Diversifying Risks with Hedge Funds

Transcription

1 presented to the Graduate School of Business of the in partial fulfilment of the requirements for the degree of Master of Business Administration by FLORIAN BÖHLANDT Supervisor: Prof. Niel Krige Date: 31 July

2 Assignment for Portfolio Management STUDENT NUMBER : SURNAME: BOEHLANDT INITIALS : FMB TELEPHONE NUMBER: SUBJECT: Portfolio Management NUMBER OF PAGES (INCLUDING THIS PAGE) 21 LECTURER: Prof. Niel Kriege COURSE: MBA FULL-TIME 2006 DUE DATE : 23/10/2006 CERTIFICATION I certify the content of the assignment to be my own and original work and that all sources have been accurately reported and acknowledged, and that this document has not previously been submitted in its entirety or in part at any educational establishment. Florian Böhlandt VIR KANTOORGEBRUIK / FOR OFFICE USE DATUM ONTVANG: DATE RECEIVED : 2

3 Table of Contents 1 Hedge Funds An introduction Investment Styles Global Macro Long-Short Equity Managed Futures Event Driven Distressed Securities Merger Arbitrage Equity Market Neutral Convertible Bond Arbitrage Fixed Income Arbitrage Diversification of Market Risks Interest Rate Risks Pricing Risks The Theory of Portfolio Diversification Portfolio Diversification with Hedge Funds Diversifying Equity Portfolios Diversifying Bond Portfolios Exchange rate related Risks Measuring the Risks of Hedge Funds Non-normal probability distribution Disrupting effects of time series analysis Changing market correlations Performance history and statistical inference Concluding Remarks List of Sources... 23

4 1 Hedge Funds An introduction Hedge Funds are generally regarded as high risk investment opportunities that can yield exceptional returns on investment. Hedge Funds offer absolute positive returns even in bearish markets. The name Hedge Funds, however, is somewhat of a misnomer. In fact, rather than hedging the investor s risk exposure, Hedge Funds use derivatives and leverage to enhance their performance. Historically, alternative investment funds (Hedge Funds, Private Equity, and Venture Capital) displayed a low or negative correlation with traditional investment opportunities. This report tries to show that Hedge Funds can be used, in accordance with Sharpe s Capital Asset Pricing Model, to limit the overall risk exposure of a combined portfolio whilst increasing the return on investment (Schneeweis, 1998). Hedge Funds differ substantially from non-alternative investments. Funds managers use derivatives to hedge their position and generate additional returns, borrow money to leverage the performance, and usually avoid disclosing information about asset allocation and performance (most Hedge Funds are located in countries such as the Cayman islands with favourable legislation concerning auditing and reporting standards of funds). The unique structure of alternative investment funds has led to the perception of many private and corporate investors that hedge and private equity funds are highrisk profile investments, utterly unsuited to be combined with conservative portfolios. The demise of the Long-term Capital Management Fund (LTCM) in 1998 has made investors suspicious about Hedge Funds and their alleged superior performance. A number of professional investment banks such as Union de la Banque de Suisse (UBS) and Dresdner Kleinwort Wasserstein lost millions of their investment in LTCM. Private investors have become more reluctant to invest directly into Hedge Funds due to feeble reporting standards and a generally low understanding about the inner workings of alternative investments. In addition, private and corporate investors may not be allowed to allocate money to Hedge Funds due to local legislation (a number of European countries require extensive reporting standards to allow pension funds and insurance companies to invest into these funds). High initial investments and lock-down periods pose an additional hurdle for private investors. 4

5 Whilst little doubt exists about the relatively high volatility of Hedge Funds returns, one should not assume that alternative investments offer unfavourable risk-return profiles. In fact, the unique structure of hedge funds allows them to achieve better risk adjusted returns as traditional investment funds (as measured by Sharpe s ratio). Because of manager s high degree of flexibility in allocating the fund s money, Hedge Funds were able to accomplish exceptional returns in downward markets. Traditional funds measure their performance against a benchmark (usually equity or bond indices such as the Dow Jones Industrial Average or Eurostoxx 50). Their within lies the problem with traditional investment funds. In downward markets, managers are able to outperform their benchmark by realizing a negative fund performance. Hedge Funds aim at producing absolute positive performance, regardless of the current market situation. Hedge Funds managers are usually rewarded with a variable performance bonus depending on the absolute positive performance of the managed fund compared to the previous year s performance. High-water marks guarantee that fund managers compensate for losses realized in a given year before receiving the performance-related component of their fees. It has been argued that Hedge and Venture Capital funds increase market efficiency and improve the functioning of international bond and equity markets. As this introduction shows, Hedge and Private Equity Funds differ significantly from traditional investments (hence the name alternative investments). Statistical evidence suggests that alternative investments can offset the risks associated with investing into traditional equity and bond portfolios, whilst increasing the overall performance. We will try to demonstrate this relationship empirically during the course of this report. In order to improve the understanding of Hedge Funds, the subsequent sections explain 9 unique investment styles (strategies) managers employ to generate exceptional returns. 2 Investment Styles One can distinguish between 9 different styles of hedge funds. Although the investment strategies are not exclusive, most managers choose to follow only one or two styles. Generally speaking, Hedge Funds follow one of two basic strategies: Directional or Non- Directional. Directional funds (Global Macro, Long-Short Equity, and Managed Futures) are dependant on the development of the overall equity and bond markets. Nondirectional funds (Event Driven, Distressed Securities, Merger Arbitrage, Equity Market 5

6 Neutral, Convertible and Fixed Income Arbitrage) generally follow a market neutral approach (Lavinio, 2000). The fund s investment focus on equity, fixed interest securities, derivatives, commodities or currencies allow for a further differentiation. 2.1 Global Macro Along with Long-Short Equity strategies, Global Macro strategies were amongst the first Hedge Funds styles that emerged. Global Macro funds invest in all kinds of financial instruments. In addition to long investments into equities, Global Macro funds use derivatives such as options and futures on currencies, interest rates and equity indices to limit their risk exposure. In addition, these funds invest into distressed securities, try to realize profit from merger arbitrage, or allocate money into Private Equity Funds. Hence, Global Macro funds represent the most holistic form of Hedge Funds. Global Macro managers try to predict macroeconomic developments and to assess their influences on international equity and bond markets ( top-down strategy). Thanks to their substantial size, Global Macro funds can utilize market inefficiencies quicker than other market participants. In many cases, Global Macro funds reach a critical size (such as George Soros Quantum Fund) to allow them to directly influence and manipulate different markets. Emerging Market funds are a special category of Global Macro funds. Their investment focus lies with emerging and developing countries. Managers of Emerging Market funds try to identify and invest into equities that have been historically undervalued. When macroeconomic developments in emerging markets (e.g. a more favourable legislative and economic policy) cause these investments to appreciate, the strategy was successful. Currency funds, on the other hand, invest exclusively into foreign exchange (interest options, currency futures, carry trades and currency swaps). 2.2 Long-Short Equity Long-Short Equity managers try to identify and buy undervalued shares whilst shortselling overvalued shares within the same industry ( pair trade ). Managers utilize a historical performance analysis to identify shares that have outperformed their benchmark index in the past ( bottom-up strategy). When managers choose to distribute their funds equally amongst long- and short strategies, the Hedge Fund can be seen as factor neutral. In theory, managers can diversify away the entire market risk. In reality, however, most Long-Short Equity funds are Equity-Non-Hedge Funds that 6

7 employ a hedge ratio of below 100%. Conversely, the smaller proportion of managers follows a short or short-only strategy. Equity-Hedge managers invest the larger part of their funds in hedging derivatives such as futures and options ( hedge overlay ). In downward markets, gains form short-positions overcompensate for the funds exposure to long equities. Hence, Equity Hedge funds are able to achieve a smoother return on investment compared to traditional investments. Dedicated Short Bias strategies focus exclusively on equity options, short-selling and forward contracts. During the bullish equity markets of the 1990 s, however, this form of short-only investment has almost disappeared. Similar to Global Macro funds, Long-Short strategies can be further subdivided into their geographic focus (e.g. emerging markets). Successful managers of Long-Short Equity Funds usually have exceptional experience and skills in the market they operate in. Long-Short Equity Funds are, on average, highly correlated with international equity markets. 2.3 Managed Futures Managed Futures developed independently from Hedge Funds and are thus not a subcategory of Hedge Funds. Commodity Trading Advisors (CTAs) were originally developed as an alternative of investing directly into forward markets. Professionals actively manage CTAs for their clients by investing into Foreign Exchange forwards and other financial forward contracts. Similar to Hedge Funds, CTA managers use derivatives and leverage to enhance the fund s performance. CTAs invest exclusively into listed and publicly traded forward contracts. With analytical methods and electronic trading models, CTA managers try to predict movements on futures markets and seek exceptional return on investments by employing a mix of long and short positions. Futures are standardized and publicly traded. Future markets are generally more liquid than other forward markets. Managers can clear their positions quickly and leverage their investments substantially (traders on future markets are required to deposit only an initial margin as a percentage of their overall investment). Since managers of CTAs trade with futures, they are subject to the requirements and regulations of the exchange supervisory authorities. Hence, CTAs are more transparent than other forms of alternative investment funds. 7

8 2.4 Event Driven Managers of Event Driven Funds either try to react quickly to changing market circumstances or occurrences, or induce changes in the markets themselves to be able to profit from rapid market movements. Managers try to identify and predict special market occurrences that will alter the performance of specific equities or bonds. One can differ between three different kinds of disruptive events: Insolvency of an existing company, mergers or acquisitions, and restructuring of a company. Whether an Event Driven strategy proves to be successful or not depends mainly on the speed and efficiency with which managers can react to these events. In addition, managers must be able to accurately predict events (or assess their probability) to estimate future movements in the price of an equity stock or bond. Under- or overvalued securities are another investment focus of Event Driven funds managers. 2.5 Distressed Securities This special form of Event driven funds tries to identify companies that are in financial or operational distress. The fund invests into undervalued securities and speculates on management s ability to restructure the distressed company. Besides directly investing into equities or bonds, a number of funds issue credits to troubled companies or take over liabilities and credits. Due to the exceptionally high default risks, Distressed Securities funds managers hedge their positions with short-positions and equity options and do not leverage their exposure with borrowed capital. The purchase and sale of orphan securities and junk bonds is another dimension of distressed securities trading. Vulture investors utilize the current situation of the company to purchase a controlling stake in the company at an undervalued price. Distressed Securities managers may opt to actively assist management in the restructuring process and thus increase the possibility for recovery. 2.6 Merger Arbitrage Companies that are faced with merger, take-over or restructuring decisions are the target for Merger Arbitrage funds. It depends on the skills and experience in the industry of the fund manager to accurately predict the outcome of these transactions. Other than financial and operational influences, decisions of local antitrust authorities determine the success or failure of merger and take-over transactions. In order to limit the funds risk exposure, managers generally speculate exclusively on publicly announced transactions. In the case of a (hostile) take-over attempt, fund managers buy stocks of 8

9 the target company whilst short-selling stocks of the bidding company. Fund managers use stock borrowing to leverage their performance to react more effectively to changing circumstances and hedge their position with derivatives. The success of the investment depends on the standstill return (the expected return on investment in case of a successful transaction) and the probability of the transaction itself. 2.7 Equity Market Neutral Market Neutral funds try to realize arbitrage gains with bonds, convertible bonds, rights issues and equity stocks. Long Short Equity funds achieve arbitrage by simultaneously purchasing and short-selling similar stocks of companies in the same industry, whilst hedging the inherent systematic risk. When arbitrage profits exceed the costs of hedging, the transaction was beneficial. Generally speaking, Market Neutral funds try to diversify away any specific risk whilst generating the highest possible return on investment. Hence, Market Neutral strategies use the highest degree of leverage compared to other Hedge Funds investment styles. Traditionally, Long Short Equity funds belonged to the Market Neutral funds (today most Long Short Equity fund managers do not manage factor neutral portfolios). 2.8 Convertible Bond Arbitrage Managers of Convertible Bond Arbitrage funds identify and purchase undervalued convertible bonds whilst simultaneously short-selling the underlying stock, thus realizing arbitrage gains. Arbitrage gains can only be realized, when pricing of convertible bonds display a different degree of volatility compared to the underlying stock (e.g. when increases in stock prices lead to only marginal increases in convertible bond prices). Gains from the convertible bonds should overcompensate losses from the short-position in the event of rising stock prices and vice versa in the even to falling prices. However, hedging through short-selling may not be sufficient to compensate for unexpected expansions of the premium on convertible bonds. Leverage can be used to enhance the performance of this strategy. 2.9 Fixed Income Arbitrage Arbitrage funds that speculate on fixed income securities try to play the pricing differences between fixed interest securities and their derivatives. One strategy involves buying under-rated securities and hedging the position with short-selling and derivatives against changes in prime rates, increases in spreads, or market risks. 9

10 Substantial leverage is necessary to generate sufficient return on investment. Yield Curve Arbitrage generates gains from disparities in the yield curve by purchasing securities with different maturities. The portfolio is automatically hedged against horizontal movements of the yield curve. Treasury/Eurobond (TED) strategies play differences in interest rates between government bonds and Eurodollars. Mortgage Backed Securities strategy funds purchase mortgages with the option of early retirement and speculate on increases in interest rates (whilst hedging themselves against falling interest rates). Credit Spreads allow funds to purchase and short-sell securities with similar spreads above the risk-free rate and realize arbitrage gains with over-/underrated securities. Capital structure arbitrage speculates on the difference between junior and senior bonds of the same issuer. 3 Diversification of Market Risks Bonds and equities have an exposure to unfavourable or unexpected pricing and interest rate movements. In the subsequent section, we will first identify the different risks bonds and equities can be exposed to and try to analyze how modern portfolio theory can be a basis for diversifying away the inherent risks of investments into single securities. 3.1 Interest Rate Risks Fixed Interest Securities are subject to unfavourable changes in market interest rates. Increasing interest rates can make a bond appear less attractive, falling interest rates can make a loan relatively more expensive. Interest rate risks can be defined as the risks resulting from realizing a lower expected interest gain in a given period due to changes in the market rate. The effects of changing market rates can be twofold. Increases in interest rates lower the par value of bonds. Conversely, falling interest rates increase the value of the bond. Changes in the interest rate premiums over the risk-free rate can limit interest gains and nullify earnings from fixed income arbitrage oriented strategies. Variable Interest Securities may respond differently to interest rate changes (inelasticity of interest rates) and pose an additional risk to the expected return of a portfolio. In close relation to interest rate changes are risks resulting from unfavourable movements of exchange rates (as local interest rates are a determinant of the cross-rates between two currencies). Currency related risks derive from the possibility of exchange 10

11 rate related losses when changing money from one currency into another. Future gains from fixed interest securities and equities can be offset by the effects of exchange rate movements. Exchange rate related risks depend on the exposure of an investor to different currencies. Investors may choose to construct portfolios in which all future currency movements cancel each other out. Swap risks result from future contracts that do not match each other in terms of maturity. Whilst positions in different currencies may cancel each other out in terms of value, investors have to account for roll-over risks. Roll-over risks can be associated with risks deriving from the necessity to roll-over shorter term contracts and the possibility of changing terms and rates. 3.2 Pricing Risks Pricing risks can be described as risks that result from unfavourable or unexpected movements in the pricing of bonds or equities. Investors need to differentiate systematic risks and unsystematic risks. Systematic risks (market risks), in the context of marketdependent pricing risks, can be seen as differences in actual and expected prices of bonds, equities, or a portfolio that derive from deviations in the overall markets. All securities are influenced by systematic risks. Diversified portfolios do not eliminate systematic risks. Unsystematic risks are risks that result from specific circumstances that influence the pricing of a single security. These specific risks can be diversified away in efficient portfolios. Changing interest rates influence the pricing of securities, and hence, the pricing risks. Higher interest rates make Fixed Interest Securities relatively more attractive compared to equity stocks, and thus exert pressure on equity markets. Currency related risks can leverage the pricing risks of securities. 3.3 The Theory of Portfolio Diversification Markowitz developed the basis principles of the modern portfolio theory. According to Markowitz, risks can be fully diversified by combining weakly or negatively correlated securities in a portfolio. Modern portfolio theory measures the risk of a portfolio with the variation (standard deviation) of its overall returns. With the exception of strictly positively correlated securities, the risk of a portfolio of securities will be lower compared to the risk of a single investment. Markowitz postulated that, for any risk level, we are only interested in that portfolio with the highest expected return. Alternatively, managers should only be interested in portfolios with the lowest 11

12 variability in returns for any targeted expected return (hypothesis of efficient market frontier). All minimum-variance portfolios can be plotted on a graph to create the efficient market line. The efficient market line is the representation of all possible portfolio combinations with superior risk-return profiles compared to all other potential portfolios (Markowitz assumed that correlations between securities remain stable in the short and medium term). According to the personal risk preference, investors then choose a portfolio on the efficient market line (assuming the efficient market hypothesis is true). The expected return of any portfolio can be described by the capital market line (Bodie, 2005): ( Pf ) E r r rf rcml = rrf + σ r * CML σ rpf Equation 3.1 With r rf = risk-free rate; σ = Standard deviation; r Pf = portfolio return; E = Expected Value Sharpe expanded on Markeowitz s original theories and developed the Capital Asset Pricing Model (CAPM). Contrary to Markowitz, Sharpe does not compare correlations between different assets, but rather determines the correlation of a single security to the market portfolio. Beta determines the relationship between a single asset and the overall market. Market Beta is used to describe the additional risk an individual security adds to a diversified portfolio. Beta describes the relationship of stocks and bonds with the overall market. A Beta of greater than one signifies a higher degree of sensitivity to changes in the market place. A Beta of lower than one indicates a lower risk of the respective security (the bond or stock responds less to changes in overall markets). It has been argued that Beta is not an ideal measure of risk because of changing market correlations and negatively/positively skewed return distributions (an argument that holds particularly true with alternative investments). Beta represents the proportion of a stock s or bond s performance standard deviation that can not be diversified away. A regression analysis of individual stock returns versus the returns of a stock index returns the security market line, which can be described with the following formula: E( r) = αi + βirmt + ε Equation 3.2 With α = alpha coefficient; β = beta coefficient; ε = error term 12

13 According to the CAPM, managers that achieve return on investments that exceed the return of the stock index by 100% can be expected to have constructed a portfolio with a Beta of two. A Beta of less than two signifies managerial skill. Portfolios with higher Beta in bullish markets and a lower Beta in falling markets can be seen as attractive investment opportunities. The error term ε stands for a stock s unsystematic risk and can be diversified away in efficient portfolios. Beta factors hold true in the event of high correlations with the market index and the long term stability of these correlations. For the purpose of assessing the risks of a combined portfolio of traditional and nontraditional investments, we can us the variance formula for two asset portfolios as described below: σ Pf = wtσ T + waσ A + 2 wt wacov( rt ; ra ) Equation 3.3 With w T = Weighting traditional investment; w A = Weighting alternative investment; Cov = Covariance of the portfolio returns We expect traditional portfolios to be lowly correlated with alternative investment portfolios. Hence, managers should be able to decrease the variability of an overall portfolio by combining hedge funds with traditional equity/bond portfolios. Whether variability is an appropriate risk measure for alternative investments will be briefly discussed in a later section of the report. 4 Portfolio Diversification with Hedge Funds In the following sections we take a look at how Hedge Funds investments influence the performance and risks of existing traditional equity and bond portfolios. Different style indices for hedge funds were combined with equity/bond portfolios to analyze the benefits of diversified portfolios. 4.1 Diversifying Equity Portfolios Two style indices were used to simulate the performance of Hedge Funds portfolios. We chose the S&P 500 index as an internationally diversified equity portfolio representing the traditional investment. Market neutral strategies (Event Driven) as well as market dependent strategies (Global Macro) were included in the analysis to assess the 13

14 diversification potential of both strategic sub-categories. For the purpose of the report, we focussed on static portfolios (weightings do not change between traditional and nontraditional investments, regardless of the individual performance or changes in volatility). It must be noted that style indices may not necessarily be representative of individual Hedge Funds. However, with fund certificates and the increasing number of fund of funds private and corporate investors can limit their risks by investing into multiple hedge funds at the same time. The expected diversification benefits of certificates and fund of funds should be somewhat lower compared to investments in Single funds (as fund of funds include the performance of many different hedge funds). The following analysis refers to an investment into the S&P 500 index between June 1995 and June 2005 (the data was received from the Reuters server on October 16 th 2006). During the same period, we assumed an investment into three different style indices. It is the purpose of the analysis to assess how hedge funds reduce the variability/volatility of portfolio returns during the ten year period. It must be noted that the two Hedge Funds indices are non-investable indices. The performance of investable indices varies slightly from the here displayed performance. The findings in Table 1 and 2 can be transferred to a limited extent to other style indices as well (taking into account differences in degree of leverage, the use of derivatives and short-selling). In tables 1 and 2, we can observe the results for a combined portfolio of investments into the S&P 500 and the Global Macro and Event Driven style index (Weightings from 0% to 50%). In addition, the tables show the minimum variance portfolio (the portfolio for which the variability of returns would have been the lowest over a ten year period) for each strategy. Due to the different development of the S&P 500 and the two Hedge Funds indices, the weighting changes over time. In reality, it can make sense to shift weightings to keep a portfolio balanced (dynamic portfolios). 14

15 Table 4.1: Global Macro Strategy (Data: Reuters, 2006) % Global Macro Return p.a. Stdev Semi-variance Sharpe Ratio Max. Drawdown 0% 9,00% 15,49% 9,04% 0,324-46,28% 5% 9,26% 14,64% 8,61% 0,368-42,61% 10% 9,71% 13,87% 8,23% 0,414-38,86% 15% 10,06% 13,16% 7,92% 0,462-35,03% 20% 10,40% 12,53% 7,65% 0,513-31,13% 25% 10,74% 11,97% 7,45% 0,565-27,15% 30% 11,07% 11,47% 7,31% 0,619-23,08% 35% 11,40% 11,05% 7,22% 0,672-18,93% 40% 11,73% 10,69% 7,14% 0,725-14,69% 45% 12,05% 10,41% 7,10% 0,776-11,14% 50% 12,36% 10,19% 7,09% 0,823-12,05% MinVar 13,53% 9,99% 7,35% 0,956-15,79% Table 4.2: Event Driven Strategy (Data: Reuters, 2006) % Event Driven Return p.a. Stdev Semi-variance Sharpe Ratio Max. Drawdown 0% 9,00% 15,49% 9,04% 0,324-46,28% 5% 9,13% 14,89% 8,70% 0,346-44,29% 10% 9,27% 14,29% 8,35% 0,370-42,25% 15% 9,40% 13,70% 8,02% 0,396-40,14% 20% 9,53% 13,12% 7,69% 0,424-37,98% 25% 9,67% 12,45% 7,36% 0,454-35,74% 30% 9,80% 11,97% 7,04% 0,486-33,44% 35% 9,93% 11,42% 6,73% 0,522-31,07% 40% 10,07% 10,86% 6,42% 0,561-28,62% 45% 10,20% 10,32% 6,11% 0,603-26,09% 50% 10,34% 9,79% 5,81% 0,650-23,48% MinVar 11,74% 5,85% 3,33% 1,328-16,05% With an increasing share of Hedge Funds as part of a combined portfolio, the annual variability decreases (The optimal combination of Hedge Funds and traditional funds has been found to be as high as 68%). At the same time, the average return on investment improves. The lowered volatility of the combined portfolio can be explained with the anti-cyclical return profile of Hedge Funds. In bearish markets, Hedge Funds compensate for the losses realized with the traditional portfolio. In bullish markets, Hedge Funds were able to outperform the traditional portfolio most of the time (hence the improvement in profitability). Because Hedge Funds try to realize absolute positive returns in any market, they are traditionally low correlated with equity indices. In addition, Hedge Funds can react more quickly and flexible to changes in the market place (since they are not bound by regulatory limitations). As could be expected, the minimum variance portfolio (in accordance with Markowitz s theorem) shows the best risk-return profile of all possible portfolios (Sharpe Ratio). In addition, the maximum variance portfolio was able to limit the maximum continuous drawdown significantly (Maximum drawdown is the maximum continuous loss an investor has to realize when investing into the combined portfolio). Hence, the minimum variance portfolio proves to be superior to any other possible combination of traditional funds with Hedge Funds. 15

16 It should be mentioned that not all style indices were able to produce the same exceptional returns as Global Macro and Event Driven strategies. Dedicated Short Bias strategies realized continuous losses throughout the 1990 s and are only slowly recovering since In addition, the performance of Single Hedge Funds can differ significantly from the here displayed performance of style indices (the LTCM fund lost 80% of its value in 1998). Also, Hedge Funds have been found to have negatively skewed performance distributions (which is indicative to the higher default risks of alternative investments). Hence, Hedge Funds influence the skewness and excess kurtosis of combined portfolios (defying the assumptions of normally distributed returns). Statistical evidence suggests that fat tails of Hedge Funds have a significant influence on default risks when using Market Neutral strategies to diversify equity portfolios. The unique risk dimensions of hedge funds will be discussed briefly in a later section of the report. Table 4.3: Beta Values (Data: Reuters, 2006) Weighting Global Macro Event Driven 5% 0,935 0,935 10% 0,883 0,914 15% 0,832 0,875 20% 0,784 0,837 25% 0,737 0,798 30% 0,691 0,760 35% 0,647 0,722 40% 0,605 0,683 45% 0,563 0,645 50% 0,523 0,606 MinVar 0,379 0,209 Table 3 refers to the changes in market beta when combining Hedge Funds with traditional investment funds. Because of the low correlation of Hedge Funds with market indices, they add less additional Beta to the combined portfolio. Table 3 emphasizes the low dependability of alternative investments on general market movements. The decreasing values of Beta (for higher proportion of Hedge Funds in the combined portfolio) explain why diversified portfolios do better in downward markets. In addition, Hedge Funds have been found to adjust their betas more quickly to upward markets (in order to benefit from higher market correlations). 4.2 Diversifying Bond Portfolios The performance of Corporate and Government Bonds is highly dependent on changes in interest rates. Arbitrage oriented Hedge Funds managers try to identify and to benefit from over-/under-evaluations of Fixed Interest Securities. Hence, Hedge Funds are 16

17 generally independent from interest movements (Hedge Funds react less sensitive to horizontal movements of the yield curve). Only when interest rates at the long end develop differently from interest rates at the short end, Hedge Funds share the same or a higher exposure to interest rate related risks as traditional bond investments. When the yield curve shifts horizontally, Hedge Funds can limit changes in par value by purchasing relatively cheaper bonds and short-selling more expensive ones with different maturities. Hedge Funds managers speculate on the difference between government bonds and Eurodollar exchanges. Hence, these managers can benefit from changes in the spreads between corporate and government bonds. The TED-spread can be seen as an interest premium on Eurodollar deposits versus risk-free Treasury Bills (to account for higher default risks). Eurodollar-futures are generally regarded as counter-image of Credit Ratings for bank and corporate bonds (Eurodollars are direct obligations of private banks). Arbitrage oriented investors expect the three-months rates of Eurodollars and Treasury bills to develop differently. Falling interest rates can be compensated with long and corresponding short positions in Eurodollars and Treasury bills (as long as the short-term rates of the two investments develop differently). When managers anticipate the widening or narrowing of the spread correctly, they can create interest rate neutral portfolios. It seems logical that the combination of traditional bond portfolios with interest rate arbitrage oriented Hedge Funds should limit the exposure of the overall portfolio to changes in the interest rate. To simulate a traditional investment in bonds, we combined the Merrill Lynch Corporate Bond Industrial Index with JP Morgan s Government Bond Index (both investments were weighted 50%). The resulting index basket was combined with Fixed Income Arbitrage strategies (Fixed Income Arbitrage style index) to assess the diversifying effects of Hedge Funds. The resulting combined portfolio was not dynamically reweighted to maintain the initial weighting. 17

18 Table 4.4: Fixed Income Strategy (Data: Reuters, 2006) % Fixed Income Return p.a. Stdev Semi-variance Sharpe Ratio Max. Drawdown 0% 6,35% 2,95% 2,11% 0,807-2,89% 10% 6,36% 2,68% 1,93% 0,890-2,63% 20% 6,38% 2,47% 1,80% 0,971-2,38% 30% 6,39% 2,34% 1,72% 1,033-2,12% 40% 6,41% 2,29% 1,70% 1,060-2,58% 50% 6,42% 2,34% 1,68% 1,045-3,75% MinVar 6,40% 2,30% 1,70% 1,057-2,40% Similar to the results for diversified equity portfolios, it can be concluded that Hedge Funds can be used to diversify interest rate related risks of bond investments. It should be noted that returns on Fixed Income Arbitrage strategies are limited. Thus, the expected annual return when increasing the proportion of Hedge Funds in the overall portfolio might actually drop (depending on the Benchmark index utilized). Annual volatility of returns and maximum continuous drawdown were decreased in the combined portfolios. As with equity oriented funds, the Minimum Variance portfolio delivered the best results. Losses in par value could be partially compensated with additional arbitrage gains from allocating more funds into Fixed Income Arbitrage funds. Surprisingly, investments in Hedge Funds can actually decrease the risks associated with investments into low-risk fixed income bonds. 60% 50% Weighting 40% 30% 20% 10% 0% 2,00% 2,10% 2,20% 2,30% 2,40% 2,50% 2,60% 2,70% 2,80% 2,90% 3,00% Volatility Figure 4.1: Volatility at different HF Weightings The above chart emphasizes the relationship between different weightings of Hedge Funds in the overall portfolio and varying degrees of volatility. As could be expected from the assumptions of the CAPM, there is a portfolio at which the overall variability is the lowest. The remaining volatility of returns of 2.30% cannot be diversified away (systematic risk). No other combination of alternative and traditional funds will produce better results. 18

19 4.3 Exchange rate related Risks Similar to the hedging of interest rate related risks, Hedge Funds can address the risks of exchange rate fluctuations in the overall portfolio. By speculating on widening or narrowing spreads, TED arbitrage oriented strategies can benefit from changing spreads in Eurodollar/Treasury bills interest rates. Depending on the geographical market, the Eurodollar can be played against different regional treasury bills (e.g. 3-month-Euribor in the euro-area). Changes in exchange rates can have detrimental effects. Between June 2002 and 2005, the Dow Jones Industrial Average appreciated by 17.61% in total. During the same period, the US Dollar lost 20% versus the Euro (resulting into an actual loss of -4.76%). Single Funds focussing on spreads between two distinctive currency regions (in this case USA and Europe) can effectively hedge part of the exposure by employing Fixed Income Arbitrage Strategies. 5 Measuring the Risks of Hedge Funds In the course of the analysis we assumed that, for the sake of simplicity, Hedge Funds can be analyzed in the very same fashion as traditional investments. We postulated that Hedge Funds earnings were normally distributed and that volatility and market Beta was a good measure of the combined portfolio risk. In reality, however, there is significant statistical evidence to infer that Hedge Funds returns are non-normally distributed. Additionally, empirical research suggests that Beta factors of alternative investments change frequently. The subsequent sections briefly address the unique risk features of Hedge Funds. Managers must be aware of the short-comings of existing risk measures when trying to evaluate the risks of Hedge Funds (the risks of combined portfolios). 5.1 Non-normal probability distribution Most alternative funds managers claim that, contrary to general believe, performance variation of hedge and private equity funds can be limited with the use of derivatives and financial leverage. Indeed, some alternative investment funds display a lower degree of overall variation in their performance history. However, there is statistical evidence that the distribution of hedge funds is significantly different from a normal distribution (Fung, 1999). More specifically, the distributions of hedge funds returns display excess and kurtosis and are negatively skewed. Whilst hedge funds returns are less likely to deviate largely from their expected mean, there is a disproportionately 19

20 higher risk for returns to fall significantly below the mean. This risk represents the higher default risk of alternative investments. Historically, Hedge Funds showed a higher weighting of short positions. Hence, these funds were actually not completely hedged from negative performance deviations (with the exception of arbitrage only funds). The use of borrowed capital emphasized this problem. As a result, any risk measures that derive from the assumption of a normal return distribution may not adequately assess the risks of alternative investments. 5.2 Disrupting effects of time series analysis Performance history of hedge and private equity funds fail to acknowledge the effects of managerial and survivorship bias (Kritzmann, 2002). The former refers to performance smoothing of fund returns by their managers. Most alternative funds grant managers a fixed and a variable compensation. The variable component of a manager s remuneration is tied to the yearly performance of the funds they manage. Usually, highwater marks are implemented to guarantee that managers only receive compensation when the fund exceeds the previous year s performance. It has been argued that managers tend to avoid extreme performance movements by realizing gains a year earlier or carrying over losses to the follow-period. Thus, the distribution of funds returns appear to be smoother than they actually are. This effect is more commonly referred to as autocorrelation. Autocorrelation describes the entire width of effects that result in correlation between time series. The latter refers to a practical problem of analyzing funds through industry indices. Sunk and defaulted funds, as well as closed funds, are excluded from alternative investment indices. Naturally, the performance of the overall industry appears better than it actually is. 5.3 Changing market correlations Beta is widely used to describe the relationship between an investment and the overall market. However, historic evidence suggests that disruptive market events can significantly change that interrelation between market and single investment (Spurgin, 2000). Alternative investment funds tend to be more susceptible to disruptive market events than traditional investment funds. Although Beta rarely reflects the risks of certain investments accurately, it is being used extensively throughout the financial industry as an accepted measurement of risk. Alternative funds managers, as well as analyst, have tried in the past to adapt Beta to different investment vehicles and 20

21 industries. Adapted Beta measures can improve the assumptions that can be derived from the CAPM in terms of estimating the inherent risks of alternative investments. 5.4 Performance history and statistical inference Both private equity and hedge funds are relatively new forms of capital investments. When analyzing alternative investments, statisticians have to work with a relative short performance history. Whilst their findings hold some merit, they are only true with a certain degree of confidence (Liang, 2003). A second and more considerable influence on statistical analysis has the availability of data. It is the declared policy of many alternative investment funds to publish and distribute as little data on performance as possible (hence we used Hedge Funds style indices in our analysis). In consequence, the analysis of Single funds is difficult to conduct. Many statisticians prefer to analyze fund of funds or industry indices to draw inferences from industry performance on the performance of single funds. Fund of funds incorporate a limited number of alternative investment funds and thus do not accurately reflect the industry s performance. In addition, fund of funds prefer to invest into successful funds. Single funds with a similar strategy exposure to different asset classes may still display a significantly different performance from fund of funds. Consequently, statistical inference from fund of funds holds limited benefit. Shortcomings of inferences from industry indices refer to the above mentioned problem of survivorship bias. 6 Concluding Remarks We were able to prove in the course of the analysis that Hedge Funds can be used to diversify the risks in traditional investment portfolios. Hedge Funds are able to address three risk dimensions: pricing risks, interest rate related risks, and exchange rate related risks. Not only were Hedge Funds able to lower the risks associated with traditional investment funds, but they were able to maintain or improve the performance of the combined portfolio (depending on the weighting of alternative investments). Minimum Variance portfolios proved to be the most efficient ones. The above mentioned shortcomings of existing risk measures must be taken into consideration when combining traditional and non-traditional investment portfolios. Adapted beta measures accounting for the effects of autocorrelation in conjunction with 21

22 different assumptions about the distribution of Hedge Funds returns can produce better results when assessing the overall risk exposure of combined portfolios. Whilst the limitations of our analysis do not nullify the findings, Hedge Funds investments tend to display higher default risks than traditional investments. When investing into Fund of Funds or style indices (via certificates), an investor may be able to spread default risks over many different Single funds. Direct investment into Single Hedge Funds remains risky for private investors and should be left to professional/corporate investors. 22

23 7 List of Sources Bodie, Z.; Kane, A.; Marcus, A.J.: Investments, Sixth Edition; McGraw Hill; New York, 2005 Fung, William; Hsieh, David A.: Is mean-variance analysis applicable to hedge funds? ; Economic Letters; vol. 62; 1999 Download: Kritzman, Mark; Rich, Don: The Mismeasurement of Risk ; Financial Analysts Journal; May/June 2002 Lavino, Stefano: The Hedge Fund Handbook ; McGraw-Hill; New York, 2000 Liang, Bing: On the performance of Hedge Funds ; Financial Analysts Journal; July/August 1999 Schneeweis, Thomas; Spurgin, Richard: Alternative Investments in the Institutional Portfolio ;CISDM Working Papers; 1998 Download: Spurgin, Richard; Martin, George; Schneeweis, Thomas: A method of Estimating Changes in Correlation Between Assets and its Applications to Hedge Fund Investments ; CISDM Working Papers; 2000 Download: umass.edu/som/cisdm/files/papers/hedgefundpaper.pdf 23