1% Winning Trades Profit $476,563,681 $507,752,715 Losing Trade Losses -$246,467,418 -$253,902,832 Average Gain on Winning Trade $101,526 $114,230 Average Loss on Losing Trade -$40,678 -$41,562 Average Winning P&L/ Average Losing P&L Standard Deviation $102,621 $124,682 No. of Trades Exceeding Average Gain + 2SD No. of Trades Less than Average Gain - 2SD 1 1 Average Holding Period for all Trades Average Holding Period for Winning Trades Average Holding Period for Losing Trades Figures 1 and 2 illustrate the differing performance based on these metrics: The last thing to look at before making a decision on which control should be used as the benchmark is to study the distribution of the returns between each strategy, and whether there is a difference in the skewness of the returns. There is a standard error for whether a calculated skew is relevant; to calculate whether a skew is relevant, we can compare the value for skewness with twice the standard error of skewness. If the value of skewness falls within this range, the skewness is considered not material. Twice the standard error of skewness = 2*0.183 = Using the data of the distribution of return for the Static and Dynamic control environment the resulting skew for each control was: Static stop loss skew = 2.19 Dynamic stop loss skew = 2.21 As the difference between the skewness of the two approaches is minimal and falls within the standard error of skewness no conclusion can be drawn from this analysis in its isolation. Hopefully it will prove to be an interesting factor for comparison when compared to the VASL Strategy. To work out which control offers the best benchmark for the volatility adjusted methodology a points system will be used, the control with the highest score will be the benchmark. A number of key metrics have been compared and scored; the results are shown in Table 2: Table 2: Score table for control stop losses Static SL Dynamic SL Average P&L $21,398 $24,052 Average Annualised Return on Capital 23.6% 21.9% Average Return on Risk Average Gain on Winning Trade $101,526 $114,230 Average Loss on Losing Trade -$40,678 -$41,562 % of trades greater than 2 STD 7.1% 6.3% Average Winning P&L/Average Losing P&L Skewness * Points Total 2½ 4½ * As the difference in skewness is minimal the point will be shared Based on the above, the Dynamic stop loss will be the control environment for the study. From analysing the table of total distribution data and the subsequent skew analysis, it seems to support the potential limitation of the Static stop loss control that was observed earlier. The data shows that the Dynamic control had a greater number of trades that resulted in returns greater than 70%: 276 trades for the Dynamic control compared to 219 trades for the Static control. This suggests that there is a limitation to using an absolute value trailing stop as the share price rises the trailing stop becomes a lower percentage of the current price, thus a smaller retracement is required to stop out a Dynamic stop. This has had a detrimental effect on the most profitable winning trades. The Volatility Adjusted Stop Loss (VASL) methodology Intuitively it doesn t make sense to maintain a rigid stop loss methodology. For example, is it correct to have a similar stop loss when trading in a utilities stock as that used trading a high PAGE 30 IFTA.ORG

31 Figure 1: Comparing average annualised return on capital Average Annualise Rtn on Capital % 60.0% 50.0% 40.0% 30.0% 20.0% 10.0% 0.0% 9% SL 8% SL 7% SL 6% SL 5% SL 4% SL 3% SL 2% SL 1% SL 13% SL 12% SL 11% SL 10% SL S top L oss Figure 2: Comparing average annualised return on initial risk % SL 15% SL 14% SL Dynamic 20% SL 19% SL 18% SL 17% SL Static beta technology company? I believe the answer is no, the stop loss should be adjusted to reflect the volatility of the underlying. It has been concluded from the investigation into the control environment that the Dynamic calculation proved most successful. With this mind, the investigation will concentrate on looking at whether a Dynamic calculated volatility adjusted stop loss better protects the trader from the downside without sacrificing the potential upside. The calculation for the stop loss is shown below: Calculation of the Volatility Adjusted Stop Loss (VASL) Retun on Initial RIsk Initial Stop Loss = Entry Price σ 20% SL 19% SL 18% SL 17% SL 16% SL 15% SL 14% SL 13% SL 12% SL 11% SL 10% SL 9% SL 8% SL 7% SL 6% SL 5% SL 4% SL 3% SL 2% SL 1% SL Stop Loss Static Stop Loss Dynamic Stop Loss Figure 3: Comparing the average annualised returns on capital for the various Volatility Adjusted Stop Losses Return on Capital 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% Number of Standard Deviations Volatility Stop Losses Figure 4: Comparing the average annualised returns on risk for the various Volatility Adjusted Stop Losses Volatility Stop Losses n = Being the number of historic data points, and thus reflecting the investment horizon of the trade, a long term investor may use 200 days, whereas a hedge fund trader interested in monthly performance might use 20 days. This can also be hours or minutes for day traders; however it is worth remembering that for an accurate calculation of standard deviation a sample of no less than 20 data points is preferred. An analysis of time frame optimisation will be looked at in more detail later. The stop loss is recalculated on a daily basis using the above formula and is always run from the highest closing price since the position was opened (for long trades) Thus Subsequent stop loss = closing high price since position inception σ Theory Put To The Test! As with the control test, the assumptions and the environment are the same, including the position size and calculation of daily prices in USD taking into account dividends. The back test was run across the standard deviation curve, from 0.5 IFTA.ORG PAGE 31

32 standard deviations to 3 standard deviations, in increments of 0.25 so 0.50, 0.75, 1.0, 1.25 etc. Interpretation of the results and comparing these to the control As with the control back test, there are some key metrics that are useful to look at when evaluating the performance of the VASL strategy. Before making any comparisons with the benchmark s performance, it is interesting to obverse the varying performance of the differing volatility levels used against each other. Figure 3 and Figure 4 show the average annualised return on capital and the average return on risk for the varying stop losses tested. Figure 3 and Figure 4 show similar trends to that of the controls tested, with the main difference being that they seem to be shifted up the chart, i.e. the VASL curve has a maximum value of 46.9% and minimum value of 22.3%, whereas the control has a maximum value 53.7% and minimum 16.4%. If we eliminate the extreme high and low values, the average annualised return on capital for the VASL test would be 31.2% whereas the control average would be 25.5%. A similar situation can be seen when comparing the return on risk; the range for the VASL is from 1.79 to 0.45 and for the control 0.83 to Using a similar method of comparing the two, the average results (excluding the highest and lowest numbers) are 1.17 and 0.48, respectively. It is also interesting to note that there seems to be some differential in the average return on risk along the standard deviation curve, average return on risk falls dramatically for 1.25 and 2.5 standard deviations with defined peaks at 0.75 and 2.25 standard deviations, whereas the trend for the control seems stable. This suggests the possibility for further optimisation of the VASL. Table 3 compares the results of the Volatility Adjusted Stop Loss (VASL) vs. the control : Table 3: Comparable table of results for the VASL & the control. Volatility Adjust Control Average Annualised Return on Capital 28.2% 21.9% Average Return on Risk Skewness Table 4: Comparable percentage stop losses for the VASL and the control. Standard Deviations Average percentage Stop Loss 4.83% 6.83% 8.63% 10.29% Nearest Comparable Control 5.00% 7.00% 9.00% 10.00% VASL AAROC 46.9% 40.0% 39.4% 35.3% Corresponding Control AAROC 32.8% 23.9% 23.7% 22.4% VASL AROR Corresponding Control AROR Standard Deviations Average percentage Stop Loss 12.35% 14.70% 14.50% 16.55% Nearest Comparable Control 12.00% 15.00% 15.00% 17.00% VASL AAROC 32.7% 29.0% 31.6% 25.7% Corresponding Control AAROC 20.3% 18.3% 18.3% 27.2% VASL AROR Corresponding Control AROR Standard Deviations Average percentage Stop Loss 17.25% 11.07% 10.00% Nearest Comparable Control 17.00% 11.00% 10.00% VASL AAROC 22.3% 24.0% 22.9% Corresponding Control AAROC 27.2% 19.0% 22.4% VASL AROR Corresponding Control AROR AAROC Average Annualised Return on Capital AROR Average Return on Risk Table 5: Splits into regions (North Africa & Turkey and the Middle East) the results of the control and VASL. Middle East Volatility Adjust Control Average Annualised Return on Capital 18.83% 14.26% Average Return on Risk North Africa & Turkey Volatility Adjust Control Average Annualised Return on Capital 12.43% 11.39% Average Return on Risk Figure 5 : Comparing the average annualised returns on capital and the average return on risk for both the control and the VASL strategies Return on Capital Risk % 5% 10% 15% 20% 25% Volatility Adjusted Stop Loss 30% Return on Capital % Linear (Volatility Adjusted Stop Loss) 35% 40% 45% Control Stop Loss 50% Linear (Control Stop Loss) 55% 60% PAGE 32 IFTA.ORG

33 The overall outperformance of utilising the VASL strategy can be best illustrated in Figure 5, where the combination of average annualised return on capital and average return on risk have been compared for both the control and the VASL strategies. Though the VASL strategy as a whole looks to have outperformed the control, there are a few standard deviations that did not, making it important to optimise the VASL strategy to make sure the most effective stop loss strategy is being employed. Before looking at the potential of optimising the VASL, it is worth reaffirming the performance of the VASL compared to the benchmark. The trend from the VASL results suggests that the wider the stop loss (in terms of standard deviations) the lower the performance (measured by average annualised return on capital & average return on risk). If this is the case it is worth investigating what the average percentage drawdown was for each standard deviation strategy. This way we can make a direct comparison with those percentage drawdowns from the control environment. If the average percentage drawdown from the VASL is comparable with one of the control s and has superior results, it can be said that the VASL strategy has added value and acts as conclusive empirical evidence to support the use of a VASL strategy over the use of a Percentage Drawdown stop loss strategy. Table 4 shows the average percentage stop loss for each of the standard deviations tested and the comparable control stop loss. Out of 22 data points the control only managed to outperform the VASL 4 times; these have been highlighted. Table 5 splits the performance of the control and the VASL results into regions, both the Middle East and North Africa & Turkey are shown. This table adds further weight to support the utilisation of a VASL strategy, as it shows that the strategy performs across markets though it is important to note that in the North Africa and Turkey region the annualised return on capital is higher than the control, but is produced on a lower average return on risk. Figure 6: Comparing the average annualised returns on capital and the average return on risk for the VASL strategies. Return on Capital Risk % 5% 10% Return on Capital % 15% 20% % % 2.0 Volatility Adjusted Stop Loss % % 45% % 55% 60% Linear (Volatility Adjusted Stop Loss) Figure 7: Comparing how varying time frames influences the average annualised returns on capital for the most successful VASL strategies Average Annualised Return on capital 60% 50% 40% 30% 20% 10% 0% Volatility Time Frame Figure 8: Comparing how varying time frames influences the average return on risk for the most successful VASL strategies Average Return on Risk Volatility Time Frame Figure 9: Analysing the consistency of returns across multiple time frame Return on Capital Risk % 5% 10% 15% 20% 25% 30% 35% 40% 45% 20 Days 50% 55% % Optimising the VASL strategy Within the VASL strategies it is Return on Capital % Linear (0.5) Linear (0.75) Linear (2) Linear (2.25) IFTA.ORG PAGE 33

34 important to distinguish the optimal standard deviation to use as the results across the stop losses investigated varies somewhat. Figure 6 illustrates the profitability within the VASL strategies. From this it can be concluded that optimal strategies to use are the 0.5, 0.75, 2.0 and 2.25 standard deviation within the VASL strategy. How does time frame influence the results? Having found what the optimal volatility is within the volatility adjusted stop loss, it is worth investigating if and how adjusting the time frame within the formula affects the results. After all a successful stop loss strategy should be able to be incorporated by traders as well as fund managers, both of which may have differing time horizons and investment objectives. Taking the optimal stop losses of 0.5, 0.75, 2.0 and 2.25, the back tests were re-run with varying time frames and the average annualised return and average return on risk were recorded. The results are illustrated in Figure 7 & Figure 8. The above investigation suggests that the most profitable time frame is up to 20 days, after which the average return on risk declines steadily. A similar trend is seen for the average annualised return on capital though there is a marked pick up after 60 days for the 0.5 and 0.75 standard deviation strategies. Though it is important to remember what was mentioned when discussing the measure of standard deviation, for a credible measure at least 20 data points are required. With this in mind the time frames of 5 to 15 will be excluded from analysis. It is the aim to see which standard deviation performs best across the varying time frames so both a Trader or Fund Managers, who may have differing investment horizons can utilise the VASL strategy. Figure 9 best illustrates which strategy performs most consistently; the graph suggests that a standard deviation of 0.75 performs consistently across all time frames. Though a short term trader might consider using a 0.5 measure with a 20 day time frame as it is by far the most successful strategy on a standalone basis. Conclusion To summarise, a detailed analysis has been carried out to find the most profitable control to test the theory: that a volatility adjusted stop loss strategy can enhance returns. The control test included back testing over 10,000 trades going back 5 years, across 9 different securities, and using 4 different technical trading strategies. It was found that using the Dynamic control produced the most profitable control environment. This control then acted as a benchmark to compare the volatility adjusted stop loss performance against. The results gave conclusive evidence supporting the use of a Volatility Adjusted Stop Loss (VASL) strategy over that of the popular Percentage Drawdown stop loss strategy. Further investigation and comparison against other stop loss strategies is needed to make any conclusions on whether the VASL strategy is the most successful stop loss strategy to employ though. Further analysis could also be conducted to see whether using real time prices (over end of day prices) yields different results. On completing this investigation and reviewing the results it became apparent that the relative performance of the longer term stop losses, for example the 3 standard deviation or the 20% drawdown stop loss, may have been negatively impacted by the decision to exclude trades that were still open as the end of the time series, as these trades might have been carrying large unrealised profits which would impact the overall results. To clarify whether the decision to exclude the open trades made a material difference, the back tests were re-run to include the unrealised P&L as of the 12 th of September The impact of this change on the VASL results was minimal, with the 1.75 standard deviation stop loss seeing the largest impact with a change in the average annualised return on capital from 29.0% to 28.7%. Further enhancement of trading returns could also result if entry price was considered: an investigation into whether an optimal entry price is possible by measuring where the stock is trading compared to its historical average, i.e. if the stock is trading between 2.0 and 2.5 standard deviations from its 20 day average does that further optimise the performance. Also an investigation into whether position sizing can impact overall returns, i.e. adjusting the size of position to match the underlying securities volatility should also be a consideration. Unfortunately both these variables are sufficiently complex to warrant their own investigation and can t be covered in this paper. Given the need of further analysis, it can be concluded from this investigation that employing a VASL strategy over more traditional stop loss strategies can enhance trading performance. The best performing VASL strategy returned a 46% average annualised return on capital with a 146% average return on risk, compared to the best control strategy which produced 53.7% and 83% respectively, with the best performing VASL averaging a $5,222 profit per trade compared to $3,994 average profit for the control. Both the control and the VASL tests have produced positive results, which is worth putting into context, when compared to a simple buy and hold strategy which would have only returned a 5% annualised return on capital. I hope this paper has demonstrated that all traders and fund managers alike should incorporate some sort of risk management into their investment process. Contact the author for questions: erowson.mifft2013@london.edu References LINTON, D. Optimisation of trailing stop losses, IFTA Journal 2008 Edition. P38-46 Bibliography KAUFMAN, P.J. New Trading Systems and Methods. Wiley, 2005 MURPHY, J. Technical Analysis of the Financial Markets. New York Institute of Finance, FAITH, C.M. Way of the Turtle. McGraw-Hill BOLLINGER, J. Bollinger on Bollinger Bands. McGraw-Hill MARBER,B. Marber on Markets: How to make money from charts. Harriman House, Software and Data Bloomberg ( Updata Technical Analyst Advance for Bloomberg ( Athena Systems ( Back testing Spreadsheet (developed by Athena Systems with special thanks to Mr. Scott Sykowski). PAGE 34 IFTA.ORG

35 Momentum Indicators: An Empirical Analysis of the Concept of Divergences By Stephan Belser, CFTe, MFTA Abstract Divergence, or the non-confirmation of price movement by a related market or technical indicator, has long been a useful part of the technician s repertoire. Identifying divergences between price and technical indicators is an important aspect of technical analysis. Especially when a trend enters a mature phase the concept of divergences can help to identify potential reversals or trend changes. The following paper provides an empirical investigation about the concept of divergences using the DAX Index and the Gold Spot Price. The aim is not only to identify the divergence between price and indicator development, but also to measure the resulting returns concerning the appearance of an expected price development. Furthermore, the study tries to answer the questions, how long it takes until the maximum return will be noticeable after an expected price development occurred and if there is a relationship between the type of divergence and the return realisation. This paper will show which assumptions about the forecasting qualities of a trading signal in the MACD or RSI indicator are possible. Introduction In technical analysis a large variation of indicators is used in order to describe the dynamics of market trends. On the one hand, an attempt is being made to depict overbought and oversold markets via the usage of an indicator s extreme value. On the other hand, trend reversals or corrections are anticipated through the concept of divergence between price and indicator development. The most commonly known indicators, which reveal the concept of divergence, are RSI and MACD. Many of the technical analysts agree on the fact that divergences are actually working, but only a few empirical studies exist which prove the veracity of this concept. Within the debate the question is raised whether oscillators generate too many false signals and hence reduce the forecasting qualities of an indicator signal overall. However, before an evaluation of forecasting qualities is possible, it needs to be analysed whether or not a divergence is actually able to predict a market trend reversal. If this is the case, the price development after a divergence will become important and the following questions turn relevant: In how many cases does the expected price reaction occur? How long does it take until the maximum price reaction sets in? To identify the most effective way of trading divergences, the following five hypotheses should help to get profitable divergence signals: H1: A more meaningful extreme (high or low) in price should be followed by a stronger price reaction in the opposite direction. H2: The longer the duration between the divergence pairs, the stronger the anticipated price reaction. H3: The longer the duration between the divergence pairs, the longer the period until the maximum price reaction sets in. H4: Bullish divergence signals are as profitable as bearish divergence signals. H5: RSI divergences are as profitable as MACD divergences. Definitions and Methodology Divergences Divergences act as a technician s early warning system, allowing valuable insight into the internal strength of a price move. One of the common uses of momentum indicators is the identification of trend completion when price and momentum begin to diverge. Divergence can be especially helpful for traders as a leading indicator when assessing possible future trend reversal situations in markets that are still trending but the strength of the trend is waning. A bullish divergence usually occurs in a down trend when new lows in price do not result in a new low in the indicator. This signifies that the prevailing downward trend is weakening and a trader should look for other possible signs of a pending reversal to the upside. A bearish divergence usually occurs in an up-trend when new highs in price do not result in a new high in the indicator. This signifies that the prevailing upward trend is weakening and a trader should look for other possible signs of a pending reversal to the downside. One of the central premises of this method is that any move in price must be confirmed by the indicator. If the price is making new highs while the indicator is unable to break old ones, the strength of the primary trend is called into question. bullish divergence = price is making a new low while the oscillator concurrently makes a higher low bearish divergence = prices make a higher high but the indicator makes a lower high IFTA.ORG PAGE 35

36 Figure 1 demonstrates a typical divergence. In it, as the price sets new records, the indicator failed to better highs. Indicators of Choice Various indicators can be used to confirm the price development of a security or index. The choice is often governed by the trader s comfort level and familiarity with the indicator s particular nuances. In this study the RSI and the MACD are used to identify divergences because these two indicators are calculated and interpreted in a different way. For a valid signal to occur the oscillator should be in overbought or oversold territory as the divergence begins to take shape. By screening Figure 1: Example of a divergence between price and indicator movement Figure 2: Divergences (1. or 2.) can occur in different time frames PAGE 36 IFTA.ORG

37 potential trades in this way, the technician can avoid many marginal patterns and unnecessary losses. Identification of divergences The first step of this analysis is to track divergences. However, their discovery is rather difficult because for every new market situation exists a different duration between the appearance of the price extreme and the extreme of the indicator in the analysed trend move. Unfortunately, divergences are also quite subjective and often noticed only in hindsight. Hypothesis 2 says that a longer duration between the observed data points the more valuable should the trading Figure 3: Detection of divergences looking 40 days back Figure 4: The trading signal IFTA.ORG PAGE 37

38 signal be. Therefore different time frames were observed to get an idea in which time intervals the trader should look for divergences (Figure 2). In order to be most flexible in tracking divergences, the (local) highs and lows are detected based on rolling 10-/20- /40-/80-day or week periods which are used as time intervals for the comparison of price and indicator movements. In the optimum case a divergence occurs hand in hand with a cycle top or bottom. To capture potential cycle highs or lows in price the data point in the middle of each observed time frame are investigated. Rolling periods are used to address every new market situation and potential new trading signals. In using different time frames it can not be excluded out that a single divergence is detected in more than one observed time frame. This can be possible if there isn t a more meaningful combination of data points in the larger time interval. Table 1: DAX Index Bearish divergences on a daily basis Indicator time interval 10 days 20 days 40 days 80 days No. of divergences Cases of expected price reaction Average Trading profit after 10 days 20 days 40 days 80 days max. average trading profit days after trading signal max. in% MACD % -0.62% -0.44% -0.45% 0.08% % RSI % -0.31% -0.40% -0.21% 0.09% % MACD % -0.49% -0.43% -0.18% 0.33% % RSI % -0.39% -0.39% -0.31% 0.05% % MACD % -0.70% -0.60% -0.49% -0.03% % RSI % -0.54% -0.52% -0.36% -0.11% % MACD % -0.57% -0.30% -0.28% 0.08% % RSI % -0.49% -0.43% -0.29% -0.05% % Table 2: Gold Spot Price Bearish divergences on a daily basis Indicator time interval 10 days 20 days 40 days 80 days No. of divergences Cases of expected price reaction Average Trading profit after 10 days 20 days 40 days 80 days max. average trading profit days after trading signal max. in% MACD % -0.15% 0.53% 0.59% 0.54% % RSI % 1.71% 0.11% 0.53% 0.42% % MACD % 0.23% 0.20% 0.38% 0.94% % RSI % -0.07% 0.20% 0.19% 0.70% % MACD % 0.38% 0.56% 0.94% 1.09% % RSI % -0.08% 0.24% 0.30% 0.66% % MACD % 0.24% 0.28% 0.30% 0.77% % RSI % -0.14% 0.18% 0.31% 0.60% % Table 3: DAX Index Bullish divergences on a daily basis Indicator time interval 10 days 20 days 40 days 80 days No. of divergences Cases of expected price reaction Average Trading profit after 10 days 20 days 40 days 80 days max. average trading profit days after trading signal max. in% MACD % 0.61% 1.54% 2.12% 4.28% % RSI % 0.19% 0.79% 1.51% 2.69% % MACD % 0.43% 1.51% 1.75% 3.93% % RSI % 0.81% 1.84% 3.35% 4.10% % MACD % 0.55% 1.43% 2.68% 3.92% % RSI % 0.78% 1.91% 2.74% 3.57% % MACD % -0.31% -0.31% 0.33% 1.54% % RSI % 0.72% 1.56% 2.25% 3.40% % PAGE 38 IFTA.ORG

39 To find divergence signals, first peaks in price and in momentum were defined and identified. A peak was defined as a high in price or momentum such that the day on which the high took place was preceded by lower or equal values in the following five data points. Once price peaks and dips were identified the indicator value and the closing price built the first pair of data points. Once a matching pair was found, the algorithm looked back up to 40 closing prices (depending on the analysed cycle) for an earlier pair of lower peaks or higher dips in price and indicator values. The two pairs of matching peaks or dips were then checked for divergence (Figure 3). In this study a bearish divergence is defined as a higher peak in price matched by a lower or equal peak in the indicator and bullish divergence as a lower dip in price matched by a higher or equal dip in momentum. The trading signal is set when a valid divergence in the analysed time interval appears. Per definition no new extreme in the upcoming five days or weeks is allowed (Figure 4). Once divergences were found the next step is to see how often prices move into the anticipated direction. For this the following points in time are examined: 10, 20, 40 and 80 periods after the trading signal, as well as the point in time at which the maximum average profit occurs. So trend reversals or at least a correction within a trend are of interest. Furthermore it is examined after how many days the maximum price movement sets in. This is done by calculating all trading profits after a recognized trading signal if the defined stop was not hit. In this study profitability is understood as the average trading profit in the analysed time frame. Money Management Money management is based on a from-entry stop. The risk per trade is defined by the difference between the entry price and the stop level. Volatility in weekly data is regularly substantially higher compared to daily data. Therefore the stop-level for daily data is tighter versus weekly data. The methodology does not allow a risk of more than 1% per trade in daily data and 5% in weekly data. Period of Investigation and Object of Study The study examines daily and weekly data of the German blue chip stock market index DAX and the Gold Spot Price between 01/01/1980 and 03/31/2011. This window is large enough to offer a great variety of up- and down-trends inside different overall market conditions (secular structure). Within this time frame, the closing prices of daily and weekly data are analyzed in terms of bullish and bearish divergences. Furthermore, it is examined how many bullish and bearish divergences occur and on which trading days after the divergence the maximum average price movement sets in. As indicators, the RSI with a default of 14 and the MACD with a default of 26, 12, 9 are used. Concerning the RSI indicator it is worth mentioning that its signal is only used if the value on the first extreme (extreme in the indicator / first pair) records more than 65 or less than 35 points while forming the divergence, in order to avoid worthless signals in the neutral range of the indicator. Divergences in daily data Bearish divergences The analysis of the bearish divergences shows for the DAX Index that in all cycles the maximum price movement sets in within a narrow time range. Furthermore, the return analysis depicts that the maximum price reaction for the DAX Index becomes already noticeable between the 36 th and the 46 th day after the trading signal (Table 1). In all analysed time frames RSI identifies more divergences compared to the MACD except of the 10-day interval. In this 10-day interval the maximum trading profit for the RSI appears. Most profitable considering both indicators is the 20-day interval. Here were higher trading profits compared to the other intervals evident. In the cases of expected price moves the MACD indicator achieves enhanced results in the 20- and 80-day interval. In contrast to that for the RSI in the 10- and 40-day intervals better results are noticeable. It is remarkable that in expanding the time interval improved results are not achievable. Comparing the maximum profit there are no major differences between both indicators. The results for the Gold Spot Price are dissimilar. Maximum trading profit appears in the 40-day interval for the MACD model with a return of 1.95%, whereas the best window for the RSI indicator is the 10-day time frame (Table 2). Most profitable for the Gold price in terms of expected price reaction is the 40- day interval. Comparing the maximum profit of the Gold price to the DAX Index there are significant higher returns after bearish divergences for Gold. Additionally the maximum price reaction set between the 49 th and the 60 th day after the signal and so considerably later versus the DAX Index. Bullish divergences The analysis of bullish divergences shows positive returns for the DAX Index in nearly all time intervals. The returns only differ in the amplitude of the maximum trading profit and for the time at which this price reaction occurs. Slightly negative results are for the 80-day interval given (Table 3). It is noteworthy that the maximal return sets in between the 60 th and 73 rd day after the divergence completely independent of the observed time frames. This leads to the assumption that the maximum price reaction can always be expected after 60 to 73 days regardless of the quoted low and analysed cycle. The period of time until the maximum trading profit sets in increases generally in the longer time intervals for both indicators. Considering the 80-day interval, the maximum return is recorded in the MACD indicator after 73 days and in the RSI indicator after 65 days. In numbers, this observation equals a plus of 1.83% after a trading signal in the MACD indicator and a plus of 4.68% in the RSI indicator. Once more the 20-day interval is best for both indicators taking the probability of expected price reaction and maximum trading profit into account. For the signals in the Gold price movement a positive profit development can be seen in all time intervals (Table 4). Most profitable results came out in the 20-day interval for the MACD and in the 40-day interval for the RSI. By looking on larger IFTA.ORG PAGE 39

40 time frames trading results for bullish divergences can not be improved. The 80-day interval is obviously too large for tracking the most valuable signals in both indicators. Finally the maximum price development after positive divergences for Gold occurs remarkably earlier than the development after bullish divergences in the DAX Index. But it needs to be pointed out that the average trading profit after Gold divergences is smaller compared to the returns after DAX divergences. Furthermore, cases of expected price reaction for bullish daily divergences lie usually higher than for bearish divergences. Divergences in weekly data Bearish divergences Looking on the DAX Index only bearish divergence signals within the MACD indicator are valuable for 10-, 20- and 40-week time frames. The biggest price reaction occurs in the 10-week Table 4: Gold Spot Bullish divergences on a daily basis Indicator time interval 10 days 20 days 40 days 80 days No. of divergences Cases of expected price reaction Average Trading profit after 10 days 20 days 40 days 80 days max. average trading profit days after trading signal max. in% MACD % -0.38% 0.34% 0.52% 1.31% % RSI % 0.13% 0.22% 0.40% -0.21% % MACD % -0.18% 1.14% 1.06% 2.62% % RSI % -0.45% -0.32% -0.08% -0.50% % MACD % 0.10% 1.42% 1.41% 2.74% % RSI % 0.02% 0.77% 0.92% 1.09% % MACD % 0.14% 0.78% 1.28% 1.88% % RSI % -0.11% 0.54% 0.61% 0.98% % Table 5: DAX Index Bearish divergences on a weekly basis Indicator time interval 10 weeks 20 weeks 40 weeks 80 weeks No. of divergences Cases of expected price reaction Average Trading profit after 10 weeks 20 weeks 40 weeks 80 weeks max. average trading profit days after trading signal max. in% MACD % -3.72% -2.98% 1.31% 2.05% % RSI % -5.00% -5.00% -5.00% -5.00% % MACD % -2.62% 1.66% 5.40% 3.11% % RSI % -4.55% -1.74% -1.86% -2.80% % MACD % -4.42% -0.80% -0.96% -2.17% % RSI % -4.73% -3.04% -3.12% -3.86% % MACD % -4.60% -2.06% -2.17% -3.02% % RSI % -4.75% -3.16% -3.23% -3.76% % Table 6: Gold Spot Bearish divergences on a weekly basis Indicator time interval 10 weeks 20 weeks 40 weeks 80 weeks No. of divergences Cases of expected price reaction Average Trading profit after 10 weeks 20 weeks 40 weeks 80 weeks max. average trading profit days after trading signal max. in% MACD % 0.50% -0.10% 1.56% 5.10% % RSI % -1.50% -1.03% -1.64% 0.00% % MACD % -2.22% -3.73% -3.56% -1.01% % RSI % -2.20% -1.82% -2.31% -1.00% % MACD % -5.00% -5.00% -5.00% -5.00% % RSI % -2.66% -2.35% -2.76% -1.66% % MACD % -5.00% -5.00% -5.00% -5.00% % RSI % -1.07% -1.08% -0.11% 1.86% % PAGE 40 IFTA.ORG

41 interval 54 weeks after the trading signal and quotes a trading profit of 4.20%. In contrast to that, the price developments following a bearish RSI signals have been consequently stopped out a few weeks after the signal. In this case negative trading results in all time intervals were received. Bearish divergences appeared not frequently higher in longer intervals. Thus, 10 bearish signals occured in the MACD and 16 bearish divergences are identified in the 80-week interval. In the case of a bearish divergence, it can be stated that the expected negative price development always sets in very fast after the signal occurred (Table 5). In the 20- and 40-week time frames the maximum trading profit appeared after 21 weeks. In all time intervals higher probabilities for the expected price reaction for the MACD indicator are discoverable compared to the RSI, since there were only negative trading results for the RSI indicator. So the RSI is obviously not a good indicator to detect bearish trend reversals on a weekly basis. In weekly data, is in case of a MACD divergence, the 20-week time frame is the most valuable interval. A longer time frame to track divergences is generally less successful. When analysing Gold it is remarkable that the trading results are pretty disappointing after a bearish divergence in weekly data. Only the MACD signal in the 10-week interval and the RSI signal in the 80-week time frame are profitable (Table 6). The maximum profit for these two trades comes in very late compared to the results for the DAX Index. Bullish divergences The analysis of the 10-week cycle in the DAX Index reveals within the whole observation period only two signals in the RSI and nine in the MACD indicator. For both RSI cases the stop was hit so apparently a 10-week interval is too short for the RSI to identify bullish divergences. For the bullish MACD divergences positive trading results are noticeable for all observed points in time. Maximum price development following the MACD signal occurs after 72 weeks and quotes 29.85% (Table 7). During the investigation of the 20-week interval one bullish divergence in the MACD indicator and three divergences in the RSI indicator revealed. Maximum price development occurs for the MACD 65 weeks after the divergence and notes 6.85%. For the RSI a maximum trading profit of 12.13% after 59 days is receivable. For the 40-week interval the analysis presents two bullish divergences in the MACD indicator and five in the RSI indicator. In terms of price developments the results are consistently positive within both indicators. For the MACD the maximum price development occurs after 80 weeks quoting 21.04% and 15.69% for the RSI 70 weeks later. Table 7: DAX Index Bullish divergences on a weekly basis Indicator time interval 10 weeks 20 weeks 40 weeks 80 weeks No. of divergences Cases of expected price reaction Average Trading profit after 10 weeks 20 weeks 40 weeks 80 weeks max. average trading profit days after trading signal max. in% MACD % 1.51% 3.44% 9.28% 25.81% % RSI % -5.00% -5.00% -5.00% -5.00% % MACD % 6.85% 7.07% 2.73% 0.73% % RSI % -2.49% -0.90% 4.72% 9.42% % MACD % 1.38% 8.93% 12.92% 21.04% % RSI % -0.94% 3.03% 8.00% 14.07% % MACD % 4.65% 14.09% 23.00% 26.22% % RSI % 1.08% 6.60% 13.86% 17.82% % Table 8: Gold Spot Bullish divergences on a weekly basis Indicator time interval 10 weeks 20 weeks 40 weeks 80 weeks No. of divergences Cases of expected price reaction Average Trading profit after 10 weeks 20 weeks 40 weeks 80 weeks max. average trading profit days after trading signal max. in% MACD % 3.77% 6.13% 9.12% 19.59% % RSI % 1.78% 1.24% 0.74% 6.05% % MACD % 3.80% 4.84% 6.58% 5.01% % RSI % 1.78% 1.24% 0.74% 6.05% % MACD % 2.40% 3.28% 3.51% 3.96% % RSI % 4.14% 3.95% 2.38% 2.70% % MACD % 0.77% 2.04% 1.59% 1.98% % RSI % 2.22% 2.82% 1.20% 2.83% % IFTA.ORG PAGE 41

42 The analysis of the 80-week interval reveals results which are similar to the 40- week interval. Data for both indicators show a consistently positive price development. The maximum return of 28.42% occurs 60 weeks after the MACD signal while the RSI signal initiates a maximum price performance after 60 weeks, noting a profit of 20.27%. All in all MACD identifies fewer divergences compared to the RSI indicator in the 20-, 40- and 80-week cycle. Therefore the probability of success is superior for the MACD signals. The maximum price reaction for the Gold price sets in between 32 and 50 weeks after the trading signal (Table 8). In the 10-week time frame the most profitable results are evident. Here the highest probability of expected price reaction, as well as the largest trading profits for both indicators, occurs. For the Gold price the results get poorer the longer the time interval gets. This is a completely different result compared to the DAX Index. Conclusions This analysis based on the DAX Index and the Gold Spot Price shows that changes in market trends can be identified with the help of the concept of divergence. At the same time a tight stop management is necessary because a divergence only indicates a trend reversal. To summarize, the following statements about profitable trading divergences can be made. Figure 5: Maximum trading profit for daily data in different time frames Figure 6: Maximum trading profit for weekly data in different time frames PAGE 42 IFTA.ORG

43 Per definition, hypothesis H1 estimates that a more meaningful extreme should be followed by a stronger expected price reaction in the opposite direction. Concurrently, the duration between the observed pairs usually expands as described in hypothesis H2. However, the analysis can not offer better results in observing larger time frames and consequently is not able to approve hypothesis H1 and hypothesis H2. In the majority of all cases the 20- and 40-day or week intervals provide the best results. Divergences in larger time intervals do not lead to more profitable trading results, neither in daily nor in weekly data. Therefore, we do not have to analyse larger time frames to track divergences (Figure 5 and 6). Interestingly the duration to the maximum trading profit appears independent from the analysed time frame. For the DAX Index the maximum trading profit for daily and weekly bearish divergences comes in earlier compared to bullish divergences. For the Gold price the maximum trading profit for daily bearish and bullish divergences appeared approximately after the same duration. Comparing daily data of the Gold price and the DAX Index maximum trading profits in bearish divergences appear much later for Gold compared to the DAX. In the case of bullish divergences the opposite effect was measurable. In weekly data maximum trading profits in bullish divergences emerge much earlier for Gold compared to the DAX (Figure 7 and 8). Figure 7: Duration to the maximum trading profit in daily data for different time frames Figure 8: Duration to the maximum trading profit in weekly data in different time frames IFTA.ORG PAGE 43

44 The results show that bullish divergences are basically more profitable than bearish divergences for both indicators. This is true for daily and weekly data. A possible explanation is the fact that down-trends are normally more erratic than up-trends. Table 9: Summary of daily data DAX bearish divergence Most profitable time frame Preferred indicator Expected max. trading profit after bullish divergence bearish divergence GOLD bullish divergence 20-day 20-day 40-day 40-day RSI or MACD RSI MACD MACD days days days days Table 10: Summary weekly data DAX bearish divergence Most profitable time frame Preferred MACD indicator Expected max. trading profit after bullish divergence bearish divergence GOLD bullish divergence 20-week 80-week 10-week 10-week weeks MACD weeks MACD or RSI weeks RSI weeks Accordingly in an up-trend more bearish divergences may be stopped out while prices continue to climb. Nevertheless there are some consistent differences between the DAX Index and the Gold price. Comparing RSI and MACD the study demonstrated that MACD divergences are on principle more profitable than RSI divergences. Furthermore it is to conclude that in daily Gold price data better results for the MACD indicator arise, whereas mixed outcomes for the DAX Index can be recorded. In weekly data the investigation showed for Gold in the shorter intervals better MACD results and for the larger time frames superior RSI trading profits are measurable (Table 9 and 10). These findings show for the DAX Index and the Gold Spot Price how prices develop after divergences. First, this analysis helps to predict the duration between the trading signal after a divergence and the resulting maximum trading profit. And second, assumptions about the forecasting probability of receiving an expected return can be made. This study illustrates the power of price to oscillator divergences. They are difficult to identify, but are usually worth the effort. It is also important to be aware of the overall technical picture (including chart patterns and trendlines) as well as likely areas of support and resistance. Combining classical chart analysis, proper risk management techniques and a healthy respect for the dominant trend with the concept of divergences can lead to prosperous trading profits. Literature Bleymüller, Josef / Gehlert, Günther / Gülicher, Herbert (2004): Statistik für Wirtschaftswissenschaftler, 14. Auflage, München. Breuer, Wolfgang / Gürtler, Marc / Schuhmacher, Frank (2002): Risikoverfahren: in Coche, Joachim / Stotz, Olaf: Asset Allocation, Köln, S Fama, Eugene F. (1976): Foundations of finance: portfolio decisions and securities prices, Oxford. Florek, Erich (2000): Neue Trading Dimensionen, FinanzBuch Verlag GmbH Garz, Hendrick / Günther, Stefan / Moriabadi, Cyrus (2002): Portfolio- Management, Theorie und Anwendung, 1. Auflage, Frankfurt am Main. Gast, Christian (1998): Asset Allocation Entscheidungen im Portfolio- Management, Bern. Gügi, Patrick (1995): Einsatz der Portfolioopimierung im Asset-Allocation- Prozess: Theorie und Umsetzung in der Praxis, Bern, Stuttgart, Wien. Heckmann, Tobias (2009): Markttechnische Handelssysteme, quantitative Kursmuster und saisonale Kursanomalien, Josef EUL Verlag, 1. Auflage Murphy, John (2004): Technische Analyse der Finanzmärkte, Finanzbuchverlag, 3. aktualisierte Auflage, Paesler, Oliver (2006): Technische Indikatoren simplified, Finanzbuchverlag, Pflüger, Patrick (2011): Möglichkeiten und Grenzen einer Aktienkursprognose mittels der technischen Analyse, GRIN Verlag, 1. Auflage Poddig, Thorsten / Dichtl, Hubert / Petersmeier, Kerstin (2003): Statistik, Ökonometrie, Optimierung: Methoden und ihre praktischen Anwendungen in der Praxis, Uhlenbruchverlag, Bad Soden, 3. Auflage. Pring, Martin J. (2003): Momentum Explained, Volume 2, McGraw Hill Rose, Rene (2006): Enzyklopädie der technischen Indikatoren Rene Rose (Hrsg.) FinanzBuch Verlag GmbH, 1. Auflage Schmidt-von Rhein, Andreas (1996): Die moderne Porfoliotheorie im praktischen Wertpapiermanagement: Eine theoretische und empirische Analyse aus Sicht privater Kapitalanleger, Bad Soden. Spremann, Klaus (2000): Portfoliomanagement, München. Vogel, Friedrich (2000): Beschreibende und schließende Statistik: Formeln, Definitionen, Erläuterungen, Stichwörter und Tabellen, 12. Auflage, München. Wilder, Welles (1978): New Concepts in Technical Trading Systems. Articles Cartwright, D. (1991): RSI as an Exit Tool, Technical Analysis of Stocks & Commodities, vol.9, no.4, 1991, pp Drinka, Thomas P. & Kille, Steven L. (1987): Profitability of Selected Technical Indicators, Technical Analysis of Stocks & Commodities, vol.5, no.9, 1987, pp Drinka, Thomas P. & Kille, Steven L. (1987): RSI profitability with money management Profitability of Selected Technical Indicators, Technical Analysis of Stocks & Commodities, vol.5, no.9, 1987, pp Ehlers, John F. (1986): Optimizing RSI with Cycles, Technical Analysis of Stocks & Commodities, vol.4, no.1, 1986, pp Ehlers, John F. (1991): MACD Indicator Revisited, Technical Analysis of Stocks & Commodities, vol.9, no.10, 1991, pp Hall, Herbert S. (1991): The Common (But Useful) RSI, Technical Analysis of Stocks & Commodities, vol.9, no.8, 1991, pp McWhorter, Lawson W. (1994): Price/Oscillator Divergences, Technical Analysis of Stocks & Commodities, vol.12, no.1, 1994, pp Merrill Arthur A. (1991): Testing Indicators Technical Analysis of Stocks & Commodities, vol.9, no.5, 1991, pp Nicholas, John (1984): Momentum Indicators and Market Cycles, Technical Analysis of Stocks & Commodities, vol.2, no.6, 1984, pp Pring, Martin J. (1997): Reverse Divergences and Momentum, Technical Analysis of Stocks & Commodities, vol.15, no.12, 1997, pp Star, Barbara (1996): Hidden Divergence, Technical Analysis of Stocks & Commodities, vol.14, no.7, 1996, pp Software Bloomberg MS-Excel PAGE 44 IFTA.ORG

45 Momentum Success Factors By Gary Antonacci Abstract Momentum is the premier market anomaly. It is nearly universal in its applicability. Rather than focus on momentum applied to particular assets or asset classes, this paper explores momentum with respect to what makes it most effective. We do this first by introducing a hurdle rate filter before we can initiate long positions. This ensures that momentum exists on both an absolute and relative basis and allows momentum to function as a tactical overlay. We then explore the factor most rewarded by momentum extreme past returns, i.e., price volatility. We identify high volatility through the paired risk premiums in foreign/u.s. equities, high yield/credit bonds, equity/ mortgage REITs, and gold/treasury bonds. Using modules of asset pairs as building blocks lets us isolate volatility related risk factors and successfully use momentum to effectively harvest risk premium profits. Introduction Momentum is the tendency of investments to persist in their relative performance. Assets that perform well over a 6 to 12 month period tend to continue to perform well into the future. The momentum effect of Jegadeesh and Titman (1993) is one of the strongest and most pervasive financial phenomena. Researchers have verified its existence in U.S. stocks (Fama and French (2008)), industries (Moskowitz and Grinblatt (1999), Asness, Porter and Stevens (2000)), styles (Lewellen (2002), Chen and DeBondt (2004)), foreign stocks (Rouwenhorst (1998), Chan, Hameed and Tong (2000), Griffen, Ji and Martin (2005)), emerging markets (Rouwenhorst (1999)), country indices ( Bhojraj and Swaminathan (2006), Fama and French (2011)), commodities (Pirrong (2005), Miffre and Rallis (2007)), currencies (Menkoff, Sarno, Schmeling, and Schrimpf (2011)), international government bonds (Asness, Moskowitz and Pedersen (2009)), corporate bonds (Jostova, Nikolova and Philipov (2010)), and residential real estate (Beracha and Skiba (2011)). Since its first publication, momentum has been shown to work going forward in time (Grundy and Martin (2001), Asness, Moskowitz, and Pedersen (2009)) and back to the Victorian age (Chabot, Ghysels and Jagannathan (2009)). There has also been considerable study of exogenous factors that influence momentum. In a recent paper, Bandarchuk, Pavel and Hilscher (2011) reexamine some of the factors that have previously been shown to impact momentum in the equities market. These include analyst coverage, illiquidity, price level, age, size, analyst forecast dispersion, credit rating, r squared, marketto-book, and turnover. The authors show that all these factors are proxies for extreme past returns, or high volatility. Greater momentum profits simply come from more volatile assets. With respect to fixed income, Jostova, Niklova and Philipov (2010) show that momentum strategies are highly profitable among non-investment grade corporate bonds. High yield, non-investment grade corporate bonds have, by far, the highest volatility among bonds of similar maturity. This may indicate that credit default risk is also a proxy for volatility risk. The real estate market and long-term Treasury bonds are also subject to high volatility due to their sensitivity to interest rate risk and economic conditions. Gold is subject to high volatility as well, due to its response to economic stress and uncertainty. In this paper, we will examine momentum with respect to high volatility associated with all four markets equities, bonds, real estate, and gold. Before proceeding, we need to distinguish between relative and absolute momentum. When we consider two assets, momentum is positive on a relative basis if one asset has appreciated more than the other has. However, momentum is negative on an absolute basis if both assets have declined in value. Most momentum researchers use long and short positions to examine both the long and short side of a market simultaneously. They are therefore only concerned with relative momentum. It makes little difference whether the studied markets go up or down, since short momentum positions hedge long ones and vice versa. Relative momentum can help one identify when assets will remain strong relative to others, but if a market as a whole is in a downtrend, then all related assets are likely to sustain losses. When looking only at long side momentum, however, it is desirable to be long only when both absolute and relative momentum is positive, since momentum results are highly regime dependent. Fortunately, there is a way to put the odds in one s favor with respect to momentum profits from long positions. Positive momentum means an asset that has outperformed over the past twelve months is likely to continue doing so. To determine absolute momentum, we see if an asset has outperformed Treasury bills over the past year. Since Treasury bills are expected to always remain positive, if our chosen asset shows positive relative strength with respect to Treasury bills, then it too is likely to continue showing a positive return. In our momentum match ups, if our selected assets do not show positive relative strength with respect to Treasury bills, then we select Treasury bills as an alternative investment until our other assets are stronger than Treasury bills. Treasury bill returns thus serve as both a hurdle rate before we can invest in other momentum assets, as well as a safe, alternative investment until our assets show both relative and absolute positive momentum. IFTA.ORG PAGE 45

46 Besides incorporating a safe alternative when market conditions are not favorable, our module approach has another important benefit. It imposes diversification on our momentum portfolios. If one were to throw all assets into one large pot, as is often the case with momentum investing, and select the top few momentum candidates, there is a good chance some of the selected assets would be highly correlated with one another. Asset pair modules help ensure that different asset classes (and risk factors) receive portfolio representation. 2. Data and Methodology All monthly return data begins in January 1974, unless otherwise noted, and includes interest and dividends. For equities, we use the MSCI US, MSCI EAFE, and MSCI ACWI exus indices. These are all free float adjusted market capitalization weightings of large and midcap stocks. The MSCI EAFE Europe, Australasia and Far East Index includes twenty-two major developed market countries, excluding the U.S. and Canada. The MSCI ACWI exus, i.e., MSCI All Country World Index ex US, includes twenty-three developed market countries (all but the U.S.) and twenty-one emerging market countries. MSCI ACWI exus data begins in January We create a composite data series called EAFE+ that is comprised of the MSCI EAFE Index until December 1987 and the MSCI ACWI exus after that time. 2 The Bank of America Merrill Lynch High Yield Cash Pay Bond Index that we use begins in November Data prior to that is from Steele System s Corporate Bond High Yield Average. All other bond indices are from Barclays Capital. REIT data is from the National Association of Real Estate Investment Trusts (NREIT). Gold returns using the London PM gold fix are from the World Gold Council. Treasury bill returns are from newly issued 90-day auctions as reported by the U.S. Treasury. No deductions have been made for transaction costs. The average number of switches per year for our modules is 1.4 for foreign/u.s.equities, 1.2 for high yield/credit bonds, 1.6 for equity/mortgage REITs, and 1.6 for gold/treasuries, making momentum transaction costs negligible. The average annual expense ratio for a representative group of exchange-traded funds corresponding to the indices we use is.25%, and their annual transaction costs are.05%. The most common metric for evaluating investment strategies is the Sharpe ratio. It is most appropriate when you have normally distributed returns or quadratic preferences. Yet the returns from financial assets usually are not normally distributed. Tail risk may be much greater than one expects under an assumption of normality. Quadratic utility implies that as wealth increases, you become more risk averse. Such increasing absolute risk aversion is not consistent with rational investor behavior. Yet despite its limitations, the Sharpe ratio is based on expected utility theory, while most alternative performance measures lack a theoretical underpinning. Therefore, we use the Sharpe ratio as a risk adjusted metric, but also present skewness and maximum drawdown as additional risk factors. 3 Maximum drawdown here is the greatest peak to valley equity erosion on a month end basis. Most momentum studies use either a six or a twelve-month formation period. Both perform well, but since twelve months is more common and has lower transaction costs, we will use that time frame. 4 One often skips the most recent month during the formation period in order to to disentangle the momentum effect from the short-term reversal effect returns that may be related to liquidity or microstructure issues with equity returns. Momentum results for non-equity assets are actually better if one does not skip a month, since they suffer less from liquidity issues. Because we are dealing with gold, fixed income and real estate, as well as equities, we adjust our positions monthly but without skipping a month. We first apply momentum broadly to the MSCI U.S. and EAFE+ stock market indices in order to create a baseline equities momentum portfolio. In bonds, we incorporate credit risk volatility using the High Yield Bond Index, which has an average duration of just over four years. We match High Yield Bonds with the Barclays Capital U.S. Intermediate Credit Bond Index, the next most volatile intermediate term fixed income index. Real estate has the highest volatility over the past five years of the eleven U.S. equity market sectors tracked by Morningstar. Real Estate Investment Trusts (REITs) make up most of this sector. The Morningstar real estate sector has both mortgage and equity based REITs. We similarly use both. Our final high volatility risk factor focuses on economic stress and uncertainty. For this, we use the Barclays Capital U.S. Treasury 20+ year Bond Index and gold. Investors generally hold these as safe haven alternatives to equities and fixed income securities subject to credit default risk. 3. Equity/Sovereign Risk Equities are the mainstay of momentum investing. Therefore, our first momentum module is composed of the MSCI U.S. and EAFE+ indices. It gives us broad exposure to the U.S. equity market, as well as international diversification. Volatility comes from the equity risk premium, as well as from sovereign risk. Table 1 presents the summary statistics from January 1974 through December 2011 for the equity indices, our momentum strategy, and momentum excluding the use of Treasury bills as a hurdle rate and alternative. Table 1 Equities Momentum Momentum ext Bills US EAFE+ Annual Return Annual Std Dev Annual Sharpe Max Drawdown Skewness The average of the annual return of both equity indices is 11.68%, and their average annual standard deviation is 16.77%. The annual return and standard deviation of our momentum strategy are 15.79% and 12.77%. This is a remarkable 400 basis point increase in return and 400 basis point reduction in volatility from the market indices. Momentum doubles the Sharpe ratio and cuts the drawdown in half. Momentum results without the use of Treasury bills are better than the index averages, but not nearly as good as the results that come PAGE 46 IFTA.ORG

47 from using momentum with Treasury bills as a trend filter and alternative asset. Figure 1: Equities Momentum Most momentum research on equities looks at individual securities sorted by momentum. All three of the fully disclosed, publically available momentum equity programs use momentum applied to individual stocks. It might be useful therefore to see how our module approach stacks up against individual stock momentum. The AQR momentum index is composed of the top one-third of the Russell 1000 stocks based on twelve-month momentum with a one-month lag. Positions are adjusted quarterly. The AQR small cap momentum index follows the same procedure with the Russell Table 2 shows the AQR results, as well those of our Equity module, from when the AQR indices began in January Table 2: AQR Index versus Equity Module AQR. Large Cap AQR. Small Cap US MSCI Equity Module Annual Return Annual Std Dev Annual Sharpe Max Drawdown Skewness The AQR indices show a modest advantage over the broad U.S. market index. However, our Equity module results are considerably better. The differences here are understated, since AQR estimates that their index results should be reduced by transaction costs of.7% per year. difference is the credit default risk of their respective holdings, as reflected in their average credit ratings. Table 3: Intermediate Fixed Income Index Rating Duration Volatility Treasury AA Government A Government/ A Credit Aggregate A Bond Credit A High Yield B In Table 4, we see that applying momentum to both bond indices produces almost a doubling of the indices individual Sharpe ratios, from.51 and.54 to.97. Table 4: Intermediate Term Fixed Income Momentum Momentum extbills High. Yield Credit Bonds Annual Return Annual Std Dev Annual Sharpe Max Drawdown Skewness Momentum gives the same profit as from high yield bonds alone, but with less than half the volatility, one-quarter the drawdown, and one-fifth the negative skewness. Our momentum strategy even has a lower standard deviation and drawdown than the investment grade, credit bond index. Momentum without the use of Treasury bills does not give nearly as much improvement in reducing volatility or drawdown. Although investors most often apply momentum to equity investments, fixed income investors should take note of the potential here for extraordinary momentum returns of an extra 196 basis points per year over intermediate term credit bonds, and with less volatility. Figure 2: Credit Risk Momentum Credit Risk Table 3 lists the average credit rating, average bond duration, and annualized standard deviations over the past five years for the most common intermediate term fixed income indices maintained by Barclays Capital. The U.S. High Yield Bond Index has by far the highest volatility. Its standard deviation over the past five years is 14.0, compared to 5.4 for the next highest one belonging to the U.S. Intermediate Credit Bond Index. Since their average bond durations are about the same, the main cause of their volatility IFTA.ORG PAGE 47

48 One possible explanation for this impressive performance is that the credit default risk associated with high yield bonds may be less when these bonds are in a positive relative and absolute momentum situation. Their risk premium is still able to flow to investors under favorable market conditions identified through momentum, when their actual risks may not be very high. 6. Economic Stress Figure 3: REIT Momentum Real Estate Risk We next look for additional asset classes with risk factors related to high volatility. Table 5 is a list of the eleven Morningstar equity sector indices with their annualized standard deviations over the five years ending 12/31/11. Table 5: Morningstar Sectors Sector Volatility Real Estate 33.9 Basic Materials 29.7 Financial Services 29.4 Energy 27.2 Consumer Cyclicals 24.4 Industrials 24.1 Technology 22.6 Communication Services 21.0 Health Care 15.9 Utilities 14.8 Consumer Defensive 12.6 At the top of the list is real estate with a standard deviation of 33.9%. The Morningstar Real Estate sector includes both equity and mortgage REITS. We will also use both to give us some separation and differentiation for momentum selection purposes. Table 6 shows an annual rate of return of 16.78% from our momentum strategy applied to REITs. This is the highest return of our momentum modules so far. It is also significantly higher than the returns of the individual equity and mortgage REIT indices of 14.6% and 8.28%. The momentum standard deviation and drawdown are substantially lower than the indices themselves. The momentum Sharpe ratio is.77, compared to.48 and.13 for the REIT indices. As with our other modules, the Sharpe ratio and volatility of momentum without Treasury bills are less than the Sharpe ratio and volatility of the portfolio with Treasury bills. Table 6: REITs Momentum Momentum extbills Equity REIT Mortgage REIT Annual Return Annual Std Dev Annual Sharpe Max Drawdown Skewness Economic stress is another volatility-based risk factor. Gold and long-term Treasury bonds respond to that stress. Both often react positively to weakness in the economy. Economic weakness tends to produce falling nominal interest rates, which raises bond prices. Gold is usually strong when long-term Treasury yields fall. There is some differentiation and separation for momentum purposes, since gold responds more favorably to inflationary expectations, while Treasuries respond positively to deflationary pressures. Gold is not highly correlated with most other assets, which makes it particularly useful from a portfolio point of view. Gold, like Treasuries, is not only a good hedge and diversifier; it is also a safe haven during times of economic turmoil (Bauer and McDermot (2010)). A safe haven is an asset that remains uncorrelated or negatively correlated with another asset or portfolio in times of market stress or turmoil. Table 7 shows the economic stress module results. Gold s average annual standard deviation of since 1974 is almost the same as the volatility of mortgage REITs, which is the highest of all our assets. Treasury bond annual volatility of is higher than the 8.67 volatility of the High Yield Bond Index. Table 7 Economic Stress Momentum Momentum Momentum extbills Gold Treasury Bonds Annual Return Annual Std Dev Annual Sharpe Max Drawdown Skewness Momentum raises annual profits substantially to 16.65%, from a return of 9.22% with gold and 9.90% with Treasuries. The Sharpe ratio increases from.17 and.39 to Robustness Checks We can divide our 38 years of data into two equal subperiods. Table 8 shows performance from January 1974 through December 1992 and from January 1993 through December PAGE 48 IFTA.ORG

49 Table 8: Performance and Equities Equities Credit Credit REIT REIT Stress Stress Annual Return Annual Std Deviation Annual Sharpe Maximum Drawdown Skeness Table 9 Formation Periods 12 and 6 Month Equities 12 Mo Equities 6 Mo Credit 12 Mo Credit 6 Mo REIT 12 Mo REIT 6 Mo Stress 12 Mo Annual Return Annual Std Deviation Annual Sharpe Maximum Drawdown Skewness Stress 6 Mo Table 10: Returns and Volatility Volatility Return Utilization Rate Weighted Avg Return Momentum Return U.S % Equities EAFE % TBill % Credit % Credit Risk Hi Yield % TBill % Equity % REITs Mortgage % TBill % Gold % Stress Treasuries % TBill % Average Sharpe ratios remain high for all the modules during both subperiods. They are very consistent across both sub-periods for the equities, credit risk, and economic stress modules. Figure 4 Economic Stress Momentum Table 9 compares performance using twelve-month and sixmonth formation periods. Performance is very good for both periods. The stress module does better with a twelve-month formation period, while equities, credit bonds, and REITs perform about the same using either six or twelve months. 8. Momentum Return versus Weighted Average Return Table 10 shows momentum return along with average return weighted by each asset s percentage usage within a module. By comparing momentum returns to weighted average returns, we see that momentum and our timing filter create 59% higher profits. IFTA.ORG PAGE 49

50 Table 11: Results Summary Equities Credit Risk REITs Economic. Stress Momentum Modules Composite. Equal Weight **p<.01 * p<.05 for normality Annual Return Annual Std Dev Annual Sharpe Maximum Drawdown Skewness Kurtosis US ** 4.83** EAFE ** 4.21** High Yield ** 10.01** Credit Bond ** 9.53** Equity REIT ** 11.57** Mortgage REIT * 8.29** Gold ** 6.72** Treasuries ** 4.81** Equities * 4.83** Credit Risk ** REITs ** 8.33** Economic Stress ** 11.86** Momentum ** 6.56** Non-Momentum ** 7.00** Figure 5: Momentum versus Benchmarks Figure 6: Composite Momentum Module Characteristics The modules are in Treasury bills from 17.8% of the time with the economic stress module to 26.2% of the time with the REIT module. Singular match ups of Treasury bills with each asset, rather than with paired combinations of assets, would lead to higher Treasury bill utilization and lower expected profits. On the other hand, more than two assets within a momentum module could make it more difficult to isolate singular risk factors. We might find higher volatility by further segmenting a market or asset class. For example, we could split equities into individual countries and find additional volatility. However, this granularity would come at the cost of individual country risks dominating our desired risk factor of high volatility from sovereign markets. Greater segmentation might also reduce the benefits we get from diversification by using multiple rather than singular assets. Table 11 is a results summary of each asset and risk module, as well as the equally weighted composite of all four modules. As a benchmark, we also present the equal weighted portfolio of all nine assets (two per module plus Treasury bills) without the use of momentum. The composite momentum portfolio gives an annual return of 14.90% with a standard deviation of 7.99%. The Sharpe ratio of this portfolio is 1.07, versus PAGE 50 IFTA.ORG

51 Sharpe ratios of.73,.97,.77, and.59 for the individual equity, credit risk, REIT, and economic stress modules. The return of this composite momentum portfolio is 50% higher than the return of the equal weight, all asset benchmark portfolio. The momentum portfolio has double the Sharpe ratio (1.07 vs. 0.50) and less than half the drawdown ( vs ). These are impressive results using just twelve-month momentum, a simple trend following filter, and a balanced portfolio of U.S and foreign equities, credit and high yield bonds, REITs, gold and Treasury bonds. The risk profile of our dynamic asset mix bears some resemblance to those of static risk parity portfolios. Successful risk parity programs can offer basis points of additional annual return when leveraged to the same level of risk (10.6 annual standard deviation) as a conventional balanced portfolio (See Dalio (2011)). Our composite momentum portfolio, leveraged to the same level of risk as a conventional balanced portfolio, shows a remarkable 950 basis points of incremental return, while avoiding derivatives, counterparty risk, and tracking error. Table 12 shows the Sharpe ratios of each of our assets and modules, as well as the composite momentum portfolio. Table 13 shows performance versus several benchmarks during the three worst periods of equity erosion over the past 38 years of data. We see that the composite momentum portfolio, through its trend following characteristics, is itself a safe haven from market adversity. 10. Correlations Table 14 shows the correlations of the modules, as well as the correlations if Treasury bills are not included in the risk modules. We have already seen that Treasury bills are very helpful in raising return and lowering volatility. Now we see that they also are beneficial from a portfolio point of view, since they lower most correlations. According to PIMCO ( Page (2010)), risk factor correlations are lower than asset class correlations. They are also more robust with respect to regime shifts. Our lower risk module correlations support those findings. Table 12: Sharpe Ratios Gold Gold Treasury Bond Economic Stress Momentum extbill Economic Stress Momentum MSCI EAFE+ MSCI US Equities Momentum extbill Equities Momentum Mortgage REIT Equity REIT REIT Momentum extbill REIT Momentum High Yield Bond Intermediate Credit Bond Credit Risk Momentum extbill Credit Risk Momentum Composite Momentum Table 13: Largest Equity Drawdowns Date MSCI US MSCI World World 60/40 Composite Momentum 3/74-9/ /02-9/ /7-2/ World 60/40 is composed of 60% MSCI World Index and 40% US Aggregate Bond Index. Table 14: Correlation Coefficients With Treasury Bill Hurdle Rate Credit Risk REITs Stress Equities Credit Risk REITs.10 Without Treasury Bill Hurdle Rate Equities Bonds REITs Portfolio Considerations Given the inequalites in the Sharpe ratios and correlations of our four modules, we may not want to allocate capital equally to all of them. The traditional way to allocate varying amounts of capital across different asset classes is via Markowitz mean variance portfolio optimization. This uses quadratic programming algorithms to determine efficient portfolios that offer the highest potential return at any given level of expected volatility, or, conversely, the lowest volatility at any given level of expected return. There are, however, several potential pitfalls IFTA.ORG PAGE 51

52 with this approach. First, the process is very sensitive to the inputs used. These are the assets past returns, volatilities, and correlations. Second, the optimization process depends on the same simplifying assumptions as the Sharpe ratio, i.e., that returns are normally distributed or that one has quadratic utility preferences. It is because these assumptions are unrealistic and/or the inputs are unpredictable, that there have been many attempted fixes to the Markowitz approach. These include shrinkage of the estimated inputs, constraining the portfolio weights, estimating expected returns from an asset-pricing model, bootstrapping outputs to correct for bias, and imposing shifts toward lower variance portfolios with less uncertainty. Yet the math can still go wrong and create allocation mistakes because of input instability. Expected returns are the least predictable of the inputs. Yet momentum makes returns more consistent and predictable. It may be tempting then to use Markowitz optimization for momentum portfolio construction. However, we need to keep in mind the non-normality of our momentum return distributions. 5 Fortunately, our momentum modules can guide us to an attractive alternative to Markowitz mean variance optimization. Modules reduce the number of portfolio inputs from eight (two assets per module) to four. One can analyze possible portfolio allocations using nothing more than a simple spreadsheet. One can search for a high Sharpe ratio, a targeted level of volatility, or other objective functions. There is no need for matrix inversions, Lagrange multipliers, or other complicated procedures associated with Markowitz optimization. 12. Conclusions We have seen how risk factors indicating high volatility contribute to momentum profitability. We also introduced the hurdle rate/alternative asset concept to help ensure that momentum is positive on an absolute, as well as a relative, basis. Our final contribution is the introduction of risk factor oriented momentum modules that facilitate portfolio diversification and enable the construction of effective momentum portfolios for harvesting risk premium profits. Using thirty-eight years of past performance data, momentum modules show significant performance improvements in all four areas we have examined equities, credit risk, real estate, and economic stress, as represented by gold and Treasuries. The Fama-French three-factor annual alphas of these four modules are 8.9, 4.2, 8.7, and respectively. The ancillary conclusions we reach are as follows: 1. Investors should consider momentum investing based on diversified risk factors rather than solely by asset class. 2. Long side momentum works best when used with a hurdle rate and safe alternative asset, such as Treasury bills, that can neutralize market risk. This puts momentum on an absolute, as well as a relative, basis. Momentum can and should be used tactically, as well as a strategically, in order to take advantage of regime persistence. 3. Investors generally wish to avoid high volatility. There is now, in fact, a propensity toward low volatility investment portfolios. Yet momentum profits are greater when using high volatility assets. Momentum can help investors harness this volatility and convert it into extraordinary returns. 4. Focused risk modules that isolate and target specific risk factors are an efficient way to incorporate volatility into momentum-based portfolios. They also facilitate the effective use of a hurdle rate/safe alternative asset. Modules provide flexibility, making it simple and easy to implement momentum-based portfolios. Otherwise, portfolio construction could be problematic given the strong nonnormality of momentum income streams. 5. Despite an abundance of momentum research, no one is sure why it works so well. The most common explanations have to do with behavioral factors, such as anchoring and the disposition effect. An alternative explanation is that investor risk aversion is wealth dependent. Investors are more risk averse under adverse conditions and less risk averse under favorable conditions. This causes prices to go to extremes beyond their reasonable values. Volatility makes bad conditions seem worse and good conditions seem better, which leads to overextension of price trends and higher momentum profits. Diversification is the closest thing to a free lunch in the investment world. This is because investors using intelligent diversification can earn the same returns with less risk than those holding undiversified portfolios. Momentum investing, which is still in its infancy, may offer even better opportunities for higher returns with less risk, if done intelligently. Just as the benefit of diversification diminishes when applied indiscriminately, the value of long side momentum also diminishes if applied too broadly, or without trying to differentiate downside from upside market conditions. When applied effectively, momentum makes diversification more efficient by selectively utilizing assets only when their momentum is strong, and they are therefore more likely to appreciate. A focused momentum approach bears market risk only when it makes the most sense, i.e., when there is positive absolute as well as relative momentum. Momentum, serving as an alpha overlay with proven success factors, can capture the high premia from volatile assets while defensively adapting to regime change. References Asness, Clifford S., Burt Porter, and Ross Stevens, 2000, Predicting Stock Returns Using Industry Relative Firm Characteristics, working paper, AQR Capital Management. Asness, Clifford S., Tobias J. Moskowitz, and Lasse J. Pedersen, 2009, Value and Momentum Everywhere, working paper, AFA 2010 Atlanta Meetings. Bandarchuk, Pavel and Jena Hilscher, 2011, Sources of Momentum Profits: Evidence on the Irrelevance of Characteristics, working paper. Baur, Dick and T.K. McDermott, 2010, Is Gold a Safe Haven? International Evidence, Journal of Banking and Finance 34, Beracha, Eli and Hilla Skiba, 2011, Momentum in Residential Real Estate, Journal of Real Estate Finance and Economics 43, Bhojraj, Sanjeev and Bhaskaran Swaminathan, 2006, Macromomentum: Returns Predictability in International Equity Indices, Journal of Business 79, Chabot, Benjamin R., Eric Ghysels, and Ravi Jagannathan, 2009, Price Momentum in Stocks: Insights from Victorian Age Data, working paper, National Bureau of Economic Research. Chan, Kalak, Allaudeen Hameed and Wilson H.S. Tong, 2000, Profitability of Momentum Strategies in International Equity Markets, Journal of Financial and Quantitative Analysis 35, PAGE 52 IFTA.ORG

53 Chen, Hsiu Lang and Werner DeBondt, 2004, Style Momentum within the S&P 500 Index, Journal of Empirical Finance 11, Dalio, Ray, 2011, Engineering Targeted Returns and Risks, Bridgewater Associates. Fama, Eugene F. and Kenneth R. French, 2008, Dissecting Anomalies, Journal of Finance 63, Fama, Eugene F. and Kenneth R. French, 2011, Size, Value, and Momentum in International Stock Returns, working paper. Griffin, John, Xiuquing Ji, and J. Spencer Martin, 2005, Global Momentum Strategies: A Portfolio Perspective, Journal of Portfolio Management 31, Grundy, Bruce D and J Spencer Martin, 2001, Understanding the Nature of the Risks and the Sources of the Rewards to Momentum Investing, Review of Financial Studies 14, Jegadeesh, Narasimhan and Sheridan Titman, 1993, Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency, Journal of Finance 48, Jostova, Gergana, Stanislova Nikolova, Alexander Philipov, and Christof W Stahel, 2010, Momentum in Corporate Bond Returns, working paper. Lewellen, Jonathen, 2002, Momentum and Autocorrelation in Stock Returns, Review of Financial Studies 15, Menkoff, Lukas, Lucio Sarno, Maik Schmeling and Andreas Schrimpf, 2011, Currency Momentum Strategies, working paper. Miffre, Joelle and Georgios Rallis, 2007, Momentum Strategies in Commodity Futures Markets, Journal of Banking and Finance 31, Moskowitz, Tobias J. and Mark Grinblatt, 1999, Do Industries Explain Momentum? Journal of Finance 54, Page, Sebastian, 2010, The Myth of Diversification: Risk Factors vs Asset Classes, Insights, PIMCO Publications. Pirrong, Craig, 2005, Momentum in Futures Markets, working paper. Rouwenhorst, K. Geert, 1998, International Momentum Strategies, Journal of Finance 53, Rouwenhorst, K. Geet, 1999, Local Return Factors and Turnover in Emerging Stock Markets, Journal of Finance 54, Note from the Editor: The author Gary Antonacci is the winner of the NAAIM Wagner Award This paper was originally submitted for this contest. IFTA is thankful to Greg Morris and the National Association of Active Investment Managers for the permission to print this document. For further information please refer also to References Since these indices are based on capitalization, the MSCI ACWI exus receives only a modest influence from emerging markets. Our results do not change significantly if we use only the MSCI EAFE Index. 3. Skewness relates directly to the symmetrical characteristics of the return distribution. Positive skewness implies the potential for greater variance of positive returns than negative returns. Risk averse investors generally prefer positive skewness over negative skewness. 4. The four disclosed momentum products available to the public use twelve-month momentum. They are AQR Funds, Russell Investments, QuantShares, and Summerhaven Index Management. 5. The Jarque-Bera, Shapiro-Wilk, Lilliefors and Anderson-Darling tests all have p values <.0001 for each of our modules, which strongly rejects normality. Certified Financial Technician (CFTe) Program IFTA Certified Financial Technician (CFTe) consists of the CFTe I and CFTe II examinations. Successful completion of both examinations culminates in the award of the CFTe, an internationally recognised professional qualification in technical analysis. Examinations The CFTe I exam is multiple-choice, covering a wide range of technical knowledge and understanding of the principals of technical analysis; it is offered in English, French, German, Italian, Spanish and Arabic; it s available, year-round, at testing centers throughout the world, from IFTA s computer-based testing provider, Pearson VUE. The CFTe II exam incorporates a number of questions that require essay-based, analysis responses. The candidate needs to demonstrate a depth of knowledge and experience in applying various methods of technical analysis. The candidate is provided with current charts covering one specific market (often an equity) to be analysed, as though for a Fund Manager. The CFTe II is also offered in English, French, German, Italian, Spanish and Arabic, typically in April and October of each year. Curriculum The CFTe II program is designed for self-study, however, IFTA will also be happy to assist in finding qualified trainers. Local societies may offer preparatory courses to assist potential candidates. Syllabuses, Study Guides and registration are all available on the IFTA website at registration/. To Register Please visit our website at certifications/registration/ for registration details. Cost IFTA Member Colleagues CFTe I $500 US CFTe II $800* US Non-Members CFTe I $700 US CFTe II $1,000* US *Additional Fees (CFTe II only): $250 US translation fee applies to non-english exams $100 US applies for non-ifta proctored exam locations IFTA.ORG PAGE 53

54 Heikin-Ashi: A Better Technique to Trends in Noisy Markets By Dan Valcu, CFTe Abstract One thousand traders, one thousand profiles. But one single element works like glue for all market participants and pushes prices up and down: The continuous quest to identify trends and position on the correct side of them. What correct means is a different story for everyone and depends on the individual profile (time frame, capital and risk management, perception of the external stimuli). This article introduces and discusses a lesser-known Japanese trend technique, heikin-ashi, that from its beginnings was used to filter out price noise in any time frame. Like many of the Japanese charting techniques, heikin-ashi is a visual add-on to any trader s existent decision tools. Since almost everything can be quantified, the technical indicators derived from the original heiki-ashi candle formulas are a step forward towards a more complete and less risky trend technique. In the end, heikin-ashi becomes a tool that appeals to both sides of the trader s brain: Right (heikin-ashi original visual charts) and Left (analytical, new heikin-ashi technical indicators). If the sequence Identification Analysis Decision Execution is high on trader s priority list then this simple trend technique is an excellent choice to reduce its duration and increase confidence in the decisions taken. Introduction Heikin-ashi is a simple price noise filtering technique based on modified open, high, low, and close values. The formulas described in Figure 1 describe how to generate modified (heikinashi) prices and are the foundation of this technique. Figure 1: These four formulas are used to define heikin-ashi open, high, low, and close values. The most important value of the set is haopen. Any heikinashi candle with the exemption of the first one of the data series, opens always at the midpoint of the previous heikinashi body. This is the core of the noise filtering mechanism it provides. Figure 2 shows the S&P 500 index both as a traditional candlestick representation and heikin-ashi candles. Heikin-ashi makes trends immediately visible while much of the price noise is filtered out. A big advantage of this technique is the low-cost entry for traders. Even without chart reading rules, anyone can identify trends better by assuming that uptrends are defined by a sequence of white heikin-ashi candles while the downtrends are associated with filled modified candles. The assumption is correct and is incorporated into the five rules that will be discussed and exemplified later in this article. A traditional candle price chart is a bi-color canvas with a variety of candle sizes and patterns. The corresponding heikinashi chart is a better visual assessment of the price action and uses only three candle types/patterns as shown in Figure 3. Figure 3: The building blocks of any heikin-ashi chart are white, filled, and doji-like candles. White Filled Doji-like The special element is the doji-like candle that consists of a small body with both upper and lower wicks. Its main function is to alert about price reversals. The appearance of a first such candle on a chart after a trend leads to preparation for a reversal. Since life and trading are far from being binary worlds, several such short-body candles are typical for a price consolidation instead of reversal. Even in this case, risk management is required to protect capital. Heikin-Ashi Chart Reading Rules Reading a traditional Japanese candlestick chart is, in many cases, an art that depends on emotions and fluid translation rules. Currently, there are over one hundred documented Japanese candle patterns, each with a more or less subjective definition and translation. Trading with subjectivity and emotions is not what traders prefer to do. Stricter rules attached to any technique are a must and heikin-ashi helps traders going into this direction. PAGE 54 IFTA.ORG

55 Figure 2: The monthly S&P 500 index is displayed as heikin-ashi (modified) candles in the top pane and Japanese candlesticks in the lower pane. The following five heikin-ashi rules are available to read and translate modified candle charts. Rule 1 (Trend) A sequence of white bodies with no lower shadows identifies an uptrend. A sequence of filled bodies with no upper shadow identifies a downtrend. Rule 2 (Strong trend) Taller the bodies, stronger the trend. Rule 3 (Trend slowdown) The trend gets weaker with the occurrence of smaller bodies and, possibly, with the emergence of both upper and lower shadows. A body inside the previous one is a sig of a possible trend slowdown. Rule 4 (Consolidation) A series of smaller bodies with both upper and lower shadows (wicks). Rule 5 (Trend reversal) A trend reversal is likely with the emergence of a small body with long upper and lower shadows or when sudden color change occurs. We will see now how the five rules work on the chart displayed in Figure 4. The chart was delimited into zones showing trends (Rules 1 and 2). For each zone, we also indicated within parenthesis other rules that apply. It is worth noting that seldom a zone on a heikin-ashi chart is defined by a single rule. Since trends (R1 and R2) morph into consolidations (R3 and R4) or reverse (R5), any heikin-ashi chart is a blend of these five flavors. For simplicity, we look at the downtrend developed since the beginning of May (R2 with R4, R3, R5). It was a stronger downtrend and this is the reason why Rule 2 (R2) was attached to this segment. The short consolidation between the two intermediary downtrends is translated with help of Rule 3 (R3) which can also apply to the first two heikin-ashi candles in the beginning of May. Rule 4 (R4) describes a trend slowdown when the size of a body candle gets smaller. Finally, Rule 5 (R5) points to a doji-like reversal candle like the last one of the downtrend or the first one in May. Quantification of Heikin-Ashi Candles The original Japanese technique is visual and consists only of heikin-ashi candles. One additional and logical step to pursue was to make the technique more suitable to the analytical Western way of thinking, i.e., to quantify heikin-ashi candles and generate one or more technical indicators. As a result, a new and very simple indicator, hadelta, was born. It is simply the difference between haclose and haopen. Figure 5 shows the S&P-500 index in a daily time frame and displayed with hadelta (black line) in the middle pane. We should remember at this point that heikin-ashi is not a mechanical technique but a component used with a discretionary trading system. The big advantage of using hadelta is its ability to generate advance signals. Since hadelta is rough in many cases, we add its simple 3-bar average, SMA(haDelta,3) to achieve a smoother indicator and also to generate crossovers. The basic signal using this pair is the crossing of hadelta above its moving average (Long) or below it (Sell). Since hadelta is in many cases noisy, traders can choose only the moving average to add or reduce positions when the average turns positive or negative. In cases when the average hovers around zero (end of February, end of March beginning of April), the index signals a consolidation period. IFTA.ORG PAGE 55

56 Heikin-Ashi vs. Japanese Candlestick Patterns The introduction of the Japanese candlesticks was a big qualitative step towards a better understanding of the trading psychology. As a result, an extensive literature on Japanese candlestick patterns, their definitions, interpretation, and recommendations in trading became available. Unfortunately, the purity of the original knowledge has been lost in subsequent translations, leading to many erroneous interpretations. A few formations are very clear such as the bullish and bearish engulfing patterns, evening and morning stars, and have a higher probability for success. Many of the patterns are either rare appearances on charts or require a translation in the Figure 4: The German DAX index is also displayed as a heikin-ashi daily chart in the top pane. The five heikin-ashi rules (R1 through R5) help to identify at a glance trends, possible reversals, and consolidations. Figure 5: The daily heikin-ashi S&P-500 chart is enhanced with the addition of hadelta and its short moving average SMA(haDelta,3) (middle pane). PAGE 56 IFTA.ORG

57 context they are generated. Subjectivity is a severe constraint despite many attempts to quantify and include them into discretionary/mechanical trading systems. On one side we have the current Japanese candlestick theory. On the other side, heikin-ashi, a simple, clean, price filtering technique that focuses on trends and reversals. Since many candle patterns are used for reversals, the idea of a cohabitation between the two has its merits and is worth pursuing. Heikin-ashi is based on precise definitions and measurements so it is logical to try to use this technique either to confirm candlestick patterns or to remove them from trading. Figure 6 shows the S&P-500 index on a weekly chart. For our discussion we look in particular at the patterns marked as P1, P2, and P3 in Figure 6. While P2 and P3 look easier Figure 6: The heikin-ashi technique can be used both as a confirmation for traditional candle patterns or replacement for many. The trader has both options available. Figure 7: Many of the popular candle patterns can be easily translated using hadelta and its short 3-bar average. IFTA.ORG PAGE 57

58 to identify them as bullish engulfing patterns, P1 requires more flexibility and indulgence to match it with a known pattern. It has some elements of an evening star but the uptrend is missing. Heikin-ashi does not pay attention to definitions, names, and interpretations of candle pattern. Once we see a potential candle pattern, we can use hadelta and its average as translators. In the case of P1, hadelta went below its average (bearish signal) on the second day of the three-bar formation, earlier that the price rolled over. As far as P2 is concerned, hadelta offers a bullish crossover at the end of the two-bar pattern. This is an example of how heikin-ashi can work in cohabitation with Japanese candle patterns. Finally, P3 (bullish engulfing) has been accompanied by an hadelta bullish signal issued one bar earlier. Several Japanese candlestick patterns and their heikin-ashi translations are seen in Figure 7 in a daily time frame. P1 and P2 are bullish harami patterns. Their heikin-ashi translations are done using hadelta and its short average and their bullish characters coincide with hadelta positive Figure 8: As with any visual technique and indicator, heikin-ashi in its dual format, improves the trend assessment when used in multiple time frames. Figure 9: Double smoothing hadelta improves the timing and confidence especially when heikin-ashi technique is used in multiple time frames. PAGE 58 IFTA.ORG

59 crossovers at the end of the patterns. P3 looks like a bullish engulfing pattern but hadelta ignores this doubt sending a bullish signal after the first bar of the uncertain pattern. Finally, P4 is a 3-bar pattern resembling, but far from, a real morning doji star. This is not a problem for heikin-ashi that uses hadelta and its short average to confirm candles patterns. The character of 3-bar pattern turns bullish after the third bar, when hadelta crosses above its average. P3 and P4 point to another interesting feature of hadelta. When the indicator reaches historical high or low values it is time to think about price reversals. In addition to these situations, on the heikin-ashi charts we notice a body-insidebody formation (Rule 3) which warns about a possible trend slowdown and reversal. Heikin-ashi and especially its quantifiable indicator hadelta prove very helpful to translate Japanese candle patterns and improve the confidence. Heikin-Ashi in Multiple Time Frames Heikin-ashi is a versatile technique and one can experiment with it in the context of existent strategies and techniques. The use of modified candles and their quantification in multiple time frames is one way to achieve improved accuracy in terms of trend assessment and, implicitly, better entry and exit timing. Figure 8 shows the S&P-500 index in three time frames: Daily, weekly, and monthly. It is well-known that higher perspectives remove more noise from the price actions. If we add heikin-ashi indicators, the timing of reversals look better. We see that the short- and medium-term heikin-ashi charts look bullish because the current candles are white. The longterm assessment is still bearish. If we look at the more accurate hadelta charts (lower panes) we see the same trend assessment. The only difference between the visual and quantifiable charts is the timing of the reversals, with hadelta offering earlier signals. It does not happen every time but when it does, the alert is worth taking. Another way to use heikin-ashi in multiple time frames is to enhance hadelta by double smoothing it. Figure 9 has in the lower panes the pair {SMA(haDelta,3), SMA(SMA(haDelta,3),)}. The loss of accuracy for reversals is not significant but the trend assessment is better. can be offset using the quantification of heikin-ashi candles: hadelta and related moving averages. hadelta not only reduces the lag between price and heikin-ashi chart reversals but it also generates, in many cases, advance signals, worth investigating. Heikin-ashi can be used in any time frame with an improved accuracy and confidence when traders use it in multiple time frames. Purists can use only heikin-ashi charts with hadelta. Other traders may add technical indicators and other techniques to confirm trading signals. Since no combination is perfect, risk and capital management remains a must-have to ensure that failures translate into small losses. A very important aspect of using heikin-ashi is to confirm Japanese candlestick patterns or even remove them from trading. Both options are available to each trader. Heikin-ashi can be used with any financial instrument in any time frame. Best results are achieved with instruments which, historically, display clear trends and display similar trends on heikin-ashi charts in two or even three time frames. Bibliography NISON, S. Beyond candlesticks: New Japanses charting techniques revealed. Wiley Finance, 1994 VALCU, D. Heikin-Ashi: How to Trade Without Japanese Candlestick Patterns. Educofin, VALCU, D. Using the Heikin-Ashi Technique. Technical Analysis of Stocks & Commodities, February Software and Data Software used for this article was AmiBroker from AmiBroker.com, Lodz, Poland. End-of-day data provided by Worden Brothers, Inc. (TC2007 software) Worden Brothers, Inc. Five Oaks Office Park, 4905 Pine Cone Drive, Durham, NC 27707, USA. About the Author Dan Valcu, CFTe is the author of the first book on this subject, Heikin-Ashi: How to Trade Without Candlestick Patterns published in September 2011 ( He is General Manager of Educofin Ltd and serves on the Board of the International Federation of Technical Analysis (IFTA). Conclusions Heikin-ashi is a charting technique designed to filter out price noise and a low-entry barrier for traders to assess trends, consolidations, and reversals. Although heikin-ashi charts look very attractive at first sight, traders should refrain from using this technique as a mechanical trading tool. Its best use and results derive from using it as a component of discretionary trading systems. Heiki-ashi s foundation is built on modified open, high, low, and close values, three candle types and five rules to assess trends, reversals, and consolidations. Once these basic concepts are well understood, the advantages of using heikin-ashi become very clear. The visual aspect has a drawback due to the modified candles construction: A very short delay, usually one bar, as far as reversals on a heikin-ashi charts concern. The impact of this lag IFTA.ORG PAGE 59

60 Mastering Market Timing, Using the Works of L.M. Lowry and R.D. Wyckoff to Identify Key Market Turning Points By Richard A. Dickson and Tracy L. Knudsen Reviewed by Regina Meani, CFTe During my time as editor of the Journal I had the pleasure of including articles by Professor Hank Pruden on the Wyckoff Method and an article by Paul Desmond, the current president of the Lowry Research Corporation. So it seemed a natural follow on that we include a review of a book which uses the works of both Wyckoff and Lowry; coming to my attention as the runner-up in The Technical Analyst: Best Book of the Year 2012 Awards in the UK. The authors work is exemplary in taking us through the historical record of the classic major tops and bottoms of the 20 th Century and into the 21 st Century, using the combined methodology of Wyckoff s laws of Supply and Demand, Cause and Effect and Effort and Result with the Lowry s indicators for the determination of supply and demand; the Buying Power and Selling Pressure. Through the Wyckoff focus on price and volume patterns and the Lowry interpretations for market breadth, we are guided through the exploration of the forces of supply and demand, with a primary reliance on price and volume. We are given an explanation of how these forces effect the development and stages of bull and bear trends and the formation of the reversal of these trends. While each experience is unique the authors explanations of the way the market works in periods of distribution and accumulation provides us with a means of identifying when the supply of the stock or entity is moving from weak to strong hands at bottoms, and from strong to weak hands at tops. Some useful indicators are brought into the mix including the Advance / Decline Line with Lowry s tweak on this and the use of the 30-week moving average. A remarkable pointer to the Authors enthusiasm and confidence for their subject is that they present a final chapter: Where are we now? The authors macro approach should not put off the short term trader but rather they should realise that they need to be aware of the lessons learned from the examination of major market tops and bottoms that is meticulously provided, and is necessary for both the trader and investor alike. I am sure that it is part of the mantra of most traders that the short-term outlook has its beginnings in the longer term and can be a major influence over the entity s movements both in the near and longer term. This in-depth investigation is a practical start for beginners and a useful reminder for the more experienced. In the words of the authors : Although many years have passed since Wyckoff and Lowry developed their tools Despite the changing world human emotions remain the same throughout the various stages of bull and bear markets. It is the consistency of human nature that causes major tops and bottoms to show little change in their basic characteristics 1 1. R A Dickson and T L Knudsen, Mastering Market Timing, Using the works of L.M. Lowry and R.D Wyckoff to Identify Key Market Turning Points, FT Press, New Jersey, 2012, p.194 PAGE 60 IFTA.ORG

61 Author Profiles Gary Antonacci Mr. Antoncacci has over 30 years experience as an investment professional focusing on under exploited investment opportunities. He received his MBA degree from the Harvard Business School and managed a stock options hedge fund during the 1970s. In the 1980s, Mr. Antonacci became a highly successful commodity pool operator. During that time, he pioneered the use of modern portfolio theory principles and optimization practices in order to allocate private and institutional investor funds to some of the world s best traders. During the past twenty years, Mr. Antonacci has concentrated on researching, developing, and applying asset allocation strategies that have their basis in academic research, such as price momentum. He is author of a number of investment articles and books on portfolio management, including the forthcoming book Optimal Momentum Investing. Mr. Antonacci serves as a consultant to private and institutional investors regarding asset allocation, portfolio optimization, and advanced momentum strategies. He is the 2011 second place and 2012 first place winner of the NAAIM Wagner Awards for Advancements in Active Investment Management. Stephan Belser, MSc, CFTe, MFTA Stephan is Head of Portfolio Management at Vermögen-Management BC GmbH, a private banking company in Germany. There, he works with high net worth clients, in all areas of asset and portfolio management. He is responsible for fundamental, technical and sentiment research for global markets and is author of their monthly market commentary. He is Chairman of the Weekly Asset Allocation meeting and fund manager for individual and institutional clients. Stephan is a lecturer for private banking and portfolio management at the DHBW Villingen-Schwenningen. He holds an MSc in Banking and Financial Management from the University of Liechtenstein and he received the Banking Award Liechtenstein for his master thesis in He holds the CFTe and MFTA qualifications in technical analysis. Stephan is a member of the Vereinigung Technischer Analysten Deutschlands (VTAD). Mohamed El Saiid, CFTe, MFTA Mohamed is currently an Executive Director and Head of the Technical Analysis department for HC Brokerage (HCB), Cairo, Egypt. He started his career working for Momentum Wavers, Ltd., a Middle East Technical Analysis firm ( ). He joined HCB as an associate/lead technical analyst ( ). Later he joined Unifund, a Geneva-based global private fund ( ) as a Chief Technical Strategist/Co-Fund Manager to the Middle East investments. Mohamed holds an MBA in Finance and is currently a Board Member, Technical Analysis instructor and Head of the R&D committee in the Egyptian Society for Technical Analysts (ESTA). Kay Ying Timothy Fong, CFTe, MFTA Timothy is Director of Analytics at Canada s federal banking regulator the Office of Superintendent of Financial Institutions Canada. He has over 10 years of experience in financial modeling and quantitative analysis for the banking industry. He has been an active member of various groups for trading book policy and implementation at the Basel Committee of Banking Supervision. Outside of the office, Tim enjoys designing and teaching courses that develop future leaders in financial trading and risk management. In 2008, he received the prestigious Excellence in Teaching Award from the School of Continuing Studies at the University of Toronto. He holds a Masters in Mathematical Finance from the University of Toronto and a number of other professional designations including FRM, PRM, DMS, CAIA and CIM. Bryan Lim Bryan is currently a Masters student at the University of Cambridge. He has a keen interest in technical analysis and the application of concepts from the physical sciences to the modelling of financial data. He is currently working on a research project involving the use of Bayesian particle filtering for the prediction of financial time series. IFTA.ORG PAGE 61

62 Shawn Lim, CFTe, MSTA Shawn is currently a student reading Economics at University College London. He has a keen interest in the study of financial markets and holds a number of relevant professional qualifications. He is a Certified Financial Technician and a Member of the Society of Technical Analysts (UK). In addition, he is a certified Professional Risk Manager (PRM) and he holds an Advanced Diploma in Data Systems and Analysis from the University of Oxford. Regina Meani, CFTe Regina covered world markets, as technical analyst and Associate Director for Deutsche Bank, before freelancing. She is an author and has presented internationally and locally and lectured for the Financial Services Institute of Australasia (FINSIA), Sydney University and the Australian Stock Exchange. She is VP of the Australian Professional Technical Analysts (APTA) and immediate past Journal Director for IFTA. Regina carries the CFTe designation. She has regular columns in the financial press and appears in other media forums. Her freelance work includes market analysis, webinars and larger seminars, advising and training investors and traders in Market Psychology, CFD and share trading and technical analysis. Regina is also a past director of the Australian Technical Analysts Association (ATAA) and has belonged to the Society of Technical Analysts, UK (STA) for over thirty years. Dan Valcu, CFTe Dan is an independent trader and founder of the first company specialized in technical analysis education and training in Romania. He also authored four books about technical analysis and strategies. He is and has been a contributor to various technical analysis magazines (TASC, Traders Magazine) and is credited with bringing Heikin-ashi charting to the western world in His latest book Heikin-Ashi: How to Trade without Japanese Candlestick Patterns, a world premiere, is written for everybody who needs simple techniques to highlight the trend, reduce the noise, and alert about possible reversals. In addition, this book is a guide for easily translating candlestick patterns. Before joining the technical analysis field, Dan worked all over the world as an IT Consultant in banking & insurance. An active promoter of technical analysis, Dan serves on the Board of the International Federation of Technical Analysis (IFTA) as VP for Europe and Director of Membership, holds the professional designation of a Certified Financial Technician (CFTe), and is an Associate Member of the Society of Technical Analysts (UK). Dan holds a Master s degree in Computer Sciences from the Polytechnic Institute in Bucharest. He is also the President and one of the founders of the Romanian Association for Technical Analysis (AATROM). IFTA Board of Directors Ed Rowson, CFTe, MFTA Ed is a Partner and the Trader at MENA Capital, as well as being the Risk Manager. Ed joined MENA Capital in April He has ten years institutional and hedge fund experience focusing on implementing risk managed technical trading strategies. MENA Capital is a London-based investment management and advisory company with focus in the stock markets of the Middle East and North Africa. While overseeing the risk management and trading duties of the funds, Ed investigated and tested the benefits of implementing a risk adjusted stop-loss strategy over the more widely used percentage drawdown stop-loss strategy while technical trading. His MFTA paper investigates whether there is empirical evidence to support this as well as exploring methods to optimise the return on capital and return on Risk that is achievable. President Adam Sorab, CFTe, FSTA (STA) Vice-President the Americas Timothy Bradley (TSAASF) Vice-President Asia Taichi Otaki (NTAA) Vice-President Middle East, Africa Mohamed Ashraf Mohfauz, CFTe, CETA (ESTA) Treasurer Michael Steele (AAPTA) Secretary Saleh Nasser, CMT (ESTA) Education Director (Academic & Syllabus), Journal Director Rolf Wetzer, Ph.D. (SAMT) Accreditation Director Roberto Vargas, CFTe (TSAASF) Examination Director Gregor Bauer, Ph.D. (VTAD) Membership Director, Vice- President Europe Dan Valcu, CFTe (AATROM) Conference Director Robert Grigg (ATAA) Directors at Large David Furcajg, CFTe, MFTA (AFATE) Akira Homma, CFA, CIIA, CFTe, FRM, CMA, CMT (NTAA) Regina Meani, CFTe (STA, ATAA) William Chin, MBA (CSTA) Staff Executive Director Beth W. Palys, FASAE, CAE Vice President, Meetings Grace L. Jan, CAE, CMP Senior Member Services Manager Linda Bernetich Senior Graphic Designer Jon Benjamin Production Manager Penny Willocks Accounting Dawn Rosenfeld PAGE 62 IFTA.ORG

63 Master of Financial Technical Analysis (MFTA) Program IFTA s Master of Financial Technical Analysis (MFTA) represents the highest professional achievement in the technical analysis community, worldwide. Achieving this level of certification requires you to submit an original body of research in the discipline of international technical analysis, which should be of practical application. The MFTA is open to individuals who have attained the Certified Financial Technician (CFTe) designation or its equivalent, e.g. the Certified ESTA Technical Analyst Program (CETA) from the Egyptian Society of Technical Analysts (ESTA) For those IFTA colleagues who do not possess the formal qualifications outlined above, but who have other certifications and/or many years experience working as a technical analyst, the Accreditation Committee has developed an alternate path by which candidates, with substantial academic or practical work in technical analysis, can bypass the requirements for the CFTe and prequalify for the MFTA. The alternate path is open to individuals who have a certification, such as: Certified Market Technician (CMT) or a Society of Technical Analysts (STA) Diploma, plus three years experience as a technical analyst; or a financial certification such as Certified Financial Analyst (CFA), Certified Public Accountant (CPA), or Masters of Business Administration (MBA), plus five years experience as a technical analyst; or a minimum of eight years experience as a technical analyst. A Candidate who meets the foregoing criteria may apply for the alternate path. If approved, they can register for the MFTA and submit their research abstract. On approval, the candidate will be invited to submit a paper. Examinations In order to complete the MFTA and receive your Diploma, you must write a research paper of no less than three thousand, and no more than five thousand, words. Charts, Figures and Tables may be presented in addition. Your paper must meet the following criteria: It must be original It must develop a reasoned and logical argument and lead to a sound conclusion, supported by the tests, studies and analysis contained in the paper The subject matter should be of practical application It should add to the body of knowledge in the discipline of international technical analysis Timelines & Schedules There are two MFTA sessions per year, with the following deadlines: Session 1 Alternative Path application deadline February 28 Application, outline and fees deadline May 2 Paper submission deadline October 15 Session 2 Alternative Path application deadline July 31 Application, outline and fees deadline October 2 Paper submission deadline March 15 (of the following year) To Register Please visit our website at certifications/master-of-financial-technicalanalysis-mfta-program/ for further details and to register. Cost $900 US (IFTA Member Colleagues); $1,100 US (Non-Members)

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