MEAN REVERSION AND ANALYSTS OVER/UNDER REACTION ON THE JSE SECURITIES EXCHANGE SA. A Research Report. Copyright UCT. presented to

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1 MEAN REVERSION AND ANALYSTS OVER/UNDER REACTION ON THE JSE SECURITIES EXCHANGE SA A Research Report presented to The Graduate School of Business University of Cape Town in partial fulfilment of the requirements for the Masters of Business Administration Degree by Estelle Cubbin & Michael Eidne November 2003 Supervisor: Professor Colin Firer

2 This report is not confidential. It may be used freely by the Graduate School of Business. We wish to thank Prof. Colin Firer for his advice and guidance through the process, Grant Irvine-Smith of Investec Asset Management for valuable discussions around the topic, and Inet for supplying us with the data required. We certify that except as noted above the report is our own work and all references used have been accurately reported. Signed: ESTELLE CUBBIN MICHAEL EIDNE 2

3 MEAN REVERSION AND ANALYSTS OVER/UNDER REACTION ON THE JSE SECURITIES EXCHANGE SA ABSTRACT This study analyses the occurrence of mean reversion and analyst over and under reaction on the Johannesburg Securities Exchange, and also investigates the link between the two areas. Both mean reversion and irrational analyst reaction provide for deviations from the efficient market hypothesis and thus provide the opportunity for the development of trading strategies. Specifically mean reversion is tested for in relation to the P/E ratios of stocks using cumulative excess returns of different portfolios over different periods. Analyst behaviour is investigated in light of the link between forecasted and real earnings per share. The results are comparable to those done on the New York Stock Exchange and show evidence of investor overreaction. KEYWORDS: Mean reversion, analyst over/under reaction, earnings forecast, Price/Earnings ratios 3

4 1. Introduction Detailed Problem Definition Literature Review Overview Mean Reversion P/E Ratio s and Mean Reversion Behavioural Finance and the Psychology Involved Investment Analyst Over/Underreaction Methodology for conducting the required studies Methodology Procedure for Data Gathering for the Mean Reversion Study Procedure for Data Gathering Data for the Analyst Over/Under reaction study Approaches Used in the Analysis Mean Reversion Study Examination of the overreaction of security analysts: Findings, Discussion and Analysis Analyst Over/Under reaction Study Mean Reversion Study Conclusions & Recommendations Appendices...38 Appendix 1 - Results for Regressions Analysis...38 Appendix 2 - Data Flows for mean reversion References

5 1. Introduction One of the cornerstones of modern financial markets is the proposition that markets are efficient. This implies that prices of securities in the market should be equal to their intrinsic value and reflect a rational forecast of the present value of expected future dividend payments. (De Bondt and Thaler, 1989) Market overreaction is a well studied field with interest dating back as far as the tulip bulb craze of the 1630 s. In 1929 Pigou in Howe commented that the links between businessmen act as conducting rods along which an error of optimism or pessimism, once generated, propagates itself about the business world. (Howe, 1986) This study looks at two anomalies to the efficient market hypothesis, namely mean reversion and analyst over/underreaction. These anomalies are specifically investigated in relation to the P/E ratios of securities for the Johannesburg Securities Exchange (JSE). The purpose is to see if these anomalies exist on the JSE and what the extent is. If evidence is found, it can then be used to develop trading strategies and to cast doubt on the efficiency of the JSE. Four of the factors that drive the re-rating of stocks are: the re-rating of the market, the growth in earnings or free cash flow, price/earnings (P/E) expectations relative to the market and dividend yield. This study examines two of these drivers, namely the relative P/E to the market and forecasted earnings growth. These drivers are firm specific and are related to earnings growth and expected future earnings. The P/E ratio is a function of expected future earnings. This study is not the application of valuation models to determine a link between share prices in the market and actual firm specific intrinsic value. It is rather an examination of the accuracy of analyst s earnings forecasts compared to actual reported numbers. These earnings forecasts are relevant because as market 5

6 professionals, analyst s earnings expectations have an influence on current share prices. The expected future earnings of a firm is essentially reflected in today s share price and therefore firms that are trading on a high price to earnings ratio relative to the market are expected to deliver on increased earnings at some point in the future in order to justify their premium to the market. The question that this study strives to answer is: do these firms with high P/E ratios relative to the market deliver this expected performance in the future and conversely do firms with low P/E ratios relative to the market deserve their low rating? The expected future earnings of a company will drive its share price which in turn will determine its P/E ratio. The group of investors that are responsible for discovering the future earnings are security analysts and therefore they are in part responsible for the level of the numerator of the P/E ratio. It therefore makes sense to look at these influences on stock price performance together in the same study. Both of these studies were done on the US markets and this study aims to replicate the same methodology using data from the JSE. The JSE does not have the depth of the US stock market due to its much smaller size. The number of companies that offer institutional investors a worthwhile investment in terms of turnover and free float are limited on the JSE to the top 100 companies by market capitalisation. This means that the investment community is watching a fairly small number of companies and it could be assumed that the stock prices of the companies on the market should more accurately reflect the underlying value of the firms due to this focus. This study will attempt to determine if the local analysts are over or under forecasting on the earnings of a firms and if the market ratings assigned to these firms are justified. Some limitations of the study are that the JSE is a relatively small exchange compared to the NYSE and LSE where a number of studies have been documented. The number of securities available is thus not very extensive which could result in inconclusive results. Due to the rapid development of the exchange over the past 20 years and the limited availability of data for earlier periods, the study will focus on the past 20 year period. 6

7 Although there are two different empirical studies they are intimately related and as such the report has been written up in a holistic fashion. The report consists of the problem definition, an overview of the literature and an explanation of the methodology. This is then followed by the findings and conclusions. 7

8 2. Detailed Problem Definition The first part of the study is focussed on the relationship between P/E ratios and returns on stocks. High P/E stocks generally have all or some of the growth premium accounted for in their price. Low P/E stocks generally have the expectation of lower growth accounted for in their price. Therefore by assigning value to the size of the P/E ratio, analysts unfairly discriminate against low P/E stocks. Hypothesis 1: The cumulative excess returns on low P/E stocks exceed the cumulative excess returns on high P/E stocks. Thus the mean return for a portfolio of low P/E stocks will be greater than the mean return for a portfolio of high P/E stocks. The second part of the study is focussed on the rationality of investment analysts earnings forecasts. Hypothesis 2: Investment analysts overreact in their earnings forecasts and place too much emphasis on recent information compared to long term fundamentals. The greater the forecasted change, the greater the error in their reaction. The bias will grow as uncertainty gets stronger. Given the relationship: AC = α + β FC + ε Where AC = Actual Change and FC = Forecasted Change Then: If the forecasted changes are too volatile, the actual changes will be less and β < 1. and If the bias grows as uncertainty gets stronger, the β for the 2-yr forecasts will be less than the β for the 1-yr forecasts. 8

9 3. Literature Review 3.1 Overview The efficiency of financial markets has long been held as a basic proposition of economics. This implies that prices of securities reflect their intrinsic value and as such prices are unpredictable and follow a random walk. Fama s classic paper (1965) presented strong evidence in favour of the random-walk hypothesis. If the efficient market hypothesis is true then it should not be possible to devise trading rules which allow abnormal profits to be made. Our study is focussed on two areas which fundamentally challenge the efficient market hypothesis. The first is the issue of mean reversion of stock prices and the second is the issue of the overreaction of security analysts. The particular focus of mean reversion is in the long-run component thereof and thus the issues emanating from a large number of short-run event studies will be ignored for the purposes of this study. 3.2 Mean Reversion The early studies leading to Fama s initial conclusion that stock prices were unpredictable focussed on short-run correlations using small data bases. (De Bondt & Thaler, 1989). However, longer time periods and larger databases reveal very different results. Pioneering work done by Summers (1986) showed that as many as 6000 data points were required in order to give a standard test for a random walk a 50% chance of rejecting a false null hypothesis. Poterba & Summers (1988) found a tendency for prices to show positive autocorrelation over short time periods and negative autocorrelation over longer time periods. 9

10 Fama & French (1988) regressed the returns for stocks over a set length period against the returns over a prior period of equal length, using monthly nominal return data. They studied both equal-weighted and value-weighted indices and also compared portfolios based on size of the firms. They generally found negative serial correlation. This implies that stock prices are made up of both transitory and permanent components. Mean-reversion has also been tested for using the variance ratio test. This evaluates the estimated variance of an asset price which is hypothesised to follow a random walk over increasing length observation intervals. (Lo and MacKinlay, 1988,1989 and Cohrane, 1988). Lo and McKinlay (1988, 1989) found strong evidence of positive serial correlation in successive weekly differences of stock prices P/E Ratio s and Mean Reversion Basu (1977) showed that buying stocks with low P/E ratio s yielded abnormal returns whilst stocks with high P/E ratio s yielded below normal returns. This was ascribed to the hypothesis that companies with low P/E s are temporarily undervalued because the market is over pessimistic about current or future earnings. This concept is backed up by evidence in the field of psychology which indicates that individuals tend to overweight recent data in making forecasts (Kahneman and Tversky, 1973). De Bondt and Thaler (1985) used the P/E ratio as an indicator of whether stocks are highly or poorly rated, and then used these ratings to evaluate future stock performance. This allowed them to compose winner and loser portfolios. They found that many of the highly rated stocks with a high P/E s fared poorly and failed to deliver the earnings implicit in their high P/E ratios. Conversely stocks with a low P/E outperformed the high P/E stocks indicating the market had been overly pessimistic about the prospects of these companies. They suggested, on the basis of this evidence, that stock prices will revert to a price that reflects the underlying fundamentals and to 10

11 the mean of the market. Power, Lonie A and Lonie R (1991) undertook a similar study on the LSE and found similar results. A number of explanations have been offered for the loser firm phenomena. Losers tend to be smaller than average and smaller firms tend to earn abnormally high returns. Zarowin (1989) matched portfolios by size and found that for size matched portfolios no statistically significant differences in future stock market performances existed. Both Fama and French (1986) and Zarowin (1988) argue that the losing firm effect is subsumed by the size effect. Another explanation is that losers have become riskier and as such demand higher returns. An investigation was done to see whether mean reversion can be attributed to asset being incorrectly priced or to the changes in the risk properties of the securities (Ball and Kothari, 1989). The pattern of serial correlation was examined for abnormal risk-adjusted returns as opposed to total returns on stock market indices. They argued that unless firms dynamically adjust their debt/equity ratio, consistently negative share price returns will both raise the equity cost of capital and increase their leverage. As risk is a linear function of leverage the higher returns observed are normal. Chopra, Lakonishok and Ritter (1992) re-examined the degree of stock market overreaction remaining after the impact of the differential size and risk properties of the companies in the sample had been allowed for. They reported that 22% of extreme loser companies are de-listed over the test period used by De Bondt & Thaler (1989) compared to only 8% of the extreme winners. This survivorship effect causes sample selection bias as only those companies which survive the 5 year test period are included in the sample. They are naturally the pick of the loser portfolio and thus skew the results. De Bondt and Thaler (1989) however claim they do not have a survivorship bias in their results. Chopra et al (1992) controlled for risk by grouping companies into similar risk classes and then estimated the beta s. Large differences between portfolio formation and test beta s were found, confirming the results of a study done by Ball and Kothari (1989). However differences in betas do not fully account for differences in returns, leading to 11

12 the questioning of the validity of the Capital Asset Pricing Model (CAPM). They suggested a revised model of asset pricing incorporating a term to capture the tendency of prices to mean revert. Chopra et al (1992) also found that 20% of price reversal occurred in the 3 days following each earning announcement, showing that earnings expectations are unduly pessimistic for losers and unduly optimistic for winners. Chopra et al (1992) also found the overreaction effect to be the largest for small firms. They attributed this to the fact that smaller firms are dominated by individual investors who are more likely to overreact. Daniel & Titman (1999) did a related study examining the book-to-market values of companies and the relation to mean reversion. They found that high book-to-market portfolio s outperformed the low book-to-market portfolios. Whilst book-to-market values and P/E ratios are linked to a certain extent, evidence of mean reversion on the one will not necessarily imply mean reversion on the other as the portfolio s will not be matched exactly. 3.4 Behavioural Finance and the Psychology Involved The assumption that individuals are rational and as such make optimal decisions based on the information available to them has always been held as the key to efficient markets. Thus prices should reflect all available information and therefore investors cannot outperform the market unless they are privy to special information. Overconfidence is one of the most strongly documented behavioural biases and according to De Bondt and Thaler (1990) the finding that people are overconfident is perhaps the most robust finding in the psychology of judgement. (Daniel and Titman, 1999). People have a tendency to overweight recent events and discount longer term fundamentals and this can lead to overreaction (Kahneman and Tversky, 1973). Experts also tend to be more overconfident than relatively inexperienced individuals 12

13 (Griffin and Tversky 1992). The degree to which individuals are overconfident depends on the situation and is generally stronger for more diffuse tasks where feedback is slower (Einhorn, 1980). From an evolutionary perspective there have to be valid reasons why such behaviour would persist. Firstly biases that distort decisions without resulting in benefits would be eliminated through natural selection. Secondly biases that make individuals less successful in the business of investment management are not likely to play a major role. Therefore any bias affecting security prices is likely to enhance long-term survival without compromising short-term success. Evolutionary theories also suggest that those individuals who appear more confident by successfully filtering information in such a way that it adds to their confidence will be more successful (Daniel and Titman,1999). A rational investor should combine all the different information at hand according to Bayes rule which implies that the weight placed on a piece of information should be proportional to its respective precision. Overconfidence results in individuals putting to much weight on information they collect themselves because they tend to overestimate the precision of the information (Daniel, Hirschleifer and Subrahmanyam, 1998). Individuals also filter information in ways which allow them to maintain confidence, and thus tend to ignore or underweight information which that lowers their self-esteem. Thus investors would be reluctant to sell losers as this means admitting to making a mistake (Odean, 1998). Investors also overweight information which confirms their original view and underweight information which is inconsistent with their views. This could produce momentum in the way of delayed overreaction. It has been shown that overconfidence is likely to influence the judgement of investors relatively more when they are analysing vague subjective information. This implies that low book-to-market (high P/E) companies prices should be more susceptible to investor overconfidence (Daniel et al, 1998). 13

14 3.5 Investment Analyst Over/Underreaction De Bondt and Thaler (1990) explore whether security analysts forecast earnings with an overly negative or positive view. Analysts published expectations of future earnings of a company are based on a rigorous examination of the company and the environment in which it operates. These earnings expectations, according to Brown Foster, and Noreen (1985) have an important influence on stock prices. People have a tendency to overweight recent events and discount longer term fundamentals and this can lead to an overreaction in forecasting earnings numbers (Kahneman and Tversky, 1973). De Bondt and Thaler (1990) compared analyst s forecasts to actual reported numbers to determine the level of accuracy of their forecasts. They concluded that analyst s forecasts are too optimistic, too extreme, and even more extreme for 2 year forecasts than for one year forecasts. In the UK similar studies were undertaken by O Hanlan and Widdett (1991) who examined consensus forecasts for a group of analysts following a company and Capstaff, Paudyal and Rees (1995) who examined a larger sample of individual analyst s forecasts. O Hanlan and Widdett (1991) studied the revision behaviour of analysts for both winner and loser portfolios and found no real evidence of any link between portfolio formation and test period revisions. They also found no sign of overreaction, but confirmed De Bondt and Thaler s (1990) finding that analysts are too optimistic. Ali, Klein and Rosenfeld (1992) reported similar results using annual earning predictions, finding that analysts are too optimistic, and on average, overestimate future earnings per share. The results of Abarbanell and Bernard (1992) do not support the De Bondt & Thaler (1990) finding of analyst overreaction and find that if anything that analysts underreact. When comparing studies that found analyst overreaction to those that found analyst underreaction, they observed that the former 14

15 studies partitioned firms based on prior stock market performance, whilst the latter studies partitioned firms based on prior earnings performance. 3.6 Methodology for conducting the required studies Whilst there are numerous methods described which could be used for the purposes of this study, it was decided to follow the methodology proposed by De Bondt and Thaler (1985) for the mean reversion study and by De Bondt and Thaler (1990) for the analyst behaviour study. The goal of the study is to determine if the same observations that they made on the US market could be achieved on the SA market. The SA market is fundamentally different from the US market in size and depth. It would therefore be interesting to determine if the results for the much smaller SA market are similar. 15

16 4. Methodology 4.1 Procedure for Data Gathering for the Mean Reversion Study The basis of the study as previously stated is the JSE. Historical data from the JSE is not obtainable from the JSE further back than It was decided that it would be better to obtain the data from a data provider whose databases contain much larger data sets. It is important that historical share prices are updated to reflect corporate actions as they occur. Therefore it is critical to obtain data from a provider who ensures that all historical share information is updated to correctly account for share splits and unbundlings. Data was sourced from INet. INet is a market data source that maintains a database of historical JSE data that dates back to Month end price, price earnings yield and dividend yield data was collected from the Inet historical database for all stocks currently listed on the JSE. It was not possible to collect data from shares no longer listed as it was not possible to source a list of de-listed stocks from the data providers. On preliminary analysis it was evident that 20 years of meaningful data could be used due to completeness of the price, P/E and Dividend Yield (DY) data. The historical index information was also sourced from Inet. For the same period being studied the overall index level was downloaded from 1980 to October This process was complicated by the fact that in 2002 the index basis was changed when the JSE became part of the FTSE. The JSE have only restated some 5 years of historical data so it was necessary to splice the returns together to get a consistent return for the JSE overall index for the 20 year period. The data was downloaded from the Inet historical database into an excel spreadsheet via the dynamic data exchange (DDE) link. Due to the fact this data needed to be scrubbed and used to build up into portfolio data the data was loaded into a Microsoft 16

17 SQL server database. This resulted in an upload of some data points representing the returns for 356 shares for the last 20 years on the JSE. 4.2 Procedure for Data Gathering Data for the Analyst Over/Under reaction study For the investor over/under reaction part of the study a group of companies was selected for which consensus analyst earnings forecasts were available. The data was obtained in a spreadsheet format courtesy of Grant Irvine-Smith of Investec Asset Management, as it had been collated for another study. Data was only available for approximately 100 companies for the period March 2000 to October Given the small number of companies available, all companies were used regardless of the financial year end month of the company. The first forecast period was taken as being 8 months prior to year end. At this point in time the announcement for the previous year s earnings would have been made. The second forecast period was taken to be at year end. 4.3 Approaches Used in the Analysis Mean Reversion Study The original De Bondt and Thaler (1989) study looked at a much larger set of data compared to the dataset used in this study. They had access to a much longer time period and a much larger universe of shares. The larger universe of shares is due to the fact the US market is much larger in relation to the SA market. An objective of the study was to replicate the De Bondt and Thaler (1989) study as far as possible. In the time constraints and difficulty in procuring historical data from the JSE there was a limitation in the amount of data available. The mean reversion study was divided into two parts. The first part, as far as possible, replicated the methodology used by De Bondt and Thaler (1989) was named method 1. The second part used a new methodology which was an adaptation of method 1 and this was called method 2. 17

18 Description of method 1 De Bondt and Thaler (1989) constructed portfolios from the top 35 and bottom 35 stocks rated by P/E. These portfolios of 35 equally weighted stocks excess returns was then tracked for 5 years from the start date. The start date was then incremented one year forward and the process repeated. They did this for 43 years and the returns for the entire portfolio were then averaged. This study copied this methodology exactly except the process was only repeated 15 times to fit in portfolios that were tracked for 5 years. The portfolios were equally weighted for each share. The returns for each stock was calculated and then used to calculate the overall return for the portfolio on a month by month basis. The monthly market return was then subtracted from the monthly portfolio return to calculate the relative outperformance/underperformance of the portfolio compared to the market. The monthly portfolio performance was then averaged into the four quartiles portfolios performance. Description of method 2 Bondt and Thaler s (1989) methodology was adapted to achieve two objectives; to overcome the issue of a smaller dataset and to take the timing element out of the study. De Bondt and Thaler (1989) found that the winner and loser portfolios performed differently in different months in the year. There was definitely more volatility in January which is called the so called January effect. The study wanted to determine what would happen to the results if the monthly timing effect was removed from the data. The market was divided into quartiles based on P/E ratios at a specific date. These divisions were then used as the basis for 4 portfolios whose performance was tracked 18

19 for 5 years or 60 months into the future. The starting date was then incremented 1 month forward and 4 new portfolios formed form the new months data. This process was repeated monthly for 15 years of data. The process for calculating the returns on the portfolio is exactly the same from this point as used in method 1. Tool Set used for analysis Due to the quantitative nature of the study it was decided to develop a Visual Basis application to crunch the data. The decision to develop a custom application to analyse the data as opposed to the use of a spreadsheet based tool was driven by the size of the dataset and the fact it would not fit on a spreadsheet. Once all the derivative portfolios had been created the data points were estimated to number well over 1,000,000. Another advantage of using a custom developed program was that it eliminated the possibility of error due to incorrect treatment of data. The consistency of calculation was guaranteed by the fact that all data was automatically run through the same calculation engine. Building spreadsheets with large data sets invariably becomes very complex, unwieldy and time consuming. The Visual Basic program consisted of a number of sub procedures that controlled each step in the analysis phase. The process was broken down into a number of steps from data loading to final calculation. The program was designed to allow each step to be run independently so that steps could be rerun if errors were detected. All the results from each step were stored in the database. The application was named JAM for easy reference. In order to scrub and add the P/E and DY data a procedure in JAM was developed to upload the data from the excel spreadsheets into the database. This made sure that the matching month end P/E and DY data was matched with the correct price data. 19

20 A further JAM module was developed to calculated returns for each of the shares in the database. Two types of returns were calculated; a price return excluding dividends and a price return including dividends. It was not possible to calculate the actual date that the dividend was paid. The dividend paid was backed out from the yield and price and this was divided by twelve and then added to the month end price. This allowed the price performance of dividend paying shares and non-dividend paying shares to be compared to each other. One hundred and eighty one start dates were identified from the 31st October 1983 to 31st October The last start date is 5 years before the end of the data set to allow for the creation and tracking of a portfolio for 5 years. These start dates created the basis for the creation of the portfolios that would track the performance of the different levels of P/E ratio. The core JAM module was the one that created each of the portfolios. This was achieved by selecting the shares in the database by start date and ordering them by P/E ratio. The shares were then divided up by P/E ratio s into 4 quartiles; upper, lower upper, upper lower and lower for method 2. In the method 1 calculation the list of shares ranked by P/E and the top 35 shares made up the winner portfolio and the bottom 35 made the loser portfolio. For each of these shares the following 60 months of returns were selected and placed in the database with a unique portfolio code representing the start date and the quartile. After the 4 portfolios were formed on the start date, the date was incremented by one month and the process was repeated. The result was some 723 separate portfolios which held an average of 34 shares for 60 months of data. This resulted in 1.5 million data points for method 2. The amount of data points created using method 1 was far less and amounted to some Following on De Bondt and Thaler s (1989) methodology these portfolios were equally weighted. This meant that each share s return counted equally towards the overall portfolio return. 20

21 The return for each of these portfolios was then calculated by JAM on a month by month basis. This was achieved by averaging the returns for each share for each month. At this point the market return was added to the monthly returns to calculate if the portfolio had out performed or underperformed the market. The portfolios had been classified at the time of formation as either a winner or a loser in method 1 and an winner, lower winner, upper loser and loser for method 2. The portfolios were then grouped into these classifications and the returns averaged across like portfolios to calculate an overall return. Therefore the final output from JAM was six portfolios consisting of 60 months returns. The returns reported were pure price return, price and dividend return, pure price return less market return and price and dividend return less market return. 21

22 4.3.2 Examination of the overreaction of security analysts: For each company the following data points were collated for each year for which data was available: EPS t-1 = Earnings per Share for year 0 EPS t = Earnings per Share for year 1 EPS t+1 = Earnings per Share for year 2 F t(1) = Forecasted Earnings per Share for year 1 at time 1(1 st forecast) F t+1(1) = Forecasted Earnings per Share for year 2 at time 1(1 st forecast) F t(2) = Forecasted Earnings per Share for year 1 at time 2(2 nd forecast) F t+1(2) = Forecasted Earnings per Share for year 2 at time 2(2 nd forecast) This allows the following to be calculated (all changes expressed as % changes): AC1 = EPS t EPS t-1 (Actual change in earnings for year 1) AC2 = EPS t+1 EPS t-1 (Actual change in earnings for years 1&2) FC1 = F t(1) EPS t-1 (Forecasted change in earnings for year 1) FC2 = F t+1(1) EPS t-1 (Forecasted change in earnings for years 1&2) FR1 = F t(2) F t(1) (Revised Forecasted change in earnings for year 1) FR2 = F t+1(2) F t+1(1) (Revised Forecasted change in earnings for year 2) AC12 = EPS t+1 EPS t (Actual change in earnings for year 2) FC12 = F t+1(2) F t(2) (Forecasted change in earnings for year 2) FR12 = FC 1+2(2) FC 1+2(1) (Change in forecasts between the 2 forecast points) 22

23 Time line of years (Y), actual earnings (A) and forecasts (F) A 1 A 2 Y 0 Y 1 Y 2 EPS t-1 EPS t EPS t+1 F t(1) F t+1(1) F t(2) Copyright F t+1(2) UCT AC1(EPS t EPS t-1 ) AC2 (EPS t+1 EPS t-1 ) FC1 (F t(1) EPS t-1 ) FC2 (F t+1(1) EPS t-1 ) FR1 (F t(2) F t(1) ) FR2 (F t+1(2) F t+1(1) ) AC12(EPS t+1 EPS t ) FC12 (F t+1(2) F t(2) ) 23

24 The following equations were then analysed and regression analysis performed on them: 1. AC1 = α 1 + β 1 FC1 + ε 1 2. FR1 = α 2 + β 2 FC1 + ε 2 3. AC2 = α 3 + β 3 FC2 + ε 3 4. FR2 = α 4 + β 4 FC2 + ε 4 5. AC12 = α 5 + β 5 FC12 + ε 5 6. FR12 = α 6 + β 6 FC12 + ε 6 All variables are normalised by using the percentage changes. 24

25 5. Findings, Discussion and Analysis 5. 1 Analyst Over/Under reaction Study The results of the regression analysis performed on data from the JSE is presented in table 1 and the results of the analysis performed by De Bondt and Thaler is presented in table 2. Equation Variables Constant t-value t-limit Rej/Acc Slope t-value t-limit Rej/Acc Adj. R2 no of obs 1 AC1,FC Accept Reject FR1,FC Reject Accept AC2,FC Accept Accept FR2,FC Reject Reject AC12,FC Reject Reject FR12,FC Reject Reject Table 1 Tests for rationality of earnings forecasts performed on the JSE Equation Variables Constant t-value t-limit Rej/Acc Slope t-value t-limit Rej/Acc Adj. R2 no of obs 1 AC1,FC Reject Reject FR1,FC Reject Reject AC2,FC Reject Reject FR2,FC Reject Reject AC12,FC Reject Reject FR12,FC Reject Reject Table 2 Tests for rationality of earnings forecasts performed on the NYSE (De Bondt & Thaler, 1990) When comparing the actual changes in 1 year earnings to the forecasted changes in 1 year earnings using equation 1, the intercept is negative. However the intercept is not statistically significantly different from 0 and as such cannot be used as proof of analyst optimism. By ignoring the intercept and focussing only on the slope, it can be inferred that only 68% of the forecasted change in earnings actually materializes. This indicates that the forecasts are too extreme. The t-value calculated for the slope indicates that this is significantly less than 1. This finding is congruent with that found by De Bondt and Thaler (1990) for the NYSE. 25

26 When comparing the actual changes in year 2 earnings to the forecasted changes in year 2 earnings using equation 3, the intercept is significantly negative, indicating that forecasts are too optimistic. By ignoring the intercept and focussing only on the slope, it can be inferred that only 76% of the forecasted change in earnings actually materializes. This indicates that the forecasts are too extreme. The t-value calculated for the slope does not indicates that this is significantly less than 1. The year 2 forecasts are thus significantly less extreme than the 1 year forecasts. This is different from the finding of De Bondt and Thaler (1990) who found the year 2 forecasts to be even more extreme than the year 1 forecasts. Equations 2 and 4 compare the forecast review to the forecasted change in earnings. Rationality would imply that the slopes should be equal to zero. In contrast to the findings of De Bondt and Thaler, the slope of the 1-year revisions is positive and that of the 2-year revisions is negative. However, only the 2-year revision slope is statistically significantly different from 0. Thus the results are stronger for the 2 year revisions and this shows that a reversal can be expected which is congruent with the initial overreaction of analysts. Equation 5 examines the relation between actual changes between years 1 and 2 and the forecasted changes. The results show that only 35% of the forecasted changes materialize. The correlation is far stronger than that found for the NYSE. Equation 6 shows very little correlation between the forecast revision and forecasted change from one year to the next. 26

27 5.2 Mean Reversion Study It is clear from figures 1 to 4 that the results for both method 1 and method 2 are consistent with the De Bondt and Thaler (1989) findings. The portfolio of low P/E stocks outperforms the portfolio of high P/E stocks and therefore revert to the mean. The difference between method 1 and 2 is that the degree of relative outperformance is different. This is more than likely due to the difference in sample size. Figure 1 and 2 graphically represent the results from the mean reversion study. The cumulative excess returns relative to the average of the winner and loser portfolio are plotted Cumulative excess returns for winner and loser portfolios relative to average Months Loser Winner Figure 1: Method 1 Winner Loser Portfolios Performance Relative to Average 27

28 Cumulative excess returns for winner and loser portfolios relative to average Months Loser Portfolio Winner Portfolio Figure 2: Method 2 Winner Loser Portfolios Performance Relative to Average Figure 4 and 5 show the wealth path for method 1 and 2. This how the value of R1.00 invested at portfolio inception has grown in the 60 months of the portfolio s life. It is clear from the graph that in both instances the loser portfolio outperforms the winner portfolio by a substantial margin. 2.5 Absolute Total Return Months Winner Loser Figure 3: Method 1 Winner Loser Portfolios Wealth Path 28

29 Absolute Total Return Months Loser Lower Winner Winner Upper Loser Figure 4: Method 2 Winner Loser Portfolios Wealth Path Figure 5 is a graph of De Bondt and Thaler (1985) results. There is a definite similarity between this graph and Figure 1 and 2. The main difference is that the rerating of stocks every January, which indicates the so called January effect, is absent in the South African data. 29

30 Figure 5: Cumulative excess returns for winner and loser portfolios (De Bondt and Thaler, 1985) Method 1 Statistical Analysis L - W Observations 60 Pearson Correlation 0.42 Hypothesized Mean Difference 0 Df 59 t Stat 3.74 P(T<=t) one-tail 0.00 t Critical one-tail 1.67 P(T<=t) two-tail 0.00 t Critical two-tail 2.00 The paired sample t-test comparing the total returns found over the different time periods show that the mean difference is statistically different from 0. Thus the 30

31 loser portfolio outperforms the winner portfolio and this is statistically significant. L - W Mean 0.85% Standard Deviation 1.75% Lower Confidence Limit (95%) 0.39% Upper Confidence Limit (95%) 1.30% The confidence interval estimates for the mean difference between the portfolios were calculated. The loser portfolio outperformed the winner portfolio by between 0.39% and 1.3% at a 95% level of confidence. The implication of this is that an investor who picks a portfolio of losers has a 95% chance of outperforming a winner portfolio by between 0.39% and 1.3%. Method 2 Statistical Analysis t-test: Paired Two Sample for Means L vs UL L vs LW L vs W UL vs LW UL vs W LW vs W Observations Pearson Correlation Hypothesized Mean Difference Df t Stat P(T<=t) one-tail 9.39E E E t Critical one-tail P(T<=t) two-tail 1.88E E E t Critical two-tail L = loser, UL = upper loser, LW = lower winner, W = winner 31

32 A paired sample t-test was done to compare the results over the 5 year portfolio period of all the portfolio s to each other. As can be seen the loser portfolio s outperformance of all 3 of the other portfolio s is statistically significant and as such confirms our hypothesis that the loser portfolio will mean revert. Confidence Interval Estimate of the Mean Difference L - UL L - LW L - W UL - LW UL - W LW - W Mean 0.64% 0.74% 0.73% 0.10% 0.09% -0.01% Standard Deviation 0.29% 0.45% 0.61% 0.28% 0.41% 0.24% Lower Confidence Limit (95%) 0.56% 0.62% 0.57% 0.03% -0.02% -0.07% Upper Confidence Limit (95%) 0.71% 0.85% 0.71% 0.17% 0.19% 0.05% L = loser, UL = upper loser, LW = lower winner, W = winner The confidence interval estimates for the mean difference between the portfolios were calculated. The loser portfolio outperformed the other portfolios by between 0.56% and 0.85% at a 95% level of confidence. We can therefore be sure that the results are statistically significant and based on this dataset the hypothesis that shares with a low P/E will out perform shares that have a high P/E at the time of portfolio formation over a period of time is confirmed. The performance in Figure 1 is far more volatile than in Figure 2. This is a function of the fact that timing differences have been removed in the result set plotted in Figure 2. The end result is however still similar with the loser portfolio still outperforming the winner portfolio by a substantial margin. The fact that the return path in Figure 1 is not as smooth as the path in Figure 2, with timing issues removed, could show that certain months of the year produce better performance for the last 20 years. It was not in the scope of this study to investigate differences in returns by months of the year but this could warrant further investigation. It will be possible to establish statistically if there are certain months that outperform other months based on this result set. 32

33 It is interesting to note that initially in all cases the winner portfolio outperforms the loser portfolio for the first 9 to 12 months. After this the loser portfolio consistently outperforms the winner portfolio. This may be that that initially the low P/E rating accorded to the loser portfolio is warranted and the share underperforms for that period. The outlook then improves and the share price begins to rerate. Conversely the high P/E that is accorded to the winner shares is carried for the first year and as the share begins to disappoint and not warrant such a high P/E ratio that share also begins to rerate. In the De Bondt and Thaler (1989) study the loser portfolio immediately outperforms the winner portfolio and jumps as opposed to these studies results where the path of returns is different. See Figure 5 which is sourced from De Bondt and Thaler s (1989) study for a comparison to the findings in this study. This as already discussed previously, is more than likely attributed to the January effect. Over the longer term from about 1 year to 5 years the loser portfolio decidedly outperforms the winner portfolio. The difference at the end of the period is about a 50% swing. This is roughly in line with De Bondt and Thaler s (1989) of about a 40% swing in performance. The method 1 end results do not tie in with De Bondt and Thaler s (1989) end results of -10% for the winner portfolio and +30% for the loser portfolio. The out performance for the loser portfolio and underperformance for winner portfolio is split between + 25% and -25% respectively. Method 2 which had a much larger dataset is very close to the De Bondt and Thaler (1989) findings with a -12% under performance for the winner portfolio and a +34% out performance for the loser portfolio. These results may be coincidental but it can be inferred that the outperforming portfolio will generate more out performance than the underperforming portfolio will lose. An important bias that this data has, is that there is a survivorship bias. De Bondt and Thaler (1989) used all stocks that were listed on the exchange at the time of portfolio formation. If one of these stocks were de-listed during the life of the portfolio the 33

34 share was sold out at the last price. Unfortunately the data set used for this study did not contain the price returns for de-listed shares. Efforts were made to source this data but it was not possible to find a reliable data vendor in the time frame allowed for the study. Stocks have been de-listed from the JSE during the period studied and the exclusion of the returns from these stocks may have skewed the dataset. This issue should be addressed in a follow up study using a more complete dataset that includes all de-listed stocks. Another issue that is taken into account is the issue of dividends and their effect on prices. The data presented here does include returns from dividends but they have been smoothed as it was not possible to determine the actual month dividends were paid. Therefore they were added in each month based on the dividend yield. Due to the fact returns from dividends have been included in the study, calculating them in a different fashion will not alter the results appreciably. It would however still be better from a point of completeness to rather add the dividend return to the share price the month the dividend was paid given the conventional wisdom that the day dividend is paid the share price will drop by the same amount. 34

35 6. Conclusions & Recommendations The study shows that as for the NYSE, investment analysts on the JSE are also too optimistic and too extreme in their earnings forecasts. The results merit further investigation and the study should be repeated over a longer time period for a larger number of companies in order to ensure that any market effects are eliminated. The results of the mean reversion study are consistent with the results that De Bondt and Thaler (1989) found in their study of the US market. The value approach to investing in terms of taking contrarian views has proved very successful for certain asset managers in the SA market. These results show that by constructing portfolios of shares with a low P/E relative to the rest of the market can produce returns above the market in the longer term as these shares will re-rate. As stated in the beginning of this paper the expected future earnings of a company will drive its share price which in turn will determine its P/E. The group of investors that are responsible for discovering the future earnings are security analysts and therefore they are in part responsible for the level of the numerator of the P/E ratio. It has been shown that analysts forecast are too extreme which is also consistent with De Bondt and Thaler s (1985) findings. Analysts are an important determinant of share prices and as stated above and previously, share prices are the numerator of P/E s and therefore there is a link between P/E s and forecasts. Therefore the view analysts take of share prices ultimately influences share prices. Valuation of financial assets are generally based on today s value of future cash flows and because we are trying to forecast the future there will always be an element of subjectivity in valuations. This fact enables people to make money from the market because they discover incorrectly priced assets that eventually revert to their true value. If one is to believe the results presented here on analyst forecasts and P/E s then there is plenty of opportunity to make money on the 35

36 market as there are many incorrectly priced shares on the market and we can identify them by low P/E s. The low P/E is caused by analysts underrating the company unfairly and overrating other companies so that other companies are underrated on a relative basis to the rest of the market. The markets are the results of many decisions made by people every day and if one can discover patterns in the way people are making these decisions one can profit from this predictability. It is possible that the concept of people overweighting recent data when making forecasts can be used as a predictor (Kahneman and Tversky, 1973). These irrational behavioural issues create trading opportunities that can be used to generate a return in excess of the market. There were a number of limitations in this study. They were focussed around the availability of data and the time frame available for the collection of data. This issue was most evident around the collection of analyst recommendation data. Extensive efforts were made to source this data but it was found that not even the information suppliers keep a substantial history of the data. Some of the major suppliers of financial information were approached but none kept a history for more than 12 months. The two years of data has been collected from these providers and stored separately. It is possible to recreate the data by approaching the various brokers who produce research and source information directly from them. They may however be reluctant to provide the information if they were to realise it is for some sort of measurement exercise no matter how academic in nature. The data collected for mean reversion study was a more complete dataset but needed to be expanded and further verified to be a longer dataset. As previously discussed it is also necessary to include de-listed companies to eliminate the survivorship bias. If the dataset on the mean reversion study could be expanded as discussed, it would be useful to redo the study to see how consistent the findings are using different time frames. It may be useful to create portfolios based on current information and then 36