Changes in Analysts' Recommendations and Abnormal Returns By Qiming Sun Bachelor of Commerce, University of Calgary, 2011 Yuhang Zhang Bachelor of Economics, Capital Unv of Econ and Bus, 2011 RESEARCH PROJECT SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN FINANCE BEEDIE SCHOOL OF BUSINESS Qiming Sun 2012 Yuhang Zhang 2012 SIMON FRASER UNIVERSITY Summer 2012 All rights reserved. However, in accordance with the Copyright Act of Canada, this work may be reproduced, without authorization, under the conditions for Fair Dealing. Therefore, limited reproduction of this work for the purposes of private study, research, criticism, review and news reporting is likely to be in accordance with the law, particularly if cited appropriately 1
Approval Name(s): Qiming Sun Yuhang Zhang Degree: Title of Project: Master of Science in Finance Changes in Analysts' Recommendations and Abnormal Returns Supervisory Committee: Amir Rubin Senior Supervisor Associate Professor Alexander Vedrashko Second Reader Assistant Professor Date Approved: 2
Table of Contents Abstract.............................................................................4 Acknowledgements................................................. 5 1. Introduction..................................................................... 6 2. Literature Review..................................................................7 3. The Data and Empirical Procedure.....................................................8 3.1 Data Collection................................................................8 3.2 Data Processing............................................................... 9 3.2.1 CAPM and Implication.................................................... 10 3.2.2 Four Factor Model and Implication............................................ 10 4. Empirical Results.................................................................12 4.1 Test Motivation...............................................................12 4.2 Findings.................................................................... 12 5. Shortcomings in Research.......................................................... 15 6. Conclusions..................................................................... 16 References.......................................................................... 18 Appendix.......................................................................... 19 3
Abstract In this paper, we evaluate whether one can achieve higher abnormal return by following analysts' recommendations. We form monthly portfolios that invest (long) in stocks with the largest upgrade in consensus (average) recommendation and short stocks that have the largest downgrade in consensus recommendation. Once the self-financing portfolio is created, we hold the portfolio during the following month and measure its abnormal return based on the CAPM and four factor model. We find that these portfolios are associated with positive and significant alphas. We also find that these portfolios' alphas are highest when the portfolios are associated with small number of stocks rather with a large number of stocks. These results suggest that consensus recommendation changes may be useful for achieving higher returns. Further, tests show that recommendation changes are more valuable in the period from 1996 to 2003 than during the period from 2004 to 2011. Keywords: Analyst recommendation; Trading Strategy; Abnormal Return 4
Acknowledgements First and foremost, we would like to thank our supervisor Dr. Amir Rubin for providing us the opportunity to work on this very interesting topic. He has guided us through the project step-by-step, and given us invaluable support, encouragement and suggestions. We also would like to thank all of the instructors in the Master of Science in Finance program for their profound dedication. We cannot walk so long without their support. Last, but not least, we would like to thank our beloved parents for their unconditional love, endless support over the years and for always being there when needed. None of this would have been possible without their support, understanding and encouragement. 5
1. Introduction In terms of investment in stock markets, analysts recommendations may be considered as references when making decisions. Analysts at Wall Street do research on companies investment highlights, investment risks, and earnings; and then come up with buy and sell recommendations. As Boni and Womack (2006) said, analysts' reports provide at least modest incremental value to investors. In our paper, we are going to test the relationship between analysts recommendation change and portfolio s return from 1996 to 2011. We focus on all the U.S. stocks across NYSE, AMEX, and Nasdaq markets. We utilize a non-industry approach, which is also called the market risk-neutral approach, to acquire information signaling future relative winners and losers through analysts recommendations across all industries. We rank all the stocks by their average consensus rating level change (a change can take on a value of -4 to +4 as recommendation scale of 1 is a strong buy and 5 is a sell). Then, we utilize a simple self-financing strategy which is similar to Boni and Womack (2006): long the firms net upgraded by analysts while short net downgraded firms in each month. The difference from them is the number of transactions executed. Instead of executing all the securities which have changing recommendations, we long and short the ones which have the most recommendation change based on the consensus recommendation estimate of the month. By following our self-financing trading strategy, our primary findings are that abnormal returns can be generated in our portfolios for a wide range of stocks. As long as the number of stocks in the portfolio is not large (i.e., less than 300 stocks long and 300 stocks short), the abnormal return decreases no matter which model is used (CAPM or Four-Factors Model). In addition, we partition our sample into two and find that the period from 1996 to 2003 generates higher returns than the period from 2004 to 2011. We also find that the portfolio returns is generated predominantly by the long position while the abnormal return from the short position is very low. This suggests that consensus recommendations are more informative for upgrades than for downgrades. 6
The remainder of the paper is organized as follows. In Section 2, we discuss the related literature we refer. Section 3 provides the data selection and descriptive statistics. Section 4 discusses our findings in detail. Section 5 discusses shortcomings of our research. Section 6 concludes this paper. 2. Literature Review In the past two decades, scholars around the world have done a lot of research on analysts recommendation. Analysts write reports and issue buy and sell recommendations. It is widely documented that investors are affected by analysts recommendations when they make investment or transaction decisions. Yet, earlier papers document that analysts rarely issue sell recommendations. Jegadeesh et al. (2004) report that the average analyst recommendations over the 1985 to 1999 period to a buy recommendation and sell or strong sell recommendations make up less than five percent of all recommendations. Literature finds that although analysts have recommendation bias, analyst recommendations add value. Boni and Womack (2006) found that analysts generate value in their recommendations primarily through their abilities to rank stocks within industries. However, they also demonstrated that recommendation information is not valuable for predicting future relative industry return. Other authors indicated that stock prices react significantly to recommendation revisions in G7 countries (Jegadeesh and Kim, 2006). Some authors find that analyst recommendation changes can be valuable. Stickel (1995) documented that recommendation upgrades tend to outperform downgrades, which is also demonstrated in our research. Also, Barber et al. (2001), Jegadeesh et al. (2004), Boni and Womack(2003) and Green (2006) find that the stocks with the better recommendations outperform the stocks with the least favorable recommendations. These findings indicate that investors can benefit from analysts recommendations if they consider the relative levels of recommendations across stocks, or if they pay attention to changes in recommendations. These findings can lead to a conclusion that investors can make profits from analysts 7
recommendations if they pay attention to changes in recommendations. Other authors also link recommendation change to the stock price. However, Loh (2011) finds that only 12% of recommendation changes are influential, and they are most likely to be influential if they are from leader, star and previously influential analysts. In our research, we are interested in the factors which play key roles in portfolio profitability. Hong. Lim, and Stein (2000) demonstrate that momentum trading strategies are profitable in the Hong Kong stock market. Chui et al. (2001) extends their work and finds that existence of momentum profitability in eight Asian countries, including Hong Kong. Moskowitz and Grinblatt (1999) argue that price momentum is an industry-driven phenomenon. 3. The Data and Empirical Procedure 3.1 Data Collection Our data is mainly collected from I/B/E/S database on analyst recommendation and consensus levels, Center for Research in Security Prices (CRSP) monthly stock returns, number of shares, and share prices. The general research time range is from 1996 to 2011. 1 To explore the detailed results, we further investigate and compare the findings for two time frames from 1996 to 2003 and from 2004 to 2011 which takes eight years respectively. The company code we refer is CUSIP which is an 8-digit ticker.. All we want is companies covered by NYSE, AMEX, and Nasdaq. From the Summary Statistics (Consensus Recommendations) in I/B/E/S, we acquire companies monthly average recommendations provided by totally sell-side analysts belonging to brokerage firms. The average recommendations released at mid-calendar month have five consensus rating levels from 1 to 5 (where 1 is a strong buy and 5 is a sell). On the whole, the important variables include companies CUSIPs, the average recommendation levels, and their related dates (usually 1 We choose the beginning of 1996 as our starting time because the analyst recommendations prior to 1996 are sparse. 8
at the middle of each month). Among all the companies, some of them are omitted due to lack of CUSIP. Total sample is inclusive of 16976 stocks. 3.2 Data Processing Base on the raw data from I/B/E/S, we merge it with companies market capitalization which is generated by multiplying stock price and number of shares which are drew from CRSP. Then, we double sort stocks based on change in monthly average recommendation change, and then by market capitalization. Next, we choose a group of stocks that have highest net upgrade and the group of stocks that have the highest net downgrade. These two groups must have the same amount of stocks. The double sorting insures that if two stocks have the same net upgrade or net downgrade, the one with higher market capitalization will be chosen. The group size varies from 10 to 500 stocks. To form our portfolio, we utilize the self-financing method which means the long and short are equal weighted (equal money invested in both long and short). 3.2.1 CAPM and Implication Next, we are able to do the transactions following the long-short strategy by using CAPM to obtain alpha. The regression formula is as follows: R t = β RMRF t + α where R t is the excess return in month t on a portfolio, RMRF t is the CRSP value-weighted market return minus the risk-free rate in month t. The estimated intercept or alpha is interpreted as the monthly abnormal return in excess of what could have been achieved by investments. Because the composition of portfolio is changing month by month, abnormal return should be calculated every month depending on the recommendation change from last month. Table 1 shows abnormal return (alpha) and its significance. The alphas, which are the abnormal returns, are all positive showing that our portfolios all beat the market. In addition, higher the t-statistic is, 9
the more significant the variable (alpha) would be. In this table, almost all alphas absolute values of t- statistics are bigger than 2, except long-short-500-stocks portfolio (1.769 which is close to 2), so all alphas are significant. From the Chart 1, it can be observed that as long as the size of portfolio increases, the alpha decreases. This makes a lot of sense to us logically. Before doing long-short transactions in portfolios, we sort all the firms by their recommendation changes along with market capitalizations. Every time we increase the size of portfolio, we collect more firms whose recommendation changes magnitude and market capitalizations are smaller than the previous portfolio. Based on our assumption, we believe that recommendation changes adding values to portfolios. The bigger the change is, the more returns would be generated. The new adding holdings less recommendation changes would generate less abnormal return. Thus, the total abnormal return would be smaller than the smaller sized portfolio. This assumption has been justified by our regression results. Beta is the coefficient of the portfolio, which in general should be zero because we go long and short a large number of stocks. Thus, in general, for the long-short strategy, it seems that no matter whether the market goes up or down, we can still make profit by following this strategy. When the market is good and most stock prices go up, we have the long side profit to offset the short side loss, and of course it is the same in reverse. This can be supported by the t-statistics. Most t-statistics absolute value beta s coefficients are less than 2, which shows that the beta s coefficient in our long-short strategy is small and insignificant. R-squared measures how well the CAPM predicts the actual performance of an investment or portfolio. A higher R-squared means that a portfolio performs more likely to the index. A portfolio with a low R-squared does not act much like the index. Besides, statistically, R-squared shows how useful the beta is. A low R-squared means the beta can be ignored. This implication also supports the usability of our beta in all CAPM tests. 3.2.2 Four Factor Model and Implication 10
Furthermore, we do the transactions following the long-short strategy by using Fama-French Three- Factor Model, plus one more factor, which is price momentum. This mixed model was mentioned by Carhart in 1997. In this model, we simulate the same kinds of portfolio as those in the CAPM. The results are similar to those in the CAPM. We run the following four factor regression: R t = α + β 1 RMRF t + β 2 SMB t + β 3 HML t + β 4 Momentum t + e t where R t is the excess return in month t on a portfolio, RMRF t is the CRSP value-weighted market return minus the risk-free rate in month t, and SMB t, HML t, and Momentum t are month t returns on portfolios based on size, book-to-market, and momentum effects. The estimated intercept or alpha is interpreted as the monthly abnormal return in excess of what could have been achieved by investments in the four factors. Table 2 shows the regression results of different size (number of stocks going long and short) of portfolio. By doing the sensitivity analysis, the same finding as using CAPM is derived. As long as the size of portfolio increases, the abnormal return decreases, which is confirmed by the related t-statistics (Table 1 and Chart 1). By using the four-factor model, we find that SMB (small market capitalization minus big), HML (high book-to-market ratio minus low), and market excess return do not contribute much due to the relative small coefficients and t-statistics. However, the price momentum, the one more factor we added to Fama-French Three-Factor Model, has a significant impact. Next, we simulate other portfolios with some changes to the above ones. In order to test Boni and Womack s work, we simply split our time range into two even parts: 1996 to 2003 (one year further than their time range) and 2004 to 2011. Besides comparing the similarity or difference with Boni and Womack s work, the new finding is that time range 1996 to 2003 generates more abnormal return than the time range 2004 to 2011 (Appendix). Then, we split our long-short strategy into only long and only short strategies. The surprising result is that long strategy contributes more abnormal return than short strategy. Short strategy generates little return and sometime even negative return. 11
4. Empirical Results 4.1 Test Motivation The motivation of writing this report is to initially test Boni and Womack (2003) partial work with updated data that includes most recent years. Further, based on our detailed research, we can have a more precise perspective on analysts recommendations. Some people state that analysts have bias when they are writing research reports on stocks. Also, there are a lot of studies saying that some sell-side analysts provide very optimistic recommendations to the firms they cover or try to gain investment banking business for their employers (journal: do IBs listen to their own). If this is the case, the value of analysts recommendations would shrink and the recommendations would not take effect as a part of investment advice. Compared with Boni and Womack (2003) work, the big differences are that we use consensus (average) recommendation change to sort stocks, and we include different number of stocks in our portfolio. Initially, our basic assumption is that professional analysts give wise recommendation with their sense on investment, so if investors listen to analysts advice, they would generate profits. To test the value of analysts recommendations and to investigate an effective investment method, we do a series of test which is described above. Generally, we construct three relative distinguished tests by utilizing CAPM and four factor model. These tests are all based on our core trading strategy (long net upgraded firms & short net downgraded firms). 4.2 Findings Table 1 and 2 are the regression results of portfolios with size difference by using CAPM and Fourfactor model through 1996 to 2011 (Appendix). We run seven portfolios with different size. From the tables we can observe the following several things below. Our first finding is that the long-short trading strategy generates abnormal returns (alpha). In the CAPM, longing and shorting 100 stocks, especially, can generate 0.984% abnormal return which is very 12
large. Furthermore, almost all abnormal returns absolute values of t-statistic are bigger than 2, showing that the results are significant, except the 400-stocks portfolio in four-factor model and both 500-stocks portfolios in CAPM. In fact, when the long-short strategy portfolio longs and shorts more than 500 stocks, even if alpha is positive, the t-statistic speaks out that it is no longer significant. Therefore, it is meaningless to construct a portfolio including more than 1000 total stocks. Further, by considering that small sized companies are usually volatile, we construct portfolios which exclude small sized companies (less than 100 million dollars market capitalization). It still generates abnormal return (Table 11 and Table 12). Compared with Table 1 and 2, it can be observed that the abnormal returns after deleting small companies are less than the original ones. However, the abnormal returns without small-cap companies probably are more stable. Based on the finding from Table 1 and 2, it is concluded that small sized portfolio generates high abnormal return. A question may be raised that why not invest only in a small number of stocks instead of in a portfolio including more than 100 stocks to achieve the higher return. Indeed, we do construct a small sized portfolio including only the best and worst 10 stocks at the beginning, and the portfolio s monthly abnormal return is 1.63% in CAPM and 1.38% in four-factor model, which are very big. However, a small sized portfolio may not be considered as a well-diversified one, which means diversifiable risk may exist to eat the abnormal return. Chart 3 in Appendix also shows that although small sized portfolio generates extremely higher abnormal return, it is more fluctuant than bigger sized portfolio. What is more, the t-statistics (3.008 in CAPM and 2.589 in four-factor model) are smaller than most of others in Table 1 and 2 indicating that the portfolio including only small number of stocks is less significant than bigger ones. In our following test, we split time horizon into two different parts (1996-2003 and 2004-2011) to investigate which time period generates more abnormal return. From Table 3, 4, 5 and 6, no matter CAPM or four-factor model, time period 1996-2003 dominates the total abnormal return. All sizes of portfolios abnormal returns between 1996 and 2003 are much bigger than those between 2004 and 2011. 13
The abnormal returns of portfolio which includes long-short 500 stocks are even negative (underperform the market). The absolute values of t-statistic also state that the abnormal returns belonging to 2004-2011 do not have significant impact on the total returns. From another point of view, in terms of the same sized portfolio, the sum of abnormal returns of 1996-2003 and 2004-2011 should be the same as the one in 1996-2011, but in fact, the sum is bigger than the abnormal return in 1996-2011. The reason behind is very technical. Because of the time series we use, the time period is exactly from February, 1996 to December, 2011 (191 months). If we split the time range into 1996-2003 and 2004-2011. The 1 st time period is from February, 1996 to December, 2003, while the 2 nd time period is from February, 2004 to December, 2011. The total months are 190, which is one month shorter than 1996-2011. From the above sensitivity analysis, conclusion is drawn that the abnormal returns between 2004 and 2011 sometimes contribute negative returns to the total abnormal return. Even though there is one month shorter, the summed abnormal return may be bigger. Next, we split our long-short trading strategy into two parts long strategy and short strategy for 1996-2011. No matter CAPM or four-factor model, long strategy generates more abnormal return than short strategy 2. Short strategy plays a useless role in generating abnormal return compared to long strategy. Especially the short strategy in four-factor model, all types of portfolio generate negative return. Chart 4 in Appendix shows this phenomenon. All portfolios belonging to long strategy outperform the market, while all ones belonging to short strategy underperform the market. Based on this finding, it can be concluded that only using long strategy generates more abnormal return. However, even though short strategy is tested out to make negative effects, it could be a good idea to diversify. From another point of view, in terms of the same sized portfolio, the sum of abnormal returns of long strategy and short strategy is smaller than the long-short strategy for the same time period. This makes sense to us because the model 2 A thought why the short strategy is not working well is because we short the companies which have net downgraded average recommendation change. However, some companies stock prices go down as long as the companies themselves. Some of them may bankrupt, which should maximize our return from short strategy. Unfortunately, if a company was bankrupt, its CUSIP would be deleted and it would not be shown on our database. Thus, even though short companies which would bankrupt generates high return, it would not be shown on our result. 14
already deducts risk free rate, so adding up the abnormal returns of both long and short strategies means that one more risk free rate is deducted from the abnormal return, leading to the smaller result than the long-short strategy. What is more, in almost all portfolios by using four-factor model, it can be observed that the absolute values of t-statistics of price momentum are bigger than 2, indicating that the price momentum is statistically significant. It has a big impact on abnormal return. 5. Shortcomings in Research Although our research is very specific and detailed, it still has some shortcomings. Because of the recommendation we utilize is the average one, which means that it is the mean recommendation derived from all individual analyst s recommendations. This is able to alleviate our workload without reducing much accuracy. However, there exist some companies which are followed and evaluated by only a few analysts (one or two). The recommendations from only one or two analysts may not be accurate and persuasive. Furthermore, the lack of more recommendations leads to that some these companies may have the same consensus recommendation change. Even though we also sort them by their market capitalizations, error may occur because of lack of recommendations. Furthermore, in our simulated test, we do not consider some costs which would occur to reduce the abnormal return. Transaction cost is a major issue for our research because we rebalance our portfolio every month depending on analysts recommendation changes. In the month after, we may have some new stocks needed to add into our portfolio because of the net upgrading and net downgrading. At the meantime, in order to keep the size of our portfolio, some stocks which are not listed next month would be sold to close the transactions. Although the size of portfolio does not change, the stocks in the next month may not be the same as the ones in the previous month. Along with the transaction cost, tax occurs when realizing profits. Besides, for short transactions, interest may also be paid to cut down the abnormal returns. 15
In addition, in terms of short strategy, we do not consider excluding the stocks priced less than $5/share due to the time constraint. The reason why these stocks have impact is because these stocks are difficult to borrow and thus difficult to short sell (D Avolio (2002). Last,, the portfolios we construct from 1996 to 2011 have an issue on time period. Originally, the 16 years period includes 192 months in total. However, in our portfolios, only 191 months are included. This is because the analysts recommendations prior to 1996 are somewhat sparse in I/B/E/S, which would not contributable to the results. The first group of recommendations we can collect is from December, 1995. Compared with the recommendations from January, 1996, we generate the changes of recommendations in January. Based on the changes, February s return tells the relationship between recommendation change and abnormal return. Due to the time issue, error may exist in our result. 6. Conclusions To test the value of analysts recommendation, we utilize Boni and Womack s long-short strategy and construct several portfolios. Our research comes up with a general conclusion that doing investment according to analysts recommendation change does outperform the market. Their recommendations take effect as a part of investment advice. The long-short trading strategy works well in the market neutral approach. By using this strategy, as long as the size of portfolio increases, the abnormal return decreases. However, this throws out a dilemma which is that investors their own should consider how to balance their abnormal returns and diversifiable risk. In addition, we conclude that from 1996 to 2011, the first eight-year period (1996-2003) contributes more abnormal return than the second period (2004-2011). Furthermore, compared with short strategy, separated long strategy generated more abnormal returns. The short strategy sometimes makes a side effect to the whole portfolio. This also provides an alternative to investors. Investors with risk tolerance may only take long strategy, while investors with risk averse may take the long-short strategy to hedge their risk. In the four-factor model, we also find that price momentum always has a significant impact on abnormal return besides our main factor analysts 16
recommendation change. Because of the time constraint, some factors which might have impacts on our results are ignored. Transaction costs, tax, and interest could potentially reduce our ideal abnormal return. Also, the shortcoming from stock price will be considered in our further research. 17
References B. Barber, R. Lehavy, M. McNichols, B. Trueman (2001). Can investors profit from the prophets Security analyst recommendations and stock returns. Journal of Finance, 56 (2001), pp. 531 563 Boni, L., Womack, K.L. (2006). The Journal of Financial and Quantitative Analysis. 41(1) 2006-03-03 P85 A.C.W. Chui, S. Titman, K.C.J. Wei (2001). Momentum, legal systems and ownership structure: An analysis of Asian stock markets. Working Paper, Hong Kong Polytechnic University D'Avolio. G. (2002) Market for Borrowing Stock. Journal of Financial Economics. 66 (2002), 271-306. N. Jegadeesh, J. Kim, S.D. Krische, C. Lee.(2004) Analyzing the analysts: when do recommendations add value? Journal of Finance, 59 (2004), pp. 1083 1124 N. Jegadeesh, Woojin Kim (2006). Journal of Financial Markets. Volume 9, Issue 3, August 2006, Pages 274 309 S.E. Stickel (1995). The anatomy of the performance of buy and sell recommendations Financial Analysts Journal, 51 (1995), pp. 25 39 18
Appendix Table 1: CAPM Model of Market Portfolio by Long-Short Strategy 96-11 Alpha is the monthly abnormal return followed by its related t-statistic in the brackets. A positive alpha is favorable. T-statistic shows the significance of its variable. If the absolute value of t-statistic is bigger than 2, it is concluded that the variable (alpha) has a significant impact. Beta is the sensitivity of the excess portfolio return to the excess market return followed by its related t-statistic in the brackets. The number of observations is the number of months the portfolio has. The test starts from February, 1996 to December, 2011. R-squared measures how well the CAPM predicts the actual performance of an investment or portfolio. Alpha (1) (2) (3) (4) (5) (6) (7) Long-Short 50 0.012 (4.014) Long-Short 100 0.00984 (4.174) Long-Short 150 0.00868 (4.483) Long-Short 200 0.00699 (3.998) Long-Short 300 0.00515 (3.377) Long-Short 400 0.00675 (2.953) Long-Short 500 0.00233 (1.769) Beta 0.0221-0.0269-0.0339-0.024-0.05 - -0.0455 (0.364) (-0.564) (-0.0865) (-0.679) (-1.622) 0.112 (-1.79) (-2.511) Number of 191 191 191 191 191 191 191 observations R-squared 0.001 0.002 0.004 0.002 0.014 0.063 0.017 19
Table 2: Four Factor Model of Market Portfolio by Long-Short Strategy 96-11 Alpha is the monthly abnormal return followed by its related t-statistic in the brackets. A positive alpha is favorable. T-statistic shows the significance of its variable. If the absolute value of t-statistic is bigger than 2, it is concluded that the variable (alpha) has a significant impact. The numbers corresponding to SMB, HML, Excess Return, and Momentum are their coefficients with their t-statistics in brackets. SMB stands for small (market capitalization) minus big. HML stands for high (book-tomarket ratio) minus low. Excess Return is the market excess return. The number of observations is the number of months the portfolio has. The test starts from February, 1996 to December, 2003. Alpha (1) (2) (3) (4) (5) (6) (7) Long-Short 50 0.00958 (3.498) Long-Short 100 0.00785 (3.631) Long-Short 150 0.00691 (3.889) Long-Short 200 0.00551 (3.482) Long-Short 300 0.00368 (2.773) Long-Short 400 0.00306 (1.583) Long-Short 500 0.00086 (0.797) SMB -0.0768 (-0.975) -0.0043 (-0.689) -0.0147 (-0.287) -0.0205 (-0.449) -0.0334 (-0.875) -0.0162 (-0.353) -0.0224 (-0.718) HML 0.227 (2.734) 0.15 (2.290) 0.151 (2.798) 0.0788 (1.639) 0.0683 (1.696) 0.145 (2.411) 0.0897 (2.729) Excess Return 0.18 (2.95) 0.0918 (1.905) 0.0625 (1.576) 0.0597 (1.691) 0.0352 (1.189) 0.0308 (0.657) 0.0304 (1.257) Momentum 0.324 (6.499) 0.257 (6.518) 0.205 (6.346) 0.201 (6.977) 0.201 (8.337) 0.221 (7.135) 0.169 (8.544) Number of observations 191 191 191 191 191 191 191 20
Table 3: CAPM Model of Market Portfolio by Long-Short Strategy 96-03 Alpha (1) (2) (3) (4) (5) Long-Short 100 0.0182 (4.807) Long-Short 200 0.0131 (4.424) Long-Short 300 0.00887 (3.428) Long-Short 400 0.00675 (2.953) Long-Short 500 0.00497 (2.331) Beta -0.151 (-2.062) -0.0998 (-1.739) -0.0982 (-1.95) -0.112 (-2.511) -0.0939 (-2.265) Number of observations 95 95 95 95 95 R-squared 0.044 0.031 0.039 0.063 0.052 21
Table 4: Four Factor Model of Market Portfolio by Long-Short Strategy 96-03 Alpha (1) (2) (3) (4) (5) Long-Short 100 0.0134 (3.953) Long-Short 200 0.00973 (3.655) Long-Short 300 0.0053 (2.374) Long-Short 400 0.00306 (1.583) Long-Short 500 0.00142 (0.812) SMB -0.0692 (-0.862) -0.0586 (-0.928) -0.0379 (-0.716) -0.0162 (-0.353) -0.012 (-0.289) HML 0.135 (1.279) 0.0618 (0.746) 0.104 (1.499) 0.145 (2.411) 0.138 (2.532) Excess Return 0.0291 (0.354) 0.0191 (0.296) 0.0354 (0.654) 0.0308 (0.657) 0.0429 (1.010) Momentum 0.328 (6.038) 0.252 (5.898) 0.244 (6.823) 0.221 (7.135) 0.217 (7.710) Number of observations 95 95 95 95 95 22
Table 5: CAPM Model of Market Portfolio by Long-Short Strategy 04-11 Alpha (1) (2) (3) (4) (5) Long-Short 100 0.00191 (0.749) Long-Short 200 0.00104 (0.619) Long-Short 300 0.00148 (0.943) Long-Short 400 0.000278 (0.184) Long-Short 500-0.00042 (-0.325) Beta 0.103 (1.926) 0.0525 (1.490) -0.00152 (-0.00461) 0.00733 (0.232) 0.00536 (0.197) Number of observations 95 95 95 95 95 R-squared 0.038 0.023 0.000 0.001 0.000 23
Table 6: Four Factor Model of Market Portfolio by Long-Short Strategy 04-11 Alpha (1) (2) (3) (4) (5) Long-Short 100 0.00208 0.835 Long-Short 200 0.00102 0.65 Long-Short 300 0.00142 (1.008) Long-Short 400 0.000278 (0.199) Long-Short 500-0.00042 (-0.341) SMB -0.0372 (-0.309) 0.0677 (0.891) 0.0112 (0.164) -0.0353 (-0.522) -0.0298 (-0.507) HML -0.162 (-1.476) -0.158 (-2.28) -0.145 (-2.338) -0.0939 (-1.528) -0.0925 (-1.725) Excess Return 0.178 (2.774) 0.0977 (2.416) 0.0649 (1.788) 0.0717 (1.997) 0.0597 (1.904) Momentum 0.00902 (1.715) 0.0788 (2.376) 0.108 (3.619) 0.0995 (3.382) 0.0763 (2.973) Number of observations 95 95 95 95 95 24
Table 7: CAPM Model of Market Portfolio by Long Strategy 96-11 Alpha (1) (2) (3) Long 100 0.00551 (2.296) Long 200 0.00447 (2.045) Long 300 0.0036 (1.779) Beta 1.176 (24.24) 1.195 (27.03) 1.199 (29.34) Number of observations 191 191 191 R-squared 0.757 0.795 0.820 25
Table 8: Four Factor Model of Market Portfolio by Long Strategy 04-11 Alpha (1) (2) (3) Long 100 0.00673 (4.597) Long 200 0.006 (4.783) Long 300 0.00532 (4.987) SMB 0.754 (17.9) 0.704 (19.52) 0.669 (21.79) HML 0.206 (4.635) 0.189 (4.964) 0.165 (5.105) Excess Return 1.026 (31.41) 1.045 (37.34) 1.050 (44.08) Momentum -0.102-0.120-0.127 (-3.842) (-5.240) (-6.519) Number of observations 191 191 191 26
Table 9: CAPM Model of Market Portfolio by Short Strategy 96-11 Alpha (1) (2) (3) Short 100 0.0019 (0.641) Short 200 0.00008 (0.0335) Short 300-0.00087 (-0.361) Beta -1.204 (-20.05) -1.22 (-23.42) -1.25 (-25.62) Number of observations 191 191 191 R-squared 0.680 0.744 0.776 27
Table 10: Four Factor Model of Market Portfolio by Short Strategy 04-11 Alpha (1) (2) (3) Short 100-0.00129 (-0.691) Short 200-0.00289 (-1.917) Short 300-0.00406 (-3.234) SMB -0.792 (-14.75) -0.720 (-16.58) -0.698 (-19.34) HML -0.0589 (-1.04) -0.113 (-2.476) -0.100 (-2.637) Excess Return -0.936 (-22.48) -0.987 (-29.33) -1.017 (-36.36) Momentum 0.355 0.317 0.324 (10.44) (11.53) (14.19) Number of observations 191 191 191 28
Table 11: CAPM Model of Market Portfolio by Long-Short Strategy 96-11 (Market Cap above 100 million dollars) Alpha (1) (2) (3) (4) (5) (6) (7) Long-Short 50 0.00833 (3.156) Long-Short 100 0.00658 (3.238) Long-Short 150 0.00507 (2.864) Long-Short 200 0.00468 (2.935) Long-Short 300 0.00312 (2.295) Long-Short 400 0.00196 (1.631) Long-Short 500 0.00088 (0.813) Beta 0.0482 (0.905) 0.00955 (0.232) 0.0155 (0.434) -0.00933 (-0.289) -0.0249 (-0.905) -0.0249 (-1.025) -0.0195 (-0.890) Number of 191 191 191 191 191 191 191 observations R-squared 0.004 0.000 0.001 0.000 0.004 0.006 0.004 29
Table 12: Four Factor Model of Market Portfolio by Long-Short Strategy 96-11 (Market Cap above 100 million dollars) Alpha (1) (2) (3) (4) (5) (6) (7) Long-Short 50 0.00718 (2.841) Long-Short 100 0.00548 (2.845) Long-Short 150 0.00394 (2.449) Long-Short 200 0.00362 (2.534) Long-Short 300 0.00197 (1.640) Long-Short 400 0.00092 (0.854) Long-Short 500-0.00015 (-0.157) SMB -0.109 (-1.492) -0.00342 (-0.0616) 0.00622 (0.134) -0.0115 (-0.280) -0.0114 (-0.328) 0.00248 (0.080) 0.0105 (0.381) HML 0.0504 (0.658) 0.0105 (0.179) -0.00139 (-0.0285) -0.0122 (-0.281) 0.0315 (0.863) 0.0364 (1.116) 0.0453 (1.561) Excess Return 0.151 (2.675) 0.0730 (1.699) 0.0785 (2.186) 0.0524 (1.644) 0.0390 (1.452) 0.0290 (1.207) 0.0323 (1.513) Momentum 0.223 (4.839) 0.184 (5.251) 0.194 (6.615) 0.185 (7.127) 0.168 (7.671) 0.143 (7.277) 0.136 (7.818) Number of observations 191 191 191 191 191 191 191 30
Chart 1: This figure shows the change of abnormal return (alpha) corresponding to the size of portfolio between 1996 and 2011. The numbers in brackets are the t-statistics related to its abnormal return. 0.018 0.016 (3.008) 0.0163 Long-short Strategy Using CAPM Model (96-11) Abnormal Return 0.014 0.012 0.01 0.008 0.006 0.004 0.002 (4.014) 0.012 (4.174) 0.00984 (4.483) 0.00868 (3.998) 0.00699 (3.377) 0.00515 (2.953) 0.00675 (1.769) 0.00223 0 0 100 200 300 400 500 600 Size of Portfolio 31
Chart 2: This figure shows the change of abnormal return (alpha) corresponding to the size of portfolio between 1996 and 2011. The numbers in brackets are the t-statistics related to its abnormal return. 32
Chart 3: Cumulative Returns of Market Portfolio by Long-Short Strategy 96-11 compared to Market Return 16 14 12 10 8 6 4 50 100 150 200 300 400 500 Mkt 2 0 Jan-96 Jul-96 Jan-97 Jul-97 Jan-98 Jul-98 Jan-99 Jul-99 Jan-00 Jul-00 Jan-01 Jul-01 Jan-02 Jul-02 Jan-03 Jul-03 Jan-04 Jul-04 Jan-05 Jul-05 Jan-06 Jul-06 Jan-07 Jul-07 Jan-08 Jul-08 Jan-09 Jul-09 Jan-10 Jul-10 Jan-11 Jul-11 33
Chart 4: Raw Return of Long Strategy Compared with Short Strategy in 96-11 18 Long vs. Short 16 14 12 10 8 6 4 Long 100 Long 200 Long 300 Short 100 Short 200 Short 300 Mkt 2 0 Jan-96 Jul-96 Jan-97 Jul-97 Jan-98 Jul-98 Jan-99 Jul-99 Jan-00 Jul-00 Jan-01 Jul-01 Jan-02 Jul-02 Jan-03 Jul-03 Jan-04 Jul-04 Jan-05 Jul-05 Jan-06 Jul-06 Jan-07 Jul-07 Jan-08 Jul-08 Jan-09 Jul-09 Jan-10 Jul-10 Jan-11 Jul-11