The Value Premium and the January Effect Julia Chou, Praveen Kumar Das * Current Version: January 2010 * Chou is from College of Business Administration, Florida International University, Miami, FL 33199; Das is from B.I. Moody College of Business Administration, University of Louisiana at Lafayette, Lafayette, LA 70504. Authors' contact information: Chou, wchou@fiu.edu, (305) 348-0533; Das, pkd8947@louisiana.edu, (337) 482-6656.
The Value Premium and the January Effect Abstract Previous studies show existence of value premium. The value premium varies with firm size and has different behaviors in January and non-january. We find that small stocks have almost no value premium in January whereas large stocks have high January value premium. On the other hand, large stocks do not have significant value premium in any of non-january months. In contrast, we find existence of value premium among small stocks in non-january months. This high value premium in January among large stocks is mainly driven by loser stocks at the turn of the year. Our study provides evidence to show that the value premium among large stocks may be explained by investors trading behavior instead of the risk. Since large stocks own 73.6% of the stock market, BE/ME should not be treated as the risk factor in the rational asset pricing model. JEL classification: G12 Keywords: value premium, January effect
1 Introduction Fama and French (1992, 1993) evaluate the joint effects of market beta, size, earnings-to-price ratio (E/P), leverage, and book-to-market ratio (BE/ME) on the explanation of average returns and find that commonly used Capital Asset Pricing Model (CAPM) cannot explain cross sectional dispersion of mean returns for the period of 1963 1990 and the combination of size and BE/ME has better explanatory power. They argue that size and BE/ME are two missing risk factors in the CAPM model. Using market portfolios and portfolios mimicking risk factors related to size and BE/ME, they show that their threefactor model captures the cross sectional variation in average returns beyond those explained by the market returns. They propose that high BE/ME stocks are distressed stocks and should be compensated with higher returns due to the risk loading. Thus, high BE/ME stocks (value stocks) generally outperform low BE/ME stocks (growth stocks). The differential return between value stocks and growth stocks is the value premium. However, there is no general consensus on the explanation of the positive relation between realized average returns and book-to-market ratios. For example, some researchers, who use a behavioral explanation, attribute the existence of value premium to over-reaction among the investors. Low BE/ME stocks have strong fundamentals and investors overreact to these strong fundamentals. This push the price of low BE/ME stocks higher than justified by the strong fundamentals. However, when there is correction, price of the stocks goes down which result in low returns for growth stocks. Similarly, high BE/ME stocks have weak fundamentals. Investors overreact to these fundamentals which push the price down than justified by these fundamentals. When correction in the price takes place, it results in higher returns for value stocks. This view is consistent with the findings of Debondt and Thaler (1987), Lakonishok, Shleifer, and Vishny (1994), and Haugen (1995). Daniel and Titman (1997) further document that value premium is caused by the stock characteristics instead of risk. Investors like to buy growth stocks and do not like value stocks. Thus, investors will ask for a higher return to hold value stocks but a lower return 1
for growth stocks. The finance literature also argues about the persistence, the January effect, and the size effect of the value premium phenomena. Some researchers content that the value premium reflects the sample selection bias. In other words, the value premium exists only in some specific periods. If the sample period is extended, the value premium is unlikely to occur again (Black (1993), and Mackinlay (1995)). Continuing with this strand of literature, Loughran (1997) documents that the value premium is limited to small stocks and there is no significant value premium for large stocks. Although Fama and French (1992) has shown that the January seasonal has an effect on the BE/ME but the strong relation between BE/ME and average return is still significant throughout the year, Loughran demonstrates that BE/ME effect in non-january months are being driven by low returns on small growth stocks, which are small proportion of total market capitalization. As a result, he concludes that the value premium does not exist. Houge and Loughran (2006) further demonstrate that value firms in practical do not earn significant higher returns than growth firms by examining the performance of equity mutual funds and stock indexes. In their study, they do not find any evidence of value premium even for small-cap stocks. We add to this debate by expanding Fama and French s findings (2006) and investigate whether the value premium exists, whether the BE/ME effect is special to January, how the value premium varies with the firm size, and whether the value premium could be treated as a risk factor. In the paper, Fama and French suggest that the absence of value premium among large stocks is mainly because Loughran (1997) uses book-to-market ratio as a value-growth indicator and the sample is limited to the period of 1963 to 1995 with U.S. stocks. They argue that using B/M ratio as a value-growth indicator restricts the value premium to small stocks. Fama and French extend the sample period to 2004 and show that if E/P ratio instead of BE/ME ratio is used as a value-growth indicator; there is little difference between value premiums for small and large stocks. The value premium does exist for both large and small-cap stocks. In this paper, we use returns of portfolios formed on basis of size and BE/ME ratios as Fama and 2
French (2006) suggest and find that high BE/ME portfolios deliver superior returns than low BE/ME portfolios but the evidence is only valid for the period of 1963 to 2004. Interestingly, our study suggests that the B/M effect is concentrated in the month of January which could not just be explained by the firm size although previous studies have identified strong size effect in the month of January. The results are consistent for sample periods of 1926 to 1963 and 1963 to 2004. Moreover, the value premium has different behaviors for large and small stocks in January and non-january. Our results show that although small size firms have considerable significant earning premium in January, there is almost negligible value premium. However, large stocks show significant value premium in January, significantly higher than small size firms. The situation is opposite in non-january months. For the non-january months, the value premium is limited to small-cap stocks. Consistent with Loughran (1997), we do not find any significant difference between returns of large value and growth stocks in non- January months. Thus, large stocks do not have the value premium but small stocks have, on average, higher and significant value premium in non-january months. The different combination of firm size and January seasonal has a different impact on the value premium. Our results are consistent for both 25 and 6 size-b/m portfolios, and with the E/P ratio as a value-growth indicator. We next examine whether the value premium can be explained as a risk factor. Particularly, we study how the value premium occurs for large and small-cap stocks through the whole year. Fama and French (1993) argue that firm size and BE/ME can be used as proxies for the underlying common risk factors and be added into the asset pricing model to form three-factor model. They show that the market factor (beta) as well as size and BE/ME capture very well the common variation in stock returns. If the value premium is related to risk, we expect to see the occurrence of value premium in all calendar months during the year not just in the January. Furthermore, the value premium should not be related to any particular investors trading behavior. Our results shows that the value premium is limited to small-cap stocks in February, April, and 3
September with the period of 1926 to 1963, and in March, and July with the period of 1963 to 2004. We do not find any value premium associated with small stocks in the month of January. However, large-cap stocks only have the value premium in January in both periods. When we look into the daily trading details in the December and January, large stocks begin to have a positive and higher value premium in the last 10 trading days of the year and the value premium becomes large and significant in the first 10 trading days of the year. The average value premium among large stocks during first 10 trading days of a year even exceeds the January value premium and the value premium for the whole year. The value premium soon decreases significantly to negative for the large-cap stocks for the rest trading days in the January. Contrary to the large stocks, the small-cap stocks do not have such a behavior. In the last 10 trading days of the year, small stocks almost have the same value premium as in the rest of trading days in the December. The same situation happens for the small-cap stocks in the January. We further find that the high January value premium among large stocks are mainly driven by loser stocks which have low/negative past eleven months cumulative return. This indicates that investors overreact to the large loser stocks with high BE/ME ratio before the year and the stock price is adjusted back during the turn of the year. Combining our findings, the value premium has different natures for small and large-cap stocks. For the small-cap stocks, the value premium may be occurred by the risk but for the large stocks, the value premium obviously reflects the investors behavior. This may be the reason that researchers usually have conflicting results about the value premium regarding whether the effect of BE/ME on the stock returns is due to the risk or just the investors preference. Since large stocks count 73.6% of the overall market capital (see, Fama and French (2006), Table II), our findings are consistent with Loughran s (1997) conclusion that the value premium may not reflect the risk nature and thus, the BE/ME should not be treated as the risk factor in the rational asset pricing model. Moreover, the behavioral explanation or the stock characteristics of the BE/ME effect may best suit our findings for the large-cap stocks. 4
Our main contribution of this paper is to put more insight into the value premium and find its causes, especially the value premium among large stocks. We use different aspects and portfolio formations to investigate the value premium and find that the value premium exists for large stocks only in January. We further disentangle the debates between the risk and behavior explanations of the value premium. Our evidence shows that the value premium for large stocks probably reflects the trading preference of investors instead of the risk nature. However, the value premium for small-cap stocks probably may be caused by the risk. Since the value premium may have different natures for large and small-cap stocks, adding the factor of HML directly into the asset pricing model may not be suitable. The organization of the paper is as follows. In section II, we describe our data and methodology to form portfolios. Section III discusses about January effect on size and BE/ME premiums. As a robustness check, we also present evidence on value premium in January and non-january returns by using 25 size- E/P portfolios, and six size-be/me portfolios. In section IV, we attempt to find an explanation for January value premium. Here, we look at the pattern of the monthly distribution of value premium, changes in value premium during the turn-of-the-year, and analyze value premium among stocks based on their past performance. Section V concludes. 2 Data We follow Fama and French (1993) to use the same data sets and apply same restrictions. The sample includes all non-financial firms listed on NYSE, Amex, and Nasdaq from Center for Research in Security Prices (CRSP) and merged COMPUSTAT annual industrial files of income statement and balance-sheet data, also maintained by CRSP. Our sample period is mainly from year 1963 to 2004. We match the accounting data of fiscal year-end in calendar year t-1 with the returns data from July of year t to June of year t+1. To be included in sample, a firm must have a CRSP stock price for December of year t-1, and 5
June of year t. And the firm must have COMPUSTAT data on total book assets, book equity, and earnings for its fiscal year ending in calendar year t-1. We exclude firms with negative book equity. At the end of June in year t, all NYSE stocks are independently sorted by size and book-to-market equity (BE/ME) into 5x5=25 groups. Size is measured at the end of June in year t using market equity. For the BE/ME, market equity is measured at the end of December of year t-1 and book equity is book value of common equity for the fiscal year ending in calendar year t-1 (data60+data35 of COMPUSTAT). BE/ME is the ratio of book equity to market equity. We then use the breakpoints of size and BE/ME ratio for all NYSE stocks to allocate NYSE, Amex, and Nasdaq stocks to five size quintiles and five BE/ME quintiles. 25 portfolios are formed from the intersections of the five quintiles of size and BE/ME. The value- and equal-weighted monthly returns from July of year t to June of year t+1 are calculated based on these portfolios formed each year. To confirm our results, we also use E/P ratio instead of BE/ME as a value-growth indicator to form 25 size-e/p portfolios by using the same methodology. When E/P ratio is used as the measure, firms with negative earnings are excluded from the sample. We also implement the similar methodology to form 6 size-be/me portfolios. 6 size-be/me portfolios are formed by intersection of two size and three BE/ME groups. Stocks are split into two equal groups, small and big using median size of NYSE stocks as breakpoints. Three BE/ME groups are formed by using NYSE breakpoints, bottom 30% (low), middle 40% (medium) and top 30% (high). 3 Value Premium and January Effect Using a sample period of 1963-1995, Loughran (1997) asserts that value premiums are mainly driven by small stocks and there is no value premium for large stocks. He further documents that the low returns on newly-listed growth stocks are the main cause to the value premiums for the small stocks. However, Fama and French (2006) argue that Loughran s findings are subject to sample-period bias. They investigate the 6
sample period of 1926-1963 and find that value premium exists for small as well as large stocks. If the years from 1963 to 2004 are used as the sample period, the value premiums still exist and are more significant. When E/P ratio instead of B/M ratio is used to group value and growth stocks, they find evidence of value premium even in post-1963 period. Based on their results and findings, they conclude that value premium exists for small as well as large stocks and the return differences between high and low BE/ME stocks can be counted as a risk factor in the asset pricing model. In order to address the problem of sample-period bias and make our results comparable, we use the same sample period as studied by Fama and French in their paper. We find strong evidence supporting that value premiums for large stocks is mainly a January event and do not exist in non-january months. BE/ME effect is present only in small size stocks and absent in large size stocks, consistent with findings of Loughran. Thus, based on our results, it is reasonable to conclude that value premiums for large stocks are conditional to seasonal effect instead of risk effect. 3.1 Size and BE/ME Effects in January and Non-January January effect has generated lot of interests among finance researchers since it was first documented by Rozeff and Kinney (1976). Using equal weighted index of New York Stock Exchange price over the period of 1904-74, they find that average monthly return in January was about 3.5 percent while returns in other months averaged about 0.5%. Further studies by Kiem (1983), Roll (1983) and Reinganum (1983) conclude that January effect is mainly a small size firm phenomenon. Kiem (1983) finds that excess returns of small size firms are concentrated in the month of January. Interestingly, most of the excess return comes in the first five trading days. His study shows that smallest market capitalization stocks have 50 basis points abnormal returns where as large stocks have negative excess returns in January. In this paper, we explore the size and BE/ME effects on stocks return in January and non-january 7
months. At the end of June each year, all stocks listed on NYSE are independently sorted by size and BE/ME to determine the NYSE deciles breakpoints. All sample stocks are then allocated to 10 size and 10 BE/ME portfolios based on NYSE breakpoints. Table 1 reports monthly average returns of 10 portfolios based on size and BE/ME ratio in Panel A and Panel B, respectively, for NYSE, Amex and Nasdaq stocks from July 1926 to December 2004. 1 The average return differences between smallest and largest size deciles and lowest and highest BE/ME deciles along with their t-statistics are also reported. To make our results comparable with results of Fama and French (2006), we separate the sample years into two subperiods, July 1926 to June 1963 and July 1963 to December 2004. All returns are value-weighted. In the Panel A of Table 1, the smallest size portfolios earn significantly higher returns than the largest size portfolios. In the sample period of July 1926 to June 1963, the average monthly return of smallest size portfolios is 1.77%, which is 0.84% higher than that of largest size portfolios. During the same sample period, the smallest size stocks earn an average return of 9.86% in January, which is 8.93% higher than the January return of the largest size stocks. In non-january months, the average monthly return of the smallest size portfolios is 1.03%. The difference of returns between the smallest and largest stocks is only 0.11% which is statistically not significant. Our results are similar and consistent for the period of July 1963 to December 2004. In this period, the smallest and the largest size stocks have average returns of 1.29% and 0.89%, respectively. In January, the smallest size portfolios earn an average return of 7.43%, which is 5.86% higher than the average return of largest size portfolios. However, in non-january months, the average monthly return is 0.74% for the smallest size stocks, which is 0.09% less than the largest size portfolios. The above results are consistent with Banz s (1981) and Kiem s (1983) findings that small stocks generate higher returns than large stocks and the size premium is concentrated mainly in January. All differences of returns are significant at conventional level except the averages of monthly returns in non-january months. 1 We thank Fama and French for providing the monthly returns and breakpoints on portfolios based on size and BE/ME. The data can be obtained from French s website. 8
Next, we analyze returns of 10 portfolios based on BE/ME. We find a strong positive association between the average return and the BE/ME ratio. Firms with low BE/ME ratios (growth stocks) earn lower returns than firms with high BE/ME ratios (value stocks). In the period of July 1926 to June 1963, value stocks in general beat growth stocks by 0.42% on average monthly returns. This number increases to 5.37% in January whereas the average monthly value premium is only -0.03% in non-january months. During the period of July 1963 to December 2004, value stocks continue to beat growth stocks by 0.56% on the average monthly returns. Furthermore, the difference of returns between value and growth stocks is larger (4.03%) in January but relatively smaller and statistically non-significant (0.25%, t=1.26) in non- January months. Consistent with Fama and French (2006), we find that the effect of BE/ME is stronger and significant during the second period than the first period (0.42%, t=1.08 for the period 1926-63 compared to 0.56%, t=2.76 for the period 1963-2004). Based on our results of Table 1, we find that average portfolio returns are positively associated with BE/ME ratio and are negatively related to firm size. Although size and BE/ME premiums do exist, they are mainly concentrated in January. This indicates that both size and BE/ME premiums seem to be a January phenomenon instead of being driven by underlying risk factors. If the value premiums are only limited to the month of January, it indicates value premium is not a risk factor but are driven by the investors trading behavior. In the following sections, we focus on the value premium and explore whether this BE/ME effect is driven by the January effect and by some stocks with particular characteristics. 3.2 Value Premium with Size and January Effects Loughran s (1997) main argument is that value premium effect is limited to small stocks. Large value stocks actually do not earn significantly higher returns than large growth stocks. Since small stocks only share a very small capital market, Loughran concludes that value premium does not exist. However, Fama 9
and French (2006) demonstrate that value premiums still exist among large stocks if different period of sample years is used in the study. Whether value premiums could be observed among large stocks is the key to untangle this puzzle. If Fama and French s findings on large stocks are still subject to the January effect, the evidence of value premium will be weaker. In this subsection, we investigate the same sample period as used by Fama and French and study how value premiums vary with the size and the January effect. Table 2 reports all months average monthly returns (Panel A), January average monthly returns (Panel B), and non-january average monthly returns (Panel C) for 25 portfolios formed on size and BE/ME with two sample periods as we have done in the previous section. All months monthly average returns are based on monthly returns of all calendar months, January average returns are based on returns realized in the month of January, and non-january monthly returns are calculated by excluding January returns. The differences of returns between value and growth stocks are also reported with their t-statistics. In Panel A, value premiums in the first period (July 1926 June 1963) for the smallest size, size 2, size 3, size 4 and the largest size quintiles are 0.92% (t=1.83), 0.66% (t=2.38), 0.22% (t=0.86), 0.48% (t=1.36), and 0.65% (t=1.85). The corresponding values for the second period (July 1963 December 2004) are 0.93% (t=4.85), 0.66% (t=3.46), 0.62% (t=3.02), 0.37% (t=1.91), and 0.17% (t=0.94). These results demonstrate different patterns for the two different sample periods. Before June 1963, value premium for all size quintiles are more or less similar and the difference of value premiums between the smallest and the largest size stocks is only 17 basis points. However, results in the second period show that value premium has an obvious negative relationship with size. The value premium of the smallest size quintile is 66 basis points higher than that of the largest size quintile. Our results of value premium among large stocks are consistent with the findings of Fama and French (2006). However, the relation between size and value premium does not show a consistent pattern in these two different periods. Based on the results of Panel A, we can make following two observations. First, consistent with Loughran (1997) and Fama 10
and French (2006), when BE/ME is used as a value growth indicator, value premium for large stocks does not exist. In both sample periods, value premiums for the large stocks are not statistically significant at 5%. Second, in the sample period 1963 2004, value premium effect is strong and evident in small stocks but decreases with increase in size. To gain a more clear perspective on monthly effect of value premiums, we separate average monthly returns into January and non-january returns. Panel B and Panel C report average monthly returns for 25 size-be/me portfolios along with value premiums in January and for non-january months, respectively. The results show a presence of January effect in the average stocks returns. All 25 size- BE/ME portfolios have higher returns in January (Panel B) compared to returns in non-january months (Panel C) and this January effect is strong among small stocks. For example, during 1926-63 period, the smallest size lowest BE/ME portfolio has average January return of 10.43% compared to 0.03% in non- January months. Except for the smallest size quintile, we find strong evidence of value premium in the month of January in both sample periods. Interestingly, we observe that large stocks have high value premiums in January and small size stocks have high value premiums in non-january. The results are consistent in both periods. During the sample period 1926-63, the largest size quintile has value premium of 3.86% (t=2.94) in the month of January, compared to 0.36% (t=1.00) during non-january months. In contrast, for the same sample period, the smallest size quintile has value premium of -1.73% (t=-0.63) in January compared to 1.16% (t=2.38) in non-january months. The January value premiums of the smallest size quintiles in both periods are small and statistically not significant at a conventional level. Returns of the smallest size quintile are always the highest in each BE/ME groups and these are consistent with the findings of Keim (1983) that the relation between returns and size is negatively correlated and it is more pronounced in January than in other months. It seems that strong January effect on the average returns of small value as well as growth stocks tends to shrink the 11
value premium of smallest size quintile. For example, in the second period, small value stocks have a very high return of 7.42%. But the high return of 6.18% among small growth stocks in January reduces the January value premium to 1.24% (t=1.63). Similarly, the high return of 10.43% for small growth stocks in January in the first period offsets the value premium (H-L=-1.73, t=-0.63) among small stocks. The January effect on value premiums of large stocks is strong and significant in both sample periods. The difference between value premiums of smallest and largest size quintiles are 5.59% and 0.83% in the periods 1926-63 and 1963-2004, respectively. Panel C reports monthly average returns of 25 size-be/me portfolios for non-january months. Even though small size stocks do not have good returns in each BE/ME groups, the smallest size quintile has highest and significant value premiums among all size quintiles in both sample periods. The value premiums of the smallest size quintiles in the first and second periods are 1.16% (t=2.38) and 0.90% (t=4.56), respectively. These two values are 0.80% and 0.90% higher than the value premiums of the largest size quintiles for the same periods. Based on the results shown in the Table 2, we conclude that the high value premiums of the smallest size quintiles are mainly driven by non-january months. In contrast, the value premiums of large stocks are mainly driven by January. The different seasonal effects on value premiums observed among small and large stocks reinforce our argument that the BE/ME effect is not an appropriate risk factor in the asset pricing model. 3.3 Robustness checks 3.3.1 Using E/P as a Value-Growth Indicator Fama and French (2006) use E/P as a value-growth indicator to show that value premium for large stocks exist in post-1963 time period. In order to make our study comparable to their results and check 12
consistency of our results, we also use E/P to substitute for BE/ME as a value-growth indicator to form 25 portfolios. Table 3 reports average monthly returns for 25 portfolios formed on the basis of size and E/P ratio for the period of July 1963 to December 2004. Panel A presents monthly average returns for the all months, Panel B presents January returns and Panel C presents non-january monthly average returns. Our results are consistent with Fama and French s findings. In Panel A, value premiums for large stocks are stronger than those observed using BE/ME as a value-growth indicator. For the largest size quintile, the value premium is 0.34% (t=2.38) and is significant at 5% level. This indicates the existence of value premium for large stocks. However, results from Panel B and Panel C of Table 3 reinforce our findings of Table 2 that value premiums among large stocks is evident only in the month of January and small stocks have significant value premium in non-january months. In Panel B, the two smallest size quintiles do not generate significantly positive value premiums in January, whereas the three largest size quintiles have positive and significant value premiums. For example, the largest size quintile has value premium of 1.49% (t=2.40). In contrast, the two largest size stocks do not earn significant value premium in non-january months. The largest and second largest size quintiles have value premium of 0.24% (t=1.65) and 0.17% (t=1.14), respectively, in non-january months. The value premium of the largest size quintile is 1.49% in January, which is 3.44% higher than the value premium of the smallest size quintile. The results are stronger than the ones in Table 1, where value premium of the largest size stocks is only 0.83% higher than the value premium of the smallest size stocks. Moreover, the January value premium of the largest size quintile is 1.25% higher than the value premium of the same quintile in non-january months. These not only reinforce the results of Table 2, but also strengthen it. 3.3.2 Using Finer Sorts to Form Size-BE/ME Portfolios To ensure that our results are not limited to 25 size-be/me portfolios, we form 2x3=6 size-be/me 13
portfolios and perform similar analysis. The median of NYSE stocks is used as the breakpoint to group stocks into small and large portfolios. The BE/ME breakpoints are the 30 th and 70 th percentiles of all NYSE stocks. We use 6 size-be/me portfolios to make sure that we have sufficient number of firms in the highest BE/ME and the largest size portfolio to enable us to perform our analysis. Fama and French (2006) document that the smallest size quintile contains almost half of the NYSE, Amex and Nasdaq stocks but only counts for 3% of the stock market cap. Thus, the sample is skewed across both size and BE/ME. It is essential for us to check whether our findings are only for specifically sorted portfolios. Table 4 shows average monthly returns for 6 size-be/me portfolios for all months, January and non-january months. Panel A reports results for the period of July 1926 to June 1963 and Panel B presents results for the period July 1963 December 2004. The results are similar and consistent with our earlier results. The average monthly value premiums of large stocks and small stocks based on all month returns are almost the same in Panel A but small stocks have a higher value premium than large stocks in Panel B. The t-statistics are only significant for small stocks. However, when we separate January and non-january effect on value premiums, we find that value premium among large stocks exists only in the month of January for both sample periods. Based on our findings of Tables 2, 3 and 4, we derive four main conclusions. First, the value premium exists for all size quintiles if E/P ratio is used as the value-growth indicator. However, large stocks do not earn significant value premiums when we use BE/ME instead of E/P to group stocks. Second, the value premium of large stocks is higher than the one of small stocks in January but not in non-january months. Third, the value premium of large stocks is mainly driven by January month irrespective of whether we use E/P or BE/ME as a value-growth indicator. Fourth, small stocks do not earn a significant value premium in January but have a significant value premium in non-january months. The January effect has different impacts on value premiums of small and large stocks. Our study shows how seasonal and size effects interact with BE/ME effect. Fama and French (1993) 14
show that BE/ME is one of the three risk factors in the asset pricing model. High BE/ME stocks earn higher returns as the compensation for the risk-taking of BE/ME. We find that returns of high BE/ME stocks are higher than low BE/ME stocks. However, we also find that the nature of risk premium for BE/ME changes with the month and with the stock size. Value premiums for large stocks only happen in January but disappear in non-january months. This could indicate that the BE/ME effect on large stocks is a result of investors trading behavior pattern instead of risk. In the next section, we explore how investors trading during the turn of the year affects the value premium for large stocks. 4 Value Premium at the Turn of the Year In the previous section, we establish that the value premium of large stocks is concentrated in January. This indicates that the higher returns of large value stocks is not driven by the underlying risk factor because risk alone could not explain the behavior of return premium which occurs mainly in January (Keim, 1983). Instead, we propose that the January effect evident in large stocks value premium is the result of investors trading behavior. If our conjecture is true, we should observe some behavioral patterns which are related to the January effect and have a direct association with the presence of January value premium for large stocks. To explore the possibility that value premium for large stocks is due to investors buying and selling strategies, we examine the large stocks value premium month by month, at the turn of the year (the last 10-day trading in December and the first 10-day trading in January), and the relation with stocks past performance. 15
4.1 Monthly distribution of value premium In this section, we look into the monthly distribution of value premiums of large stocks. If the value premium of large stocks is due to underlying risk, then the value premium should be evenly distributed among all the calendar months and should not appear only in January. On the other hand, no value premiums in non-january months will be strong evidence against the risk based explanation of value premium and support our argument that the value premium for large stocks is likely caused by the behavioral reasons. Table 5 shows the monthly average value premiums for different calendar months and for each size quintiles of 25 size-be/me portfolios. As in our previous analysis, we analyze two different periods, July 1926 to June 1963 and July 1963 to December 2004, to examine whether our results are subject to period bias or there is a consistent evidence to show the existence of value premium for large stocks in any months other than January. The t-statistics of the monthly average value premium are shown in the second rows of each month and the boldface indicates the significance at the 5% level. Our results in general confirm that the value premium among large stocks exists only in January. It is evident from the Table 5 that the value premium among the largest size quintiles is highest in January in both sample periods; value premiums in non-january months are low and not statistically significant. Similar and consistent pattern can be observed for second and third largest size quintiles portfolios; value premiums are highest and significant in January and low and statistically not significant in non-january months. In contrast, the smallest size quintile does not show any significant value premium in January. For the sample period 1926 63, the smallest size quintile has January value premium of -1.73% (t=-0.63). The corresponding January value premium in period 1963 2004 is positive but statistically not significant (1.24%, t=1.63). Interestingly, small stocks have significant value premiums in some non- 16
January months. For example, in the first period, the smallest size quintile has value premium of 3.24% (t =2.29), 3.24% (t=1.97), and 3.52% (t=3.16) for the month of February, April, and September, respectively. In the second period the value premiums of smallest size quintile is positive and significant in the month of March (1.58%, t = 2.91) and July (2.24, t = 3.90). It is apparent from our results of Table 5 that the January effect on value premiums of small and large stocks is different. This evidence of strong and significant January value premium among large stocks and negligible January value premium among small stocks contradicts the risk based explanation of value premium. 4.2 Value Premium and the Turn-of-the-Year Effect In this section, we examine whether high January value premium observed among large stocks is caused by investors trading behavior during the turn-of-the-year. A significant and high value premium at the turn-of-the-year indicates that January value premium observed among large stocks is being driven by investors buying and selling behavior. Table 6 shows the average daily returns of a ten-trading-day period before and after the beginning of a year to gain more perspective about change in value premiums during the turn-of-the-year. Due to limited availability of daily returns data for period before 1963, we restrict our analysis to post-1963 period. We calculate average daily return for each 25 size BE/ME portfolios for the last ten trading days of December in year t, the first ten trading days of January in year t+1, and the rest trading days of December in year t and January in year t+1. The Panel A of Table 6 presents average daily returns of first ten and rest trading days in January. Consistent with the findings of Kiem (1983), the smallest size stocks earn the highest returns and the largest size stocks generate the lowest returns in January in each BE/ME group. For example, in the 17
lowest BE/ME group, the smallest size quintile has average daily return of 0.38% in the first ten trading days in January compared to 0.04% of largest size quintile. Also, there is a negative relationship between stock size and January returns. In general, within each BE/ME group, the average daily returns in January decreases with increase in stock size. During the first ten trading days in January, the largest size quintile has the highest value premium of 0.22% (t=5.15). Also, the value premium, in the first ten trading days of the year, increases with increase in stock size. However, during the rest trading days in January, large stocks do not exhibit similar behavior. For example, the largest size quintile has value premium of -0.01% (t=-0.33) during the rest trading days in January. It is evident that value premiums among large stocks are concentrated mainly in the first ten days of January. The average daily returns of last ten and rest trading days in December are shown in Panel B. There is no significant value premium for all size quintiles in the rest trading days in December. However, the largest size quintile has positive value premium in the last ten trading days in December (0.06%, t=1.81). A similar pattern is observed in the second largest size quintile; value premium is positive (0.04%, t=1.20) in the last ten trading days of the year. Our evidence clearly shows that value premium is more pronounced in January than in the other months for large stocks, and it is only significant during the turn of the year. If we exclude the first and last ten days of trading in a year, the value premium of large stocks disappears. Our results provide evidence of the-turn-of-the-year effect on value premium among large stocks and support Loughran s (1997) argument that value premium for large stocks is possibly caused by investment behaviors not risk. Since the-turn-of-the-year effect reflects the investment strategies of investors, there may be no value premium for large stocks. 18
4.3 The Effect of Winners and Losers on Value Premium In this section, we investigate whether past performance affects the January value premium. We use the methodology of He, Ng, and Wang (2004) and categorize each stock into winner and loser stock based on its past 11-month (January November) cumulative return. Two different methods are used to classify a stock as a winner and a loser. In the first approach, a stock having non-negative past 11-month cumulative return are defined as a winner stock and a stock with negative past 11-month cumulative return is considered a loser stock. The second classification is based on quintiles. Within each 25 size-be/me portfolio, stocks are sorted in descending order based on their past 11-month cumulative returns. Top onefifth stocks form winner portfolios and bottom one-fifth form loser portfolios. Table 7 presents the average monthly return of portfolios of winner and loser stocks for each 25 size-be/me groups. In Panel A, winners are stocks having non-negative cumulative returns and losers are stocks having negative returns. Based on our results shown in Panel A, we can make following three observations. First, there is no significant value premium in January for winner stocks. This is true for small as well as large stocks. For example, the value premium of largest size quintile of winner stocks is 1.37%, statistically not significant at 5% level. Similarly, for smallest size quintile, the value premium is statistically non-significant 0.99%. Second, except for the smallest size quintile, all size quintiles of loser stocks show positive and significant value premium in January. The largest size quintile has value premium of 6.49%, which is statistically significant at 5% level. Third, the high January value premium of loser stocks is driven by high returns of loser value stocks. For example, in the largest size quintile, winner growth stocks have average January return of 1.33% compared to 1.70% of loser growth stocks. However, winner value stocks have average return of 2.70% in January compared to 8.19% of loser value stocks. The evidence that loser value stocks of all size quintiles realizing superior returns to winner value stocks does not support the risk hypothesis of value premium as proposed by Fama and French (1993). As 19
a robustness check, we use quintiles to define a stock as a winner or a loser and present our results in the Panel B of Table 7. The results are similar and consistent. 5 Conclusion There is a disagreement in finance literature on the causes of value premium. Some of the numerous explanations for value premium attributed in the literature are underlying risk factors, overreaction to strong and weak fundamental of stocks, and sample selection bias. In this paper, we revisit value premium with the intent of disentangling the causes and the seasonal effect of the value premium. We provide strong evidence of January effect in the value premium phenomenon. However, this January effect is different for large and small size stocks. Our result shows that large stocks have pronounced value premium in January, whereas there is no significant January value premium for small stocks. Interestingly, the value premium of large stocks is absent for rest of the year, whereas small stocks do show sign of value premium during some non-january months. The results are similar when we use different 6 size- BE/ME portfolios instead of 25 size-be/me portfolios and E/P ratio instead of BE/ME ratio as valuegrowth indicator. If BE/ME proxy for underlying risk factors, then our results indicate that the nature of risk premium changes with the month and stock size. We also examine the turn-of-the-year effect on the value premium of the large stocks. It is interesting to note that the value premium for the large stocks is concentrated in the first ten days of the January. In addition, the value premium begins to increase in the value in the last ten days of the December. When first and last ten trading days of a calendar year are excluded, the value premium of large stocks is not significant anymore. Based on the results, it is reasonable to argue that observed value premium among large stocks in the month of January is being driven by trading strategies of investors. We further investigate whether past performance of stocks influence the value premium of large 20
stocks. Based on its past 11 months cumulative return, each stock is categorized into winner and loser stocks. All stocks are again independently sorted into 25 size-be/me groups. Within each size-be/me group, loser stocks have superior returns compared to winner stocks. This contrast in average returns of winner and loser stocks is more pronounced in value stocks. Except for smallest size quintile, loser stocks have significantly higher value premiums compared to winner stocks. None value premium in the winner group is significant. The results indicate that the value premium of large stocks in January is mainly driven by high returns on loser stocks. Overall, our work highlights the causes of the value premium. Since large stocks own 73.6% of the stock market, there is no particular reason to explain the different nature of value premium for small and large stocks. We can only focus on large stocks to examine the causes of the value premium. Moreover, the value premium of large stocks limited to first and last ten trading days of the year and more pronounced in loser stocks lend support to the view that book-to-market effect on the stock return is caused by investors trading behavior instead of risk-bearing. Our results provide no evidence supporting the risk-based interpretation of the value premium. On the other hand, we find strong evidence in favor of behavioral explanation of the value premium. 21
References Banz, Rolf W., 1981, The relationship between return and market value of common stocks, Journal of Financial Economics 9, 3-18. Black, Fischer, 1993, Beta and return, Journal of Portfolio Management 20, 8-18. Daniel, Kent, and Sheridan Titman, 1997, Evidence on the characteristics of cross sectional variation in stock returns, Journal of Finance 52, 1-33. Davis, James L., Eugene F. Fama, and Kenneth R. French, 2000, Characteristics, covariances, and average returns: 1929 to 1997, Journal of Finance 55, 389-406. De Bondt, Werner F. M., and Richard Thaler, Further evidence on investor overreaction and stock market seasonality, Journal of Finance 42, 557-581. Fama, Eugene F., and Kenneth R. French, 1992, The cross-section of expected stock returns, Journal of Finance 47, 427-465. Fama, Eugene F., and Kenneth R. French, 1993, Common risk factors in the returns on stocks and bonds, Journal of Financial Economics 33, 3-56. Fama, Eugene F., and Kenneth R. French, 2002, The equity premium, Journal of Finance, 57, 637-659. Fama, Eugene F., and Kenneth R. French, 2006, The value premium and the CAPM, Journal of Finance 61, 2163-2185. Haugen, Robert, 1995, The new finance: the case against efficient markets, Prentice Hall, Englewood Cliffs, New Jersey. He, Jia, Lilian Ng, and Qinghai Wang, 2004, Quarterly trading patterns of financial institutions, Journal of Business 77, 493-509 Houge, Todd, and Tim Loughram, 2006, Do investors capture the value premium, Financial Management 35, 5-19. Keim, Donald B., Size-related anomalies and stock return seasonality: further empirical evidence, Journal of Financial Economics 12, 13-32. Lakonishok, Josef, Andrei Shleifer, and Robert W. Vishny, 1994, Contrarian investment, extrapolation, and risk, Journal of Finance 49, 1541-1578. 22
Loughran, Tim, 1997, Book-to-market across firm size, exchange, and seasonality, Journal of Financial and Quantitative Analysis 32, 249-268. MacKinlay, A. Craig, 1995, Multifactor models do not explain deviations from the CAPM, Journal of Financial Economics 38, 3-28. Ng, Lilian, and Qinghai Wang, 2004, Institutional trading and the turn-of-the-year effect, Journal of Financial Economics 74, 343-366. Reinganum, Marc R., 1983, The anomalous stock market behavior of small firms in January: Empirical tests for tax-loss selling effects, Journal of Financial Economics 12, 89-104 Roll, Richard, 1983, Vas ist Das? The turn-of-the-year effect and the return premia of small firms, Journal of Portfolio Management 9, 379-402 Rozeff, Michael S. and William R. Kinney, 1976, Capital Market Seasonality: The Case of Stock Returns, Journal of Financial Economics 3, 379-402. 23
Table 1 Average Monthly Value-Weighted Returns for Portfolios Based on Size and BE/ME Deciles At the end of June in year t, securities which have records on both CRSP and Compustat databases listed on NYSE, Amex, and Nasdaq are sorted into size deciles in Panel A and BE/ME deciles in Panel B. Size is calculated by using the market value in June of year t and the cutoffs are determined by NYSE firms. The BE/ME ratio is the book equity (total assets liabilities + balance sheet deferred taxes and investment tax credit liquidation redemption carrying value of preferred stock) for the last fiscal year ending in t-1 divided by market value at the end of December of t-1. Firms with negative book equity and financial firms are excluded from the sample. Panel A and Panel B show average monthly returns, January and non-january monthly returns for ten portfolios based on size and BE/ME ratio with sample periods of July 1926 to June 1963 and July 1963 to December 2004. All returns are value-weighted and are in percent. * denotes significance at the 5 percent level. Panel A: Returns Based on Size Deciles July 1926 to June 1963 July 1963 to December 2004 Size All Jan. Non-Jan. All Jan. Non-Jan. Small 1.77 9.86 1.03 1.29 7.43 0.74 2 1.47 7.26 0.94 1.23 5.12 0.88 3 1.34 5.55 0.96 1.24 4.39 0.96 4 1.30 4.83 0.97 1.20 3.41 1.00 5 1.22 4.29 0.94 1.23 3.06 1.06 6 1.27 3.68 1.05 1.10 2.65 0.96 7 1.16 2.77 1.02 1.15 2.32 1.05 8 1.09 2.24 0.98 1.10 2.15 1.00 9 1.07 2.08 0.97 1.02 2.03 0.93 Big 0.93 0.93 0.93 0.89 1.57 0.83 S-B 0.84* 8.93* 0.11 0.40* 5.86* -0.09 t-stat 1.82 5.23 0.23 1.74 6.50-0.42 Panel B: Returns Based on BE/ME Deciles BE/ME Low 0.92 0.49 0.95 0.84 1.21 0.80 2 1.01 1.08 1.00 0.97 1.71 0.91 3 0.98 1.29 0.95 1.00 1.97 0.91 4 0.91 1.55 0.85 1.00 1.69 0.94 5 1.12 1.98 1.04 1.01 1.75 0.94 6 1.01 2.69 0.86 1.11 2.41 0.99 7 1.09 3.07 0.91 1.18 2.72 1.05 8 1.29 3.69 1.07 1.21 3.12 1.04 9 1.44 4.68 1.15 1.26 3.73 1.04 High 1.34 5.86 0.93 1.40 5.24 1.05 H-L 0.42 5.37* -0.03 0.56* 4.03* 0.25 t-stat 1.08 3.87-0.06 2.76 4.27 1.26 24