Growth Beats Value on the Bombay Stock Exchange. Satneet K. Sabharwal World Markets Canadian Imperial Bank of Commerce Toronto, Canada

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1 Growth Beats Value on the Bombay Stock Exchange Satneet K. Sabharwal World Markets Canadian Imperial Bank of Commerce Toronto, Canada Timothy Falcon Crack* Department of Finance and Quantitative Analysis Otago University Dunedin, New Zealand October 15, 2009 Key words: Bombay Stock Exchange, Growth, India, Momentum, Value. * Corresponding author. Contact information: Department of Finance and Quantitative Analysis, Otago University, PO Box 56, Dunedin, New Zealand; tel: +64(0) ; fax: +64(0) ; tcrack@otago.ac.nz. Opinions expressed in this paper are those of the authors and do not necessarily represent those of Canadian Imperial Bank of Commerce. We thank P. J. King and an anonymous referee. Any errors are ours.

2 Growth Beats Value on the Bombay Stock Exchange Abstract We fill a gap in the finance literature by re-examining the performance of value and growth strategies in India. Fama and French (1998) note that stock returns in India increase with market capitalization and price-to-earnings ratio (P/E). Their emerging market data are limited, however, and their counter-intuitive results for Indian markets are neither statistically nor economically significant. We use a large and recent data set, and we are surprised to find that Fama and French s odd results have maintained their sign and strengthened dramatically. In particular, we find that stock returns in India increase strongly with both market capitalization and P/E, and decrease strongly with dividend yield. International investors need to be aware that Indian markets do not follow the patterns that we have seen in most other markets, and that growth beats value on the Bombay Stock Exchange. I. Introduction The Bombay Stock Exchange (BSE) is the oldest stock exchange in Asia. More than 2,500 stocks trade on the BSE, and electronic trading has recently replaced the old open outcry system. The BSE s most popular index, the Sensex, rose at roughly 18% per annum on average from its introduction in 1979 through to 2005 (almost twice the S&P 500 s roughly 10% per annum growth over the same time period). 1 Although the BSE is a large modern active stock exchange, existing research on value and growth strategies on the BSE is sparse, out of date, uses little data, and is contradictory as to significance of the results. We fill this gap in the literature by investigating the relative performance of value and growth strategies on the BSE, using a large and recent data set that wholly predates the upheavals of the recent global economic crisis. 1

3 Fama and French (1998) devote one row in one table to value and growth strategies in India, but they use a small sample in both time series and cross-section, they find no significant results, and some of what they do find for India is at odds with the majority of U.S. and international evidence on value and growth strategies (e.g., a weak positive relationship between price-to-earnings ratio (P/E) and returns, and a weak positive relationship between size and returns). The weak Fama and French results for India are at odds with statistically strong results (of the same sign) reported for India by Claessens et al. (1995) using almost identical data but different estimation techniques. Before examining our data, we fully expected that Fama and French s weak results for India would reverse sign and become significant and consistent with the majority of the international evidence on value and growth strategies. In fact, the opposite has happened; the relationships found by Fama and French maintain their contrary signs and strengthen dramatically. We find that growth stocks significantly outperform value stocks on the BSE over the period January 1990 to August We also find a strong positive relationship between average returns and firm size. These results are so strong and so different from what we expected that any international investor thinking of investing in India needs to be aware of them. The rest of this paper is organized as follows. In Section II, we briefly review the U.S. and international evidence on value and growth strategies. In Section III, we describe our BSE data and the pattern of returns to size-sorted and beta-sorted portfolios. In Section IV, we use these latter portfolios to risk adjust the returns to value and growth strategies based on decile portfolios formed on price-to-earnings ratios and dividend-to-price ratios. In Section VI, we conclude with a possible explanation for our findings and directions for future research. 2

4 II. Value versus Growth Firms with high book-to-market (B/M), earnings-to-price (E/P) dividend yield (D/P), or cash flow-to-price (C/P) ratios are generally classified as value stocks (their prices are depressed relative to fundamentals); firms with low B/M, E/P, D/P, and C/P ratios are generally classified as growth stocks (their prices are optimistic relative to fundamentals). The majority of the international evidence finds that value stocks outperform growth stocks. In this study, we use D/P-sorted and P/E-sorted decile portfolios to investigate value versus growth on the BSE. Lakonishok, Shleifer, and Vishny (LSV) (1994) argue that investors tend to over invest in stocks that have done well in the past, leading to overpriced glamour/growth stocks. Similarly, investors oversell stocks that have performed poorly in the past and these out-offavor value stocks become underpriced. LSV argue that a premium in average returns for value stocks arises because the market undervalues the out-of-favor value stocks and overvalues the glamour/growth stocks. When the market adjusts to dissipate these mispricings, the value stocks have higher returns in comparison to the growth stocks. LSV say that most investors do not take into consideration the mean reversion of stock returns when predicting future returns. Contrarian investors thus have an advantage over naïve investors. De Bondt and Thaler (1985) give the same argument, and they also argue that the value premium in average returns arises because the market undervalues distressed stocks and overvalues growth stocks. Fama and French (1992, 1998) argue, however, that the value-premium is compensation for risk missed by the CAPM, and that value strategies produce superior returns because they are fundamentally riskier. U.S. studies of D/P and P/E strategies usually find that low P/E strategies outperform high P/E strategies (Basu, 1977, 1983; Jaffe et al., 1989; Wu and Wang, 2000), and high D/P strategies outperform low D/P strategies (Litzenberger and Ramaswamy, 1979; Naranjo et al., 3

5 1998; O Higgins and Downs, 1991; Gardner and Gardner, 1996; Wu and Wang, 2000). Hirschey (2000) concludes, however, that there is no convincing evidence to support high D/P strategies. He states that mistaken return calculations and inadequate accounting for transaction costs give a false impression of outperformance. The international evidence is almost unanimous in finding that value beats growth. Fama and French (1998) find that value beats growth in 12 out of the 13 developed countries they look at (Italy is the exception). They also consider emerging markets, including India, but they state quite generally of their 16 emerging markets that they do not have enough data to conclude that the value premium is reliably positive there (Fama and French, 1998, p. 1996). 2 Their results for India are all weak (returns increase weakly with B/M, P/E, and size), with t- statistics close to zero. Claessens et al. (1995) look at 19 emerging markets, including India. They find results for India of the same sign as Fama and French for each of B/M, P/E, and size. They use a different estimation technique, however, and they report statistically significant relationships between returns and P/E and returns and size, respectively. Fama and French (1998, p. 1997) attribute the general inconsistency of their results compared with those of Claessens et al. (they do not discuss India in particular) as being due mainly to Claessens et al. using cross-sectional techniques that are sensitive to outliers. Our methods are much closer to the time series techniques of Fama and French (1998) than the crosssectional techniques of Claessens et al. Capaul et al. (1993) find that value stocks outperform growth stocks, on average, in six countries (France, Germany, Switzerland, U.K., Japan, U.S.) between 1981 and 1992 on a raw and risk-adjusted basis. Da Silva (2001) finds that a high D/P strategy adds value as an investment strategy in all Latin American countries studied except Brazil: Argentina, Chile, Colombia, Mexico, Peru, and Venezuela. Visscher and Filbeck (2003) find that high D/P strategies work well in the Canadian market. 4

6 The bottom line is that, with very few exceptions, the empirical studies say that value beats growth in most markets and in most time periods. III. BSE Data We use just over 14 years of monthly data (176 months) from the BSE. The data are from DataStream and they include price, P/E ratio, 3 market capitalization, and D/P ratio for stocks listed on the BSE during the period January 1990 to August This time period wholly predates the dramatic upheavals that preceded and accompanied the global economic crisis. 4 Our 176 months of prices give us at most 175 monthly returns for any stock. 5 Our initial download of data contains 876 Indian stocks. We discard 16 BSE stocks that have been suspended by the BSE for non-compliance with listing agreements. We discard 68 stocks listed on the National Stock Exchange of India (NSE) because many of these are also cross-listed on the BSE with almost identical empirical data, and also because we want to focus on the longer-established BSE. This leaves 792 BSE stocks for our study. The majority of our analysis is conducted on a subsample of 203 stocks with very few missing return observations. In practice, these are the more liquid stocks, and these are thus the stocks that an international investor cares most about. At the end of our sample period, these 203 stocks comprise roughly 93% of the market capitalization of the 792-stock BSE sample, which in turn we estimate to contain roughly 97% of the total BSE capitalization at that time. 6 Although we conduct most of our analysis on the 203-stock subsample, we also confirm the generality of our results by conducting analysis on the 792-stock sample where possible. IV. Method and Results Before looking at returns to value and growth strategy portfolios, we first look at returns to size-sorted and beta-sorted portfolios. We calculate returns to size-sorted decile portfolios, 5

7 beta-sorted decile portfolios, and 25 portfolios found by first forming size-sorted quintile portfolios and then by subdividing each into beta-sorted sub-quintile portfolios. These portfolios tell us how BSE stock returns vary with size and with beta, and they serve as benchmarks for risk adjusting our value and growth strategy returns Size-Sorted Decile Portfolios In any given month, we sort all stocks in the sample in ascending order by beginning-ofmonth firm size. We choose only those stocks with 173 or more valid returns over the 175 months. 8 We form 10 decile portfolios with as close as possible to the same number of stocks in each portfolio. We get very close to 20 stocks in each size-sorted decile portfolio in each month, and, in any given month, the number of stocks in any decile differs by no more than one from the number of stocks in any other decile. After allocating stocks to size deciles, the return on each monthly decile is calculated as an equally weighted average. The smallest stocks go into the first portfolio, and so on, until we get to the largest stocks in the 10th portfolio. Monthly size decile portfolio returns are compounded carefully through the 175- months of returns to give annualized average returns to size decile portfolios and accompanying standard errors (see details in Table I, Panel A). [insert Table I about here] Average returns in Table I, Panel A, clearly increase almost monotonically with firm size. This BSE result is completely contrary to the classic U.S. result in Banz (1981). 9 Fama and French (1998, Table VII) report a positive but insignificant relationship between size and stock returns using data from 1987 to 1995; our data indicate that this relationship is now firmly positive and much stronger than previously thought. 4.2 Beta-Sorted Decile Portfolios We calculate betas relative to our own value-weighted market index. We create this index using stocks that have 173 or more valid returns over the 175-month returns sample. 6

8 The correlation between monthly percentage returns to the BSE-100 index 10 and to our market index is 76.8%. Each month, we calculate Dimson betas (Dimson, 1979) for each stock using plus/minus one monthly lag and 60 months of returns. We use only the 203 stocks with 173 or more valid returns. The 60-month estimation window requirement means we can calculate betas only over the last 115 months of the sample. In any given month, our stocks are ranked in ascending order based on their Dimson s betas. Based on this ranking, beta decile portfolios are formed at the end of each month, with as close as possible to an equal number of stocks in each portfolio. In practice, we get very close to 20 stocks in each decile portfolio in each month, and, in any given month, the number of stocks in any decile differs by no more than one from the number of stocks in any other decile. After allocating stocks to beta deciles, the return on each monthly decile is calculated as an equally weighted average. Monthly beta decile portfolio returns are then compounded carefully through the 175-month sample period to give annualized average returns to the beta decile portfolios and accompanying standard errors (see details in Table I, Panel B). We find no relationship between average returns and beta. Fama and French (1992) find in U.S. data that the simple relation between beta and average returns is weak when beta alone is used to explain average returns; we find a similar result on the BSE. 4.3 Size-Beta-Sorted Portfolios Using a similar approach, we also form 25 portfolios with a cross-sorting on both size and beta (size quintiles that are each then sorted into beta sub-quintiles). These sub-quintiles typically end up with eight stocks in each. Table II reports the average annual returns to these 25 size-beta-sorted portfolios, together with standard errors. Table II shows that the results of Table I hold up: larger-capitalization stocks have higher average returns, and there is no consistent relationship between beta and returns. [insert Table II about here] 7

9 4.4 D/P- and P/E-Sorted Portfolios We calculate annualized returns to D/P-sorted and P/E-sorted portfolios in essentially the same way as we calculate the returns to the size-sorted and beta-sorted portfolios. We restrict ourselves first to the 203 stocks with 173 or more valid monthly returns observations. The number of these stocks with valid D/P ratios varies between 180 per month and 203 per month during the sample. In any month, we rank these stocks in ascending order based on their beginning-of-month D/P ratios. D/P-sorted decile portfolios are then formed with as near as possible to equal numbers of stocks in each portfolio. These portfolios are rebalanced each month. In any given month, the cross-sectional equally weighted average of returns to each D/P decile portfolio is calculated. These monthly D/P decile portfolio returns are carefully compounded and annualized to get the raw returns to the D/P decile portfolios reported in Table III, Panel A. [insert Table III about here] We similarly sort stocks in an ascending order based on beginning-of-month P/E ratios. Of the 203 stocks with 173 or more valid monthly returns, the number of stocks with valid P/E ratios varies between 160 per month and 199 per month during the sample (not counting the first two months which have very poor P/E ratio data). P/E-sorted decile portfolios with as near as possible to equal numbers of stocks in each portfolio are formed and rebalanced each month and the raw annualized returns on these P/E deciles are carefully compounded and annualized and reported in Table III, Panel B. From the raw returns in Table III, we see that there is a strong negative relationship between level of D/P and returns, and a strong positive relationship between level of P/E and returns. In both cases, the relationship is nearly monotonic. Fama and French (1998, Table VII) report a positive but insignificant relationship between P/E and stock returns using data from 1987 to 1995; 11 our data indicate that this relationship is now firmly positive and much 8

10 stronger than previously thought. 4.5 Abnormal Returns to P/E- and D/E-Sorted Portfolios The annualized returns to our P/E-sorted and D/P-sorted decile portfolios are adjusted for size and beta risk. The abnormal return calculation is explained in Tables III, IV, and V. We adjust for size and beta simultaneously (Table III), size alone (Table IV), and beta alone (Table V). Note that the raw returns reported in Tables III and V agree, but they differ from those reported in Table IV. This is because the beta adjustment (either alone or in combination with the size adjustment) requires a 60-month beta estimation window, so, when beta sorting, the returns are calculated only over the last 115 months of the data set. [insert Tables III, IV, and V about here] The strong relationships between D/P deciles and raw returns (negatively) and between P/E deciles and raw returns (positively) are attenuated slightly in the size-beta-adjusted abnormal returns in Table III, but the relationships are still extremely strong and in the same direction. The relationships are stronger when we adjust for size only (Table IV) or beta only (Table V). A simple two-sample t-test for difference in means of the time series of abnormal returns between D/P-sorted decile portfolios 10 and 1 (Table III, Panel A), when adjusted for both size and beta, rejects the null hypothesis of no difference with a t-statistic of 4.94 (see Table VI). Similarly, we reject the null hypothesis that there is no difference in the means of the time series of abnormal returns between P/E-sorted decile portfolios 10 and 1 with a t- statistic of 7.17 (see Table VI). The statistical results are similar whether we adjust for size and beta simultaneously (Table VI), for size only (Table VII), or for beta only (Table VIII). Thus, tilting portfolios away from D/P or toward P/E gives very statistically and economically significant size and beta-adjusted abnormal returns. These results are not confined to stocks with very few missing observations: Panels A and B in Table IX give qualitatively similar results (for size-adjusted returns) using all 792 BSE stocks without any 9

11 restriction on missing observations. [insert Tables VI, VII, VIII, and IX about here] We do not estimate transactions costs, but we believe that the differences in the riskadjusted abnormal returns are so large that they must have significant implications for any investor in Indian stocks. It is well known that measures of value tend to be negatively correlated with price momentum, and thus that pursuing a value strategy entails, to some extent, buying firms with poor momentum (Asness, 1997). Our value-growth results are, therefore, consistent with a strong price-momentum effect on the BSE. If this price-momentum effect is strongest in large-capitalization stocks, this would also explain our contrary size-effect findings. We leave this for future research. V. Conclusion We investigate the relative performance of value and growth strategies on the Bombay Stock Exchange using a large and recent data set. There are two major findings. Our first finding is that growth beats value on the BSE over the period January 1990 to August We find a very strong negative relationship between D/P deciles and size-beta-adjusted abnormal returns, and a very strong positive relationship between P/E deciles and size-betaadjusted abnormal returns. We see the same results in our raw (unadjusted) returns. These findings are contrary to the findings in almost every other market. Our second finding is that stock returns increase strongly with market capitalization on the BSE over the same period. This finding is also contrary to the results of almost every other market. The P/E and size findings confirm and strengthen very weak results reported for India by Fama and French (1998). An additional minor result is that betas do not seem to be related to returns on the BSE. This is consistent with the Fama and French (1992) results in the U.S. Finally, we 10

12 suspect that a long-lived price-momentum effect may explain our results, but we leave this for future research. 11

13 Notes 1 See 2 Claessens et al. (1995) report that they have 98 firms in their Indian sample. Fama and French (1998) do not report their cross-sectional sample size for India, but they use the same data source as Claessens and almost exactly the same time period, so we suspect that it is similarly small. We use a sample of 203 firms, with some of the analysis repeated on a sample of 792 firms. 3 All P/E ratios in our data are positive; negative P/E ratios are classified as missing observations. 4 Our data set ends in August From then until January 2008, the Sensex bubbled up four-fold, from roughly 5,000 to 20,873. This was followed by an equally dramatic 60% tumble in the level of the index to 8,160 between January 2008 and March The recovery that followed included a near doubling to over 16,000 by September By stopping in August 2004, we avoid the bubble, tumble and recovery. 5 In several cases, in the event of non-trading in the current month, DataStream uses the previous month s figures as current values across all variables. In cases where there is a repeated datum for more than two consecutive months, we suspect that the repetitions are invalid and we overwrite them as missing. For example, we replace a time series of prices 26.4, 27.2, 27.4, 27.4, , -99 by 26.4, 27.2, 27.4, -99, -99, -99, -99 (where -99 denotes a missing observation). 6 The BSE reports that the BSE-500 contains nearly 97% of the market capitalization of the Bombay Stock Exchange ( Our 792 stocks are likely to be amongst the most liquid stocks and should thus include the majority of the BSE-500 stocks, plus nearly 300 others. 7 With our large sample, book-to-market information on Indian firms is not available to us. Otherwise, we would also use book-to-market ranked portfolios for the risk adjustment. 8 This choice is made in our deciles for ease of subsequent beta estimation, to avoid the worst effects of the most thinly traded stocks, and because these are the liquid stocks that an international investor cares about. There are 203 such stocks in our 792-stock sample. 9 We report qualitatively similar results in Table IX for the unrestricted sample of 792 stocks. 10 The BSE-100 data are taken from 11 To be precise, they report a negative but insignificant relationship between E/P and stock returns. 12

14 References Asness, C. S., (1997), The interaction of value and momentum strategies, Financial Analysts Journal, 53, Banz, R. W., (1981), The relationship between return and market value of common stock, Journal of Financial Economics, 9, Basu, S., (1977), Investment performance of common stocks in relation to their priceearnings ratios: A test of the efficient market hypothesis, Journal of Finance, 32, Basu, S., (1983), The relationship between earnings yield, market value and return for NYSE common stocks: Further evidence, Journal of Financial Economics, 12, Capaul, C., Rowley, I. & Sharpe, W. F., (1993), International value and growth stock returns, Financial Analysts Journal, 49, Claessens, S., Dasgupta, S. & Glen, J., (1995), The cross-section of stock returns: Evidence from the emerging markets, Working Paper. World Bank, World Development Report Office, and International Finance Corporation. Da Silva, A. L. C., (2001), Empirical tests of the Dogs of the Dow strategy in Latin American stock markets, International Review of Financial Analysis, 10,

15 De Bondt, W. F. M. & Thaler, R., (1985), Does the stock market overreact?, The Journal of Finance, 40, Dimson, E., (1979), Risk measurement when shares are subject to infrequent trading, Journal of Financial Economics, 7, Fama, E. F. & French, K. R., (1992), The cross-section of expected stock returns, The Journal Of Finance, 47, Fama, E. F. & French, K. R., (1998), Value versus growth: The international evidence, The Journal of Finance, 53, Gardner, D. & Gardner, T., (1996), The Motley Fool Investment Guide. (New York: Simon and Schuster) Hirschey, M., (2000), The Dogs of the Dow myth, The Financial Review, 35, Jaffe, J., Keim, D. & Westerfield, R., (1989), Earnings yields, market values and stock returns, The Journal of Finance, 44, Jegadeesh, N. & Sheridian, T., (1993), Returns to buying winners and selling losers: Implications for stock market efficiency, The Journal of Finance, 48,

16 Lakonishok, J., Shleifer, A. & Vishny, R. W., (1994), Contrarian investment, extrapolation, and risk, The Journal of Finance, 49, Litzenberger, R. H. & Ramaswamy, K., (1979), The effect of personal taxes and dividends on capital asset prices, Journal of Financial Economics, 7, Naranjo, A., Nimalendran, M. & Ryngaert, M., (1998), Stock returns, dividend yields, and taxes, The Journal of Finance, 53, O Higgins, M. & Downs, J., (1991), Beating the Dow. (New York: Harper-Collins) Visscher, S. & Filbeck, G., (2003), Dividend-yield strategies in the Canadian stock market, Financial Analysts Journal, 59, Wu, C. & Wang, X., (2000), The predictive ability of dividend and earnings yields for longterm stock returns, The Financial Review, 35,

17 Table I Average Annual Returns to Decile Portfolios Ranked on Size and Ranked on Beta These size- and beta-sorted portfolios are formed using 203 BSE stocks with 173 or more valid monthly returns over the 175 months from January 1990 to August Size deciles are formed by ranking stocks on beginning-of-month size and allocating an almost equal number of stocks to each portfolio. All portfolios are resorted and reformed size each month. In any given month, we take an equal-weighted average of simple net returns over the stocks in each decile portfolio (e.g., R j, t is the simple net return so th calculated to the j size decile portfolio in the t th size month). To get economically meaningful average returns, we work with log returns, loge (1 + R j, t ). The annual average 1 return numbers in Panel A are thus the exponentiation of 12 times the sample mean of these log returns over the 175 months, all less 1: exp( 12 log (1 + R size )) e j, t t This calculation correctly compounds the simple net returns over the sample period, correctly annualizes them, and gives the simple net return answer reported in the table. The standard error reported in each panel is, however, 12 times the standard error of the arithmetic mean of the simple net returns because the standard error of the geometric average return in the table is not defined. Our standard error is a very good proxy because the arithmetic and geometric means are close (not reported). The beta-decile returns in Panel B are calculated similarly, except that pre-ranking betas are estimated relative to our value-weighted market index using five years of monthly returns up to and including the month before the beta ranking. So, the calculations in Panel B are only over the remaining 115 months of the 175-month sample period. Panel A: Average Annual Returns to Size Decile Portfolios Small Large Avg. Ret Std. Error Panel B: Low Average Annual Returns to Beta Decile Portfolios High Avg. Ret Std. Error

18 Table II Average Annual Returns to Decile Portfolios Ranked on Both Size and Beta These size-beta-sorted portfolios are formed using 203 BSE stocks with 173 or more valid monthly returns over the 175 months from January 1990 to August Size quintiles are formed after ranking stocks on market capitalization and allocating an equal number of stocks to each portfolio (with the fifth portfolio potentially having a slightly different number). Within each size quintile, stocks are sorted into beta quintile portfolios based on pre-ranking betas estimated relative to our value-weighted market index using five years of monthly returns up to and including the month before the beta ranking. Each beta sub-quintile portfolio has the same number of stocks (with the fifth portfolio potentially having a slightly different number). All portfolios are resorted each month. In any given month, and for any one of the 25 portfolios, the simple net return to this portfolio in this month is calculated as an equal-weighted average of simple net returns over the stocks in the portfolio (e.g., size beta th th R j, t is the simple net return to the j size-beta sorted portfolio in the t month). To get size beta meaningful average returns, we work with log returns, loge (1 + R j, t ). The annual average return numbers in the table are 12 times the sample mean of these log returns over the 115 months 1 following pre-ranking beta estimation all less 1: exp( 12 log (1 + R size beta )) 1. This 115 e j, t t calculation correctly compounds the simple net returns over the sample period, correctly annualizes them, and gives the simple net return answer reported in the table. The standard error reported in each panel is, however, 12 times the standard error of the arithmetic mean of the simple net returns because the standard error of the geometric average return in the table is not defined. Our standard error is a very good proxy, especially when the average return is small. β - Low β - High Size Small ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Size Large ( ) ( ) ( ) ( ) ( ) 17

19 Table III Average Annual Returns on D/P-Sorted and P/E-Sorted deciles, Adjusted for Both Size and Beta These portfolios are formed using 203 BSE stocks with 173 or more valid monthly returns over the 175 months from January 1990 to August A 60-month pre-sorting beta estimation window means that returns in the table are calculated only over the last 115 months of the sample. The D/P and P/E decile portfolios are rebalanced each month and adjusted for both size and beta. Annualized average returns to D/P-sorted decile portfolios adjusted for both size and beta are reported in Panel A; P/E-sorted portfolio returns are reported in Panel B. The average abnormal return to each decile portfolio is calculated as the simple difference between its raw and expected average annual returns. The average annual raw returns to decile portfolios are calculated using the same sorting, averaging, compounding, and annualizing technique described in Table I (but applied here to D/P and P/E). The expected returns to the decile portfolios are the size-beta-matched returns to the decile portfolios. That is, the expected return calculation is identical to the raw return calculation, except that in each month, each individual stock in each D/P or P/E decile portfolio has its return replaced by the monthly return to the size-beta-sorted portfolio (as described in Table II) that that stock is a member of during that month. The standard error that we report is the standard error of the arithmetic mean of the time series of the monthly abnormal returns. Although it is not exactly the standard error of the (difference of geometric means) abnormal return reported here (because this does not exist), it is a very good proxy because the arithmetic and geometric means are close (not reported). Panel A: Average Annual Returns to D/P Deciles Adjusted for Size and Beta Small Large Raw Expected Abnormal Std. Error Panel B: Average Annual returns to P/E deciles adjusted for size and beta Raw Expected Abnormal Std. Error

20 Table IV Average Annual Returns on D/P-Sorted and P/E-Sorted Deciles, Adjusted for Size Only These portfolios are formed using 203 BSE stocks with 173 or more valid monthly returns over the 175 months from January 1990 to August The D/P and P/E decile portfolios are rebalanced each month and adjusted for size only. Annualized average returns to D/P-sorted decile portfolios adjusted for size are reported in Panel A; P/Esorted portfolio returns are reported in Panel B. The average abnormal return to each decile portfolio is calculated as the simple difference between its raw and expected average annual returns. The average annual raw returns to decile portfolios are calculated using the same sorting, averaging, compounding, and annualizing technique described in Table I (but applied here to D/P and P/E). The expected returns to the decile portfolios are the size-matched returns to the decile portfolios. That is, the expected return calculation is identical to the raw return calculation, except that in each month, each individual stock in each D/P or P/E decile portfolio has its return replaced by the monthly return to the size-sorted portfolio (as described in Table I) that that stock is a member of during that month. The standard error that we report is the standard error of the arithmetic mean of the time series of the monthly abnormal returns. Although it is not exactly the standard error of the (difference of geometric means) abnormal return reported here (because this does not exist), it is a very good proxy because the arithmetic and geometric means are close (not reported). Panel A: Average Annual Returns to D/P Deciles Adjusted for Size Small Large Raw Expected Abnormal Std. Error Panel B: Average Annual Returns to P/E Deciles Adjusted for Size Raw Expected Abnormal Std. Error

21 Table V Average Annual Returns on D/P-Sorted and P/E-Sorted Deciles, Adjusted for Beta Only These portfolios are formed using 792 BSE stocks with no missing data over the 175 months from January 1990 to August A 60-month pre-sorting beta estimation window means that returns in the table are calculated only over the last 115 months of the sample. The D/P and P/E decile portfolios are rebalanced each month and adjusted for beta only. Annualized average returns to D/P-sorted decile portfolios adjusted for beta are reported in Panel A; P/E-sorted portfolio returns are reported in Panel B. The average abnormal return to each decile portfolio is calculated as the simple difference between its raw and expected average annual returns. The average annual raw returns to decile portfolios are calculated using the same sorting, averaging, compounding, and annualizing technique described in Table I (but applied here to D/P and P/E). The expected returns to the decile portfolios are the beta-matched returns to the decile portfolios. That is, the expected return calculation is identical to the raw return calculation, except that in each month, each individual stock in each D/P or P/E decile portfolio has its return replaced by the monthly return to the beta-sorted portfolio (as described in Table I) that that stock is a member of during that month. The standard error that we report is the standard error of the arithmetic mean of the time series of the monthly abnormal returns. Although it is not exactly the standard error of the (difference of geometric means) abnormal return reported here (because this does not exist), it is a very good proxy because the arithmetic and geometric means are close (not reported). Panel A: Average Annual Returns to D/P Deciles Adjusted for Beta High Low Raw Expected Abnormal Std. Error Panel B: Average Annual Returns to P/E Deciles Adjusted for Beta Raw Expected Abnormal Std. Error

22 Table VI T-Tests of the Difference in Average Annual Returns to D/P-Sorted and P/E-Sorted Deciles Adjusted for Size and Beta T-tests are reported for the difference in the average annual size-beta-adjusted abnormal returns to the D/P-sorted decile portfolios (Panel A) and P/E-sorted decile portfolios (Panel B) over the 115 months ending August 2004 (e.g., D/P Decile 6 average return less D/P Decile 1 average return has t-statistic -2.93). The numerator of the t-statistic is the difference of the (geometric) average annual size-beta-adjusted abnormal returns reported in Table III; the denominator of the t-statistic is the standard error of the difference in the (arithmetic) means of the time series of monthly abnormal returns to the decile portfolios (accounting for the correlation between the two time series). The t- statistics are thus approximate only, but the arithmetic and geometric means are so close (not reported) that the approximations should be very good. Large statistics in the northeast and southwest corners of the matrices indicate significant differences between extreme decile portfolios; smooth transitions from the diagonal out to these extremes indicate near monotonicity in the average returns to the decile portfolios. Panel A: Small Large Small D/P 1 N/A N/A N/A N/A N/A N/A N/A N/A N/A Large D/P N/A Panel B: Small P/E 1 N/A N/A N/A N/A N/A N/A N/A N/A N/A Large P/E N/A 21

23 Table VII T-Tests of the Difference in Average Annual Returns to D/P-Sorted and P/E-Sorted Deciles Adjusted for Size Only T-tests are reported for the difference in the average annual size-adjusted abnormal returns to the D/P-sorted decile portfolios (Panel A) and P/E-sorted decile portfolios (Panel B) over the 115 months ending August 2004 (e.g., D/P Decile 6 average return less D/P Decile 1 average return has t-statistic -4.24). The numerator of the t-statistic is the difference of the (geometric) average annual size-adjusted abnormal returns reported in Table IV; the denominator of the t-statistic is the standard error of the difference in the (arithmetic) means of the time series of monthly abnormal returns to the decile portfolios (accounting for the correlation between the two time series). The t-statistics are thus approximate only, but the arithmetic and geometric means are so close (not reported) that the approximations should be very good. Large statistics in the northeast and southwest corners of the matrices indicate significant differences between extreme decile portfolios; smooth transitions from the diagonal out to these extremes indicate near monotonicity in the average returns to the decile portfolios. Panel A: Small Large Small D/P 1 N/A N/A N/A N/A N/A N/A N/A N/A N/A Large D/P N/A Panel B: Small P/E 1 N/A N/A N/A N/A N/A N/A N/A N/A N/A Large P/E N/A 22

24 Table VIII T-Tests of the Difference in Average Annual Returns to D/P-Sorted and P/E-Sorted Deciles Adjusted for Beta Only T-tests are reported for the difference in the average annual beta-adjusted abnormal returns to the D/P-sorted decile portfolios (Panel A) and P/E-sorted decile portfolios (Panel B) over the 115 months ending August 2004 (e.g., D/P Decile 6 average return less D/P Decile 1 average return has t-statistic -2.68). The numerator of the t-statistic is the difference of the (geometric) average annual beta-adjusted abnormal returns reported in Table III; the denominator of the t-statistic is the standard error of the difference in the (arithmetic) means of the time series of monthly abnormal returns to the decile portfolios (accounting for the correlation between the two time series). The t-statistics are thus approximate only, but the arithmetic and geometric means are so close (not reported) that the approximations should be very good. Large statistics in the northeast and southwest corners of the matrices indicate significant differences between extreme decile portfolios; smooth transitions from the diagonal out to these extremes indicate near monotonicity in the average returns to the decile portfolios. Panel A: Small Large Small D/P 1 N/A N/A N/A N/A N/A N/A N/A N/A N/A Large D/P N/A Panel B: Small P/E 1 N/A N/A N/A N/A N/A N/A N/A N/A N/A 0.21 Large P/E N/A 23

25 Table IX Average Annual Returns on D/P-Sorted and P/E-Sorted Deciles, Adjusted for Size Only (Unrestricted Sample) These portfolios are formed using 792 BSE stocks over the 175 months from January 1990 to August 2004 without any restriction on valid observations. We first report average annual returns to size deciles using the same method as in Table I. The D/P and P/E decile portfolios are rebalanced each month and adjusted for size only. Annualized average returns to D/P-sorted decile portfolios adjusted for size are reported in Panel A; P/E-sorted portfolio returns are reported in Panel B. The average abnormal return to each decile portfolio is calculated as the simple difference between its raw and expected average annual returns. The average annual raw returns to decile portfolios are calculated using the same sorting, averaging, compounding, and annualizing technique described in Table I (but applied here to D/P and P/E). The expected returns to the decile portfolios are the size-matched returns to the decile portfolios. That is, the expected return calculation is identical to the raw return calculation, except that in each month, each individual stock in each D/P or P/E decile portfolio has its return replaced by the monthly return to the size-sorted portfolio (as described in Table I) that that stock is a member of during that month. Average Annual Returns to Size Decile Portfolios Small Large Return Panel A: Average Returns on D/P Deciles Adjusted for Size Raw Expected Abnormal Panel B: Average Returns on P/E Deciles Adjusted for Size Raw Expected Abnormal