To what extent does 2008 financial
crisis affect the performance of
stocks regarding volatility in the U.S.?
Name Jiani Geng
Student number 10830685
Programme Economics and Business
Track Finance and Organization
Supervisor Zou Liang
Date 29 January 2017
Abstract ： The empirical relation between total volatility and stock return is
examined before and after the 2008 financial crisis. First of all, the results partially agree with the theoretical model that stocks with high systematic risk have high returns because of the positive relation between systematic risk and return. Next, the performance of stocks with low volatility violates the theory but is consistent with the empirical findings that low volatility stocks outperform than the prediction of theoretical model. Finally, the 2008 financial crisis does have influences on stock returns with both pre crisis and post crisis effects.
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Table of content
1. Introduction ... 1
2. Related Literature... 4
3. Data and methodology ... 6
3.1 Data ... 6 3.2 Methodology ... 7 4. Hypotheses ... 8 5. Main results ... 9 5.1 Sample period 2000-2015... 9 5.2 Sub-sample period 2000-2008 ... 10 6. Analysis ... 12 7. Conclusion ... 14 8. References ... 16 9. Appendix ... 18
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1. Introduction
The Capital Asset Pricing Model, or CAPM, developed by Sharpe (1964) and Lintner (1965), lays the foundation of asset pricing theory. The CAPM predicts that there is a consistent positive relationship between assets’ expected returns and systematic risks (Sharpe, 1964). Systematic risk, a common risk representing market-wide news about the whole economy, affects all stocks in the market (Berk & DeMarzo, 2013). Besides, firm-specific risk is mitigated when individual stocks are combined into a large portfolio. Thus, the diversified firm-specific risk does not have much influence. That is, systematic risk plays a decisive role in asset pricing. According to the CAPM, the greater the systematic risk, the higher the expected return. Intuitively, in order to persuade an investor to purchase a stock with higher risk, a higher expected return is required in exchange for accepting higher risk. And it makes sense in the real world. However, some empirical results are at variance with the predictions of the theory.
Fama and French (2004) find contrary results that portfolios with low systematic risk exert higher returns and portfolios with high systematic risk generate lower returns. Blitz and van Vliet (2007) study the time period from 1985 to 2006 in the U.S, Europe and Japan, and show that stocks with low historical volatility exert superior returns in terms of CAPM alphas. Blitz, Pang and van Vliet (2013) apply the CPAM to the emerging markets. Their sample period is from 1989 to 2010 and their findings indicate that the relation between risk and return in emerging markets is flat, or even negative, for portfolios of stocks ranked on historical volatility. Ang, Hodrick, Xing, and Zhang (2006) studied US stock market from January 1986 to December 2000 and find that stocks with high idiosyncratic volatility bear abnormal low returns in the U.S. market. Idiosyncratic volatility, which is firm-specific risk, affects the return of the company itself only. The effect of idiosyncratic volatility is also found by Lintner (1965), who finds that
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idiosyncratic volatility has a positive coefficient in cross-sectional regressions. Afterwards, Ang et al. (2009) expended their sample period from January 1980 to December 2013 and included firms from 23 developed countries. The findings that low idiosyncratic volatility stocks outperform high idiosyncratic volatility stocks also apply to other developed countries.
These empirical findings violate the theory and the findings indicate that the stocks with low volatility outperform the stocks with high volatility seem to be pertinent worldwide. Nevertheless, the volatility is defined differently. The total volatility is mainly divided into two parts, systematic volatility and idiosyncratic volatility. As shown in the findings of these studies, both types of volatility play a role in the asset pricing. However, the two types of volatility have opposite effects on stock returns. Additionally, these studies mainly focused on a long time period and ignored the effect of an incident happened in the chosen time period. Such an incident may influence the stock returns enormously, for example stock market crash. Therefore, it brings the interest to me whether a financial event influences the performance of the stock returns. 2008 financial crisis, which led to the great depression, swept across the world. Obviously, the stock market suffered extremely. Thus, my research question is: to what extent does 2008 financial crisis affect the performance of stocks with regards to total volatility in the U.S?
The total volatility is measured by historical volatility of monthly returns. 200 companies in the U.S are randomly selected and they are sorted into quintile portfolios according to their past five year historical volatility of monthly returns. To study the effect of the financial crisis, two sample periods are tested which are ranging from January 2000 to August 2008 and ranging from September 2008 to December 2015. Carhart four-factor model is applied as the regression model in this paper (Carhart, 1997). The four-factor adjusted alphas obtained from the four-factor model show that both low and high volatility stocks have positive alphas in both sample periods. Additionally, the 2008 financial crisis does have
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effects on stock returns. Pre crisis effects count for the changes of stock returns except for the stocks with middle volatility. Post crisis effects influence the performance of stocks with higher volatility.
The main contributions to the existing literature are as follows. Firstly, a new sample period January 2000 through December 2008 extends the existing literature. Secondly, the findings are partially in line with Blitz and van Vliet (2007) and Fama and French (2004) that low volatility stocks outperform than predicted by the theory. Nevertheless, the performance of high volatility stocks is consistent with the theoretical model (Sharpe, 1964). Finally, the 2008 financial crisis does influence the stock returns regarding volatility. There are both pre crisis effects and post crisis effects.
An outline of the rest of the paper follows. In section 2, the related literature of the evolution of the Capital Asset Pricing Model (CAPM) is described. The reason why 4-factor model is used and how the model fit the paper are discussed. In section 3, data obtained and the methodology applied are explained. The hypotheses generated by the research question are to be tested are described in section 4. In section 5, the main results are presented and interpreted. In section 6, analysis and possible explanations to the results are included. In section 7, a conclusion is drawn, including limitations and suggestions for further research.
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2. Related Literature
In this section, the background of the regression model used in the paper is represented in detail.
Sharpe (1964) and Lintner (1965) first introduce Capital Asset Pricing Model (CAPM) to estimate the cost of capital, which has been the common method in practice. The CAPM model states that the return of a stock in excess of risk-free rate depends on risk premium for the stock. The stock’s risk premium equals market risk premium (market portfolio return in excess of risk free rate) multiply stock’s beta (stock’s sensitivity with respect to the market portfolio). The beta here is the systematic volatility. According to the CAPM model, there is a security market line along which all stocks should lie on this line based on their expected returns and volatility (Berk & DeMarzo, 2013). That is, there is a positive linear relation between volatility and return. The CAPM model is formulated as:
However, there are several empirical contradictions of the Sharpe-Lintner model. Banz (1981) finds the size effect that smaller firms had higher returns than larger firms. Chan, Haomao and Lakonishok (1991) examine Japan stock market and discovered that book to market ratio also played a role in expected returns. Besides, Basu (1983) shows that stocks of high earnings price ratio (E/P) firms earn higher risk-adjusted returns than stocks of low E/P. These empirical findings indicate the inefficient explanatory power of market beta because market beta fails the tests.
Fama and French (1992) find that the relation between market beta and return is weak and even flat when market is the only dependent variable. They included size and book-to-market equity variables that are significant in determining the expected returns to complete the Sharpe-Lintner model. It is the Fama-French 3-factor model, which is shown as:
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Carhart (1997) constructs 4-factor model using Fama-French 3-factor model (1993) and includes an additional momentum variable. Carhart (1997) finds that the 4-factor model explains spread and pattern in the portfolios better than the Sharpe-Lintner model. The model is as follows:
The Sharpe-Lintner CAPM model does not predict the alphas precisely because the market factor cannot fully capture the stock returns. Compared with Sharpe-Lintner CAPM model and Fama-French 3-factor model, the Carhart 4-factor model predicts the alphas more precisely as more explanatory variables are added. In this paper, 4-factor model is applied to predict adjusted alphas that are going to be tested.
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3. Data and methodology
In this section, the data and methodology used throughout the paper are described.
3.1 Data
Data sources are Wharton Research Data Services (WRDS) for four factors and return data. 200 firm stocks are randomly chosen from the data base for the research purposes. Starting from January 2000 to December 2015, the monthly holding period returns at the end of every month are taken as the monthly returns for the chosen companies. To study the effect of 2008 financial crisis on stock returns, two sample periods are to be focused. The two sample periods range from January 2000 to August 2008 and range from September 2008 to December 2015. On September 15, 2008, the bankruptcy of Lehman Brothers marked the beginning of the financial storm. Hence, September 2008 is treated as the splitting date and the second sample period (September 2008 through December 2015) is treated as post crisis period.
One month Treasury bill rate is used for risk free rate. Firms’ monthly returns in excess of risk free rate are denoted as firms’ excess returns. Market excess returns, small-minus-big returns, high-minus-low returns, momentum factors are collected on monthly basis for the same sample period.
Historical volatility of monthly return is chosen to measure the total volatility. Based on the past five year volatility of monthly returns, stocks are ranked from lowest volatility to highest and equally weighted quintile portfolios are constructed. Compared with the previous study where the past three year volatility of monthly returns is chosen, the past five year volatility of monthly returns used here is to reduce the portfolio turnover (Blitz & van Vliet, 2007). Stocks with lowest volatility are assigned to the top quintile, and the bottom quintile is composed of highest volatility stocks. A point worth noting is that there is not enough data to calculate past five year volatility for the period 2008-2015. The solution used is to calculate
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the volatility from September 2008 to December 2013. And this time period is still included when testing the post crisis effect.
In each portfolio, there are 192 observations for the whole sample period, among which 104 observations are for the period before the crisis and 88 observations are for the period after the crisis.
3.2 Methodology
The methodology applied is the four-factor model, which is an ordinary least squares (OLS) regression. The model is as follows:
is the portfolio excess return, is the four-factor adjusted alpha, is the market excess return and is the beta of the portfolio with respect to market. , and denote the return on size, value and momentum factors. , and are the betas regarding size, value and
momentum factors respectively. is the residuals that are not captured by the model. The standard deviation of is the idiosyncratic volatility. In this model, is the dependent variable, and , , and are the independent variables. Statistical significance of the alphas and betas is obtained directly from the OLS regression.
The four-factor adjusted alphas are more precise. Therefore, the t-tests on the alphas are more accurate. The differences between alphas in two-sub time periods are also tested to check whether the performance of stocks changes before and after 2008 financial crisis. The method used here is chi-square test, which is automatically done by STATA.
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4. Hypotheses
In this section, the hypotheses regarding the research question are formalized.
Three hypotheses are considered. The first two hypotheses are that realized returns of stocks with low volatility outperform than expected returns, and stocks with high volatility underperform than expected. The hypotheses can be formulated parametrically as,
and represent the constant of portfolios with low volatility and high volatility respectively.
The third hypothesis is that stock performances change after the 2008 financial crisis, which can be expressed as,
and denote the constant of portfolios before the crisis and after the
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5. Main results
In this section, main empirical findings are presented. Full sample results are described firstly, followed by sub sample results.
5.1 Sample period 2000-2015
Table 1 contains an overview of the main results on the two time periods for the quintile portfolios ranked on past five year volatility. Regression results of sample period January 2000 through August 2008 are presented in panel A of Table 1, and results of sample period September 2008 through December 2015 are presented in panel B of Table 1. The top quintile portfolio, which is portfolio 1, contains the lowest risk stocks. The bottom quintile portfolio, which is portfolio 5, contains highest risk stocks. Mean denotes each portfolio’s monthly excess return. Total volatility is each portfolio’s standard deviation of the sample period involved with the correlations. Idiosyncratic volatility is the standard deviation of the residuals. , , and are the estimations of the coefficients where the regressions are run at a monthly frequency using each portfolio’s returns in excess of the one-month U.S. Treasury bill yield.
In panel A, the mean monthly excess returns of all portfolios are positive. The mean excess return of top quintile portfolio is 0.54% and that of bottom quintile portfolio if 2.11%. The difference between top and bottom quintile portfolios is 1.57%. Total volatility of the top quintile portfolio is 2.87%. Total volatility of bottom quintile portfolio is almost three times as large as that of top quintile portfolio. Idiosyncratic volatility of the top quintile portfolio is 1.81% and idiosyncratic volatility of the bottom quintile portfolio is 3.69%, nearly twice as that of the top quintile portfolio. Regression results show that the sensitivities of all portfolios to market movement and size factor are all positively significant at 1% level. Coefficients of all portfolios on momentum factor are all negatively significant at 1% level. Coefficients of portfolios that have low to middle volatility on value factor are positively significant at 1% level, while coefficients of higher
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volatility portfolios on value factor are insignificant. Besides, the positive alphas of higher volatility portfolios are statistically significant at 1% level.
In panel B, the mean monthly excess return is 0.95% for top quintile portfolio, which is slightly higher than that in panel A. The mean monthly excess return for bottom quintile portfolio is 1.74%, which is lower than that in panel A. Total volatility of all portfolios increase after the financial crisis, and the volatility of bottom quintile portfolio (3.11%) is still three times as large as that of top quintile portfolio (9.12%). Idiosyncratic volatility of the top quintile portfolio is 1.24%, which is 2% less than that of the bottom quintile portfolio (3.26%). The positive coefficients on market factor and size factor are all statistically positive at 1% level. The positive coefficients on value factor are significant for top quintile portfolio at 1% level. The coefficients on momentum factor decrease with increasing volatility, and are only statistically significant for top and bottom quintile portfolios at 1% level. The alpha of top quintile portfolio is positively significant, which is consistent to the previous findings (Ang A. , Hodrick, Xing, & Zhang, 2009). The alpha of bottom quintile portfolio is insignificantly different from zero. The Chi-square test, which tests whether the alphas change after the 2008 financial crisis, shows that only the alphas of middle to high volatility stocks changes significantly.
5.2 Sub sample period 2000-2008
As the findings of panel A in Table 1 are different from empirical studies, the full time period is split to see whether the alphas are significantly larger than zero till some specific date. By regressing the model year by year, the alphas are significantly positive until the end of 2004. Therefore, December 2004 is decided to be the splitting date of the sub sample period.
Table 2 reports the results of the four-factor regressions using monthly returns for 2 sub-sample periods. The regression results of period January 2000 through December 2004 are shown in panel A, and the results of period January 2005 through August 2008 are shown in panel B. There are 60 observations in panel A and 44 observations in panel B.
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In panel A, the monthly average excess returns are positive for all portfolios, increasing from 1.06% for top quintile portfolio to 2.93% for bottom quintile portfolio. Total volatility of top quintile portfolio is 3.04%, and total volatility of bottom quintile portfolio is 10.5% which is more than three times than that of top quintile portfolio. Idiosyncratic volatility is 1.90% for the top quintile portfolio and 4.49% for the bottom quintile portfolio. The coefficients on market factor and size factor are all positive at 1% significance level. The coefficients on value factor are positively significant for lower volatility portfolios. The coefficients on momentum factor are negatively significant for higher volatility portfolios. The alpha of top quintile portfolio is now statistically larger than zero and so as the alpha of bottom quintile portfolio.
In panel B, the average monthly excess returns decrease for all portfolios, and the monthly excess return of top quintile portfolio even turns to negative. The excess return of top quintile portfolio drops to -0.18% and that of bottom quintile portfolio declines to 0.89%. The main reason is that the risk-free rate (U.S monthly Treasury bill rate) increases in this period. As shown in Figure 1, the risk-free rate increases form the end of 2004 and peaks at 2006. Total volatility of all portfolios also decreases. Total volatility of top quintile portfolio is 2.65%, and total volatility of bottom quintile portfolio is 4.17% which is less than twice of that of top quintile portfolio. Idiosyncratic volatility of the top quintile portfolio does not change much, which is 1.51%, while idiosyncratic volatility of the bottom quintile portfolio decreases to 1.74%. The coefficients on market factor and size factor are all positively significant at 1% level. The coefficients of lower volatility portfolios on value factor are statistically positive at 5% level. The coefficients on momentum factor are only negatively significant for top and bottom quintile portfolios. The alphas of low volatility portfolios are insignificantly different from zero and the alpha of bottom quintile portfolio is positively larger than zero at 5%. The Chi-square test of alphas shows that the alphas of lower and higher volatility portfolios change significantly after 2005. The alphas of portfolios with middle volatility do not have significant differences.
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6. Analysis
In this section, the differences between alphas in different sample periods are analyzed. Possible explanations for the abovementioned differences are given.
In each panel of two tables, the mean excess returns increase with the systematic volatility and also the total volatility. Nonetheless, the alphas of all portfolios are positive, partially inconsistent with the findings of Fama and French (2004) that low-beta (low systematic risk) stocks have positive alphas and high-beta (high systematic risk) stocks have negative alphas. Although all the alphas are positive, they are not all statistically larger than zero.
According to the results of the two tables, since the beginning of 2005, the performance of lower volatility portfolios started to underperform than before. After the crisis, the lower volatility portfolios perform well as usual. That is, the alphas of lower volatility portfolios become indifferent from zero in sub-sample period January 2005 through August 2008. However, in the sample periods before 2005 and after the 2008 crisis, the alphas of lower volatility portfolios are significantly larger than zero, which implies that the lower volatility portfolios outperform than what the theory predicts. The possible explanation that could explain the change of alphas is that lower volatility portfolios have low systematic volatility (low ) but may have high idiosyncratic volatility. Fluctuations of stock returns are influenced by both systematic risk and idiosyncratic risk. The idiosyncratic risk is firm specific and independent of the market effect (Berk & DeMarzo, 2013). In Panel B of Table 2, the total volatility of the top quintile portfolio is rather low (2.65%), while idiosyncratic volatility is 1.51%, which is more than half of the total volatility. As shown in the findings of Ang et al. (2006) (2009), stocks with high idiosyncratic volatility tend to have lower returns than stocks with low idiosyncratic volatility. In their research, the value of idiosyncratic volatility is calculated and they do not measure the ratio of idiosyncratic volatility in the total volatility. However, the high ratio might lower returns and thus causing the insignificant positive alphas.
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The alphas of the bottom quintile portfolios are significantly positive before the 2008 financial crisis, and are still positive but insignificant after the crisis. The positive alphas of the bottom quintile portfolios are in line with the CAPM theory which states that higher beta stocks have higher returns. On the other hand, this is inconsistent with what Blitz and van Vliet (2007) and Blitz et al. (2013) find. In their research, the alphas of the bottom quintile portfolios are significantly negative. This might be explained by idiosyncratic volatility if the ratio of idiosyncratic volatility does have influence on the stock returns. The ratio of idiosyncratic volatility of the bottom quintile portfolio is 35.7% (3.26%/9.12%) after the crisis, while the ratios are above 40% in other sample periods. As the ratio of idiosyncratic volatility declines, it has positive effects on stock returns. Consequently, the alpha of the bottom quintile portfolio is positive but insignificantly different from zero since September 2009 when the bottom quintile portfolio started suffering the crisis and generating low or even negative returns.
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7. Conclusion
In this paper, the relation between stock return and volatility and whether the 2008 financial crisis affect this relation are studied based on U.S market. The main findings are concluded as follows. In the sample period 2000-2008, the alphas of both low and high volatility stocks are positive. However, the alphas of lower volatility stocks are insignificant and that of higher volatility stocks are statistically significant. The results reverse in the sample period 2008-2015, where alphas of lower volatility stocks are positively significant and positive alpha of highest volatility stocks is insignificant. The changes of the alphas are significant for higher volatility stocks, indicating that the 2008 crisis does affect the performance of stocks with high volatility. In the sub sample period 2000-2004, alphas of low and high volatility stocks are all positively significant, while only the alpha of high volatility stocks is positively significant in the sub sample period 2005-2008. The changes of the alphas in the two sub sample periods are significant for both lower and higher volatility stocks. This implies that there could be pre crisis effects. Thus, the 2008 financial crisis may both have pre crisis and post crisis influences on stock returns regarding volatility. The pre crisis effects affect stocks except those with middle volatility and the post crisis effects affect stocks with higher volatility.
Overall, stocks with low systematic volatility have low total volatility and vice versa for stocks with high systematic volatility. Both low and high total volatility stocks have positive alphas. The positive alphas of low volatility stocks are contrary to the predictions of the theory, but are consistent with the empirical findings (Blitz & van Vliet, 2007). The positive alphas of high volatility stocks are in line with the theoretical model, stating that the relation between return and systematic volatility should be positive (Sharpe, 1964). That is, high systematic volatility stocks are expected to exert high returns. Nonetheless, in studies of Ang et al. (2006) (2009) and Blitz et al. (2013), the results show that high volatility stocks generate lower returns than prediction, implied by the negative alphas.
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Ang et al. (2006) (2009) further show that idiosyncratic volatility is negatively related to the stock returns. In this paper, effects of idiosyncratic volatility are not clear but the ratio of idiosyncratic volatility might be responsible for the insignificance of alphas of low volatility stocks in period 2005-2008. Therefore, the study of the effect of the ratio of idiosyncratic volatility on stock returns when suffering financial crisis may provide more evidence to support the findings in the paper. Besides, the period after 2008 financial crisis can be further studied on a yearly basis to test whether some policy implemented for economic recovery after the crisis may influence the stock returns. In such way, the effects of the crisis are investigated intensively.
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8. References
Ang, A., Hodrick, J. H., Xing, Y., & Zhang, X. (2006). The Cross-Section of Volatility and Expected Returns. Journal of Finance , 61(1), 259-299.
Ang, A., Hodrick, J. R., Xing, Y., & Zhang, X. (2009). High Idiosyncratic Volatility and Low Returns: Internation and Further U.S. evidence. Journal of Financial Economics , 91(1), 1-23.
Banz, R. W. (1981). The Relationship Between Return and Market Value of Common Stocks. Journal of Financial Economics , 9(1), 3-18.
Basu, S. (1983). The Relationship Between Earnings' Yield, Market Value and Return for NYSE Common Stocks: Further Evidence. Journal of Financial Economics , 12(1), 129-156.
Berk, J., & DeMarzo, P. (2013). Corporate Finance. Pearson.
Blitz, D. C., & van Vliet, P. (2007). The Volatility Effect: Lower Risk Without Lower Return. Journal of Portfolio Management , 1-17.
Blitz, D., Pang, J., & van Vliet, P. (2013). The Volatility Effect in Emerging Markets. Emerging Markets Review , 16, 31-45.
Carhart, M. M. (1997). On Persistence in Mutual Fund Performance. Journal of Finance , 52(1), 57-82.
Chan, L. K., Hamao, Y., & Lakonishok, J. (1991). Fundamentals and Stock Returns in Japan. Journal of Finance , 46(5), 1739-1764.
Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics , 33(1), 3-56.
Fama, E. F., & French, K. R. (2004). The Capital Asset Pricing Model:Theory and Evidence. Journal of Economic Perspectives , 18(3), 25-46.
Fama, E. F., & French, K. R. (1992). The Cross-Section of Expected Stock Returns. Journal of Finance , 47(2), 427-465.
Jobson, J. D., & Korkie, B. M. (1981). Performance Hypothesis Testing with the Sharpe and Treynor Measures. Journal of Finance , 36, 889-908.
Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. Review of Economics and Statistics , 47, 13-37.
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Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk. Journal of Finance , 19, 425-442.
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9. Appendix
Table 1 Regression of portfolios’ excess returns on four factors for periods January 2000 through August 2008 and September 2008 through December 2009
Dependent variable = portfolio’s excess return=portfolio’s return- risk-free rate Panel A: January 2000 through August 2008
p1 p2 p3 p4 p5 Mean Total Volatility Idiosyncratic Volatility 0.54% 2.87% 1.81% 0.92% 3.60% 1.99% 1.13% 4.22% 2.09% 0.98% 5.44% 1.97% 2.11% 8.39% 3.69% 0.429*** 0.563*** 0.954*** 0.941*** 0.964*** (0.0636) (0.0719) (0.104) (0.0920) (0.201) 0.280*** 0.496*** 0.459*** 0.746*** 1.728*** (0.0776) (0.0891) (0.133) (0.0851) (0.219) 0.568*** 0.717*** 0.716*** 0.0890 -0.279 (0.0795) (0.0917) (0.0986) (0.0909) (0.231) -0.117*** -0.206*** -0.167*** -0.195*** -0.296*** (0.0377) (0.0485) (0.0598) (0.0587) (0.110) Alpha 0.000694 0.00294 0.00544* 0.00767*** 0.0177*** (0.00232) (0.00241) (0.00316) (0.00286) (0.00493) Observations 104 104 104 104 104 R-squared 0.539 0.654 0.700 0.811 0.761
Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
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Panel B: September 2008 through December 2015
p1 p2 p3 p4 p5 Mean Total Volatility Idiosyncratic Volatility 0.95% 3.11% 1.24% 1.15% 6.64% 1.30% 1.05% 5.94% 1.24% 1.52% 6.64% 1.77% 1.74% 9.12% 3.26% 0.593*** 0.724*** 0.787*** 0.821*** 1.241*** (0.0415) (0.0520) (0.0636) (0.0600) (0.108) 0.232*** 0.315*** 0.879*** 0.915*** 1.288*** (0.0753) (0.0883) (0.101) (0.174) (0.220) 0.217*** 0.0257 0.387** 0.312* 0.0490 (0.0745) (0.0928) (0.152) (0.181) (0.203) 0.109*** 0.0354 0.0146 -0.0472 -0.657*** (0.0346) (0.0610) (0.0638) (0.0796) (0.101) Alpha 0.00500*** 0.00524** 0.00394* 0.00812** 0.00503 (0.00157) (0.00199) (0.00229) (0.00330) (0.00494) Chi Square 0.70 0.47 6.28** 3.15* 3.83* Observations 88 88 88 88 88 R-squared 0.849 0.825 0.890 0.764 0.823
Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
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Table 2 Regression of portfolios’ excess returns on four factors for periods
January 2000 through December 2004 and January 2005 through August 2008
Dependent variable = portfolio’s excess return=portfolio’s return- risk-free rate
Panel A: January 2000 through December 2004
p1 p2 p3 p4 p5 Mean Total Volatility Idiosyncratic Volatility 1.06% 3.04% 1.90% 1.70% 3.70% 1.91% 1.83% 4.62% 2.28% 1.62% 6.20% 2.23% 2.93% 10.5% 4.49% 0.412*** 0.548*** 0.962*** 0.908*** 0.986*** (0.0528) (0.0877) (0.130) (0.105) (0.266) 0.157** 0.398*** 0.411*** 0.759*** 1.742*** (0.0776) (0.0957) (0.152) (0.106) (0.263) 0.438*** 0.623*** 0.701*** 0.0939 -0.261 (0.0613) (0.0977) (0.125) (0.124) (0.312) -0.0571 -0.183*** -0.174** -0.238*** -0.305** (0.0356) (0.0555) (0.0707) (0.0562) (0.135) Alpha 0.00533*** 0.00831** 0.00953* 0.0120** 0.0217** (0.00193) (0.00312) (0.00536) (0.00452) (0.00882) Observations 60 60 60 60 60 R-squared 0.607 0.652 0.690 0.836 0.759
Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
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Panel B: January 2005 through August 2008
p1 p2 p3 p4 p5 Mean Total Volatility Idiosyncratic Volatility -0.18% 2.65% 1.51% -0.15% 3.48% 2.01% 0.17% 3.65% 1.77% 0.10% 4.27% 1.38% 0.98% 4.17% 1.74% 0.435*** 0.541*** 0.856*** 1.048*** 0.942*** (0.160) (0.121) (0.0845) (0.150) (0.130) 0.585*** 0.812*** 0.775*** 0.665*** 1.567*** (0.178) (0.197) (0.159) (0.175) (0.214) 0.446** 0.637** 0.492** 0.0676 -0.350* (0.176) (0.241) (0.224) (0.183) (0.205) -0.393*** -0.258* -0.109 0.0419 -0.214* (0.122) (0.136) (0.109) (0.122) (0.108) Alpha 5.51e-05 -0.00131 0.000742 -0.000372 0.0114** (0.00352) (0.00388) (0.00329) (0.00328) (0.00443) Chi Square 2.78* 2.90* 1.43 1.65 6.19** Observations 44 44 44 44 44 R-squared 0.583 0.680 0.773 0.769 0.788
Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
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Figure 1 The change of risk-free rate from 2000 to 2015
0.000% 0.100% 0.200% 0.300% 0.400% 0.500% 0.600% 2000/01/31 2000/09/29 2001/05/31 2002/01/31 2002/09/30 2003/05/30 2004/01/30 2004/09/30 2005/05/31 2006/01/31 2006/09/29 2007/05/31 2008/01/31 2008/09/30 2009/05/29 2010/01/29 2010/09/30 2011/05/31 2012/01/31 2012/09/28 2013/05/31 2014/01/31 2014/09/30 2015/05/29
