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The Expected Value Premium Long Chen∗ Eli Broad College of Business Michigan State University Ralitsa Petkova† Weatherhead School of Management Case Western Reserve University Lu Zhang‡ Simon School of Business University of Rochester and NBER November 2005 Abstract We estimate the expected value premium using expected rates of dividend growth and expected dividend-price ratios for value and growth portfolios. We find that during the 1941—2002 period, the expected value premium is positive in every year, significant in various subsamples, and countercyclical. Unlike the equity premium, there is no noticeable trend in the expected value premium. Potential driving sources of our results are suggested. ∗ East Lansing, MI 48821; tel: (517)353-2955, fax: (517)432-1080, email: [email protected]. 10900 Euclid Avenue, Cleveland OH 44106. Tel: (216)368-8553, email: [email protected]. ‡ Carol Simon Hall 3-160B, University of Rochester, Rochester, NY 14627. Tel: (585)275-3491, fax: (585)273-1140, and email: [email protected]. † Contents 2 1 Introduction It is well known that value stocks outperform growth stocks in terms of realized average returns. However, there still exists a heated controversy around the issue of whether this value premium is due to rational compensations for risk or irrational behavior on the side of investors. Furthermore, some recent studies (e.g., Schwert (2002)) suggest that the value premium has declined over time, implying that academic research might have influenced the efficiency of capital markets. In this paper we offer a fresh look at the controversy about the value premium. We use fundamentals (dividends) to estimate the expected value premium rather than the average realized historical return. The main advantage of this approach is that the average realized return is at best a noisy proxy for the expected return (e.g., Elton (1999)). The expected value premium estimates based on fundamentals will help us shed more light on the debate about the source of the value premium and its magnitude. In this study, we focus on three main economic questions. First, is there an ex ante expected value premium? In the current literature, the majority of papers documenting the existence of the value premium implicitly assume that the average realized return is an unbiased proxy for the expected return (e.g., Fama and French (1993); Lakonishok, Shleifer, and Vishny (1994); and Davis, Fama, and French (2000)). However, recent studies have cast doubt on this practice. In particular, the average realized return might not converge to the expected return in finite samples. For example, Elton (1999) observes that there are periods longer than ten years during which the stock market return is on average lower than the risk free rate (1973—1984), and periods longer than 50 years during which risky bonds underperform on average the risk free rate (1927—1981).1 1 See also Brav, Lehavy, and Michaely (2003) and Campello, Chen, and Zhang (2003). 3 In light of these issues, we construct an ex ante measure of the expected value premium. The logic behind our measure can be explained through a simple rearrangement of Gordon’s growth formula: R= where R is the equity return, D P D + g, P is the dividend-price ratio, and g is the dividend growth rate. If we take expectation on both sides, the formula implies that the expected equity return can be decomposed into an expected dividend-price ratio component and an expected dividend growth component. Blanchard (1993) regresses the dividend-price ratio and the future dividend growth rate on a set of conditional macroeconomic variables to analyze the path of the expected market risk premium. The fitted values from the regressions are then used to construct the time series of the expected equity premium. We follow the same method in analyzing the expected value premium. More precisely, we use the dividend growth rates of value and growth stocks to estimate their corresponding expected rates of dividend growth, which can then be combined with the expected dividend-price ratios to obtain expected returns. The conditional expected return is the sum of the fitted values from time-series regressions of the realized dividend-price ratio and a weighted average future dividend growth rate on a set of predetermined variables. This method avoids the use of the average realized return as a proxy for the expected return. Our work is thus in the spirit of a growing literature that uses valuation models to estimate expected returns (e.g., Claus and Thomas (2000), Gebhardt, Lee, and Swaminathan (2000), Fama and French (2002)). Note that the method we use to construct the value premium lets us compute the path of the conditional expected return spread between value and growth portfolios rather than 4 the unconditional expected return spread (e.g., Fama and French (2002)). The advantage of analyzing the conditional expected value premium is that we can answer the second research question on our agenda: is the expected value premium countercyclical? The cyclicality of the expected value premium might be the key to distinguishing alternative theories about the value premium. Recent rational theories (e.g., Zhang (2003)) predict that the expected value premium should be countercyclical. Specifically, in bad times firms usually invest at a lower rate than the long run average. In bad times, value firms, having lower profitability than growth firms, will start to disinvest. Since cutting capital is more costly than expanding capital, value firms do not have enough flexibility to scale down. Therefore, value firms are affected more by economic downturns, and are hence riskier than growth firms in bad times. The countercyclical risk dispersion between value and growth, combined with a constant or a countercyclical price of risk, implies a countercyclical expected value premium. In contrast, the overreaction theory on the value premium focuses on the predictability of the abnormal return of the value strategy, as opposed to its time-varying expected return (e.g., DeBondt and Thaler (1985); Lakonishok, Shleifer, and Vishny (1994); and Daniel, Hirshleifer, and Subrahmanyam (1998)). The third question we address is: is there a long-run trend in the expected value premium? Recent studies (e.g., Schwert (2002)) have argued that the value premium has decreased over the past ten years, suggesting that academic research has made capital markets more efficient. We investigate this hypothesis using an ex ante measure of the expected value premium. Our main findings can be summarized as follows. First, there exists a significantly positive expected value premium. Its sample average (measured by the expected HML return) is 5.1% per year in the period from 1941 to 2002. Similar results are obtained in the subsample from 5 1963 to 2002. This evidence reinforces the view that the value premium is real and is not due to sample selection or data-snooping biases. Second, the expected value premium exhibits countercyclical movements. For example, in the sample from 1941 to 2002, the correlation between the expected value premium (measured by the expected HML return) and the default spread (a countercyclical variable) is 0.39 (pvalue 0.00). The correlation between the expected HML return and the growth rate of real investment (a procyclical variable) is -0.28 (p-value 0.03). The results are similar over the period from 1963 to 2002. This evidence provides support for the theoretical prediction in Zhang (2003) that the expected value premium is countercyclical. Third, we find that the expected value premium responds to macroeconomic shocks significantly and in the direction predicted by rational asset pricing theory. A positive shock to real consumption growth or real investment growth leads to lower expected value premia. Therefore, the evidence suggests that the ex ante value premium goes up with negative macro shocks, and it goes down with positive macro shocks. The covariance of the expected value premium with macroeconomic factors whose risks cannot be diversified away provides support for the view that the expected value premium is a compensation for systematic risk. Finally, we document an increase in the expected value premium from 1950 to the early 1980s and a decrease thereafter. A combination of technological innovation and investor learning may be responsible for this finding. In summary, we contribute to the current literature on the value premium by providing new evidence on the magnitude and cyclical movements in the expected value premium. The rest of the paper is organized as follows. Section 2 describes in detail the methods we use to construct the expected value premium. In Section 3 we document various descriptive 6 statistics for the ex ante value premium and its components—the expected dividend-price ratio and the expected dividend growth rate. Section 4 studies the trend and cyclical movements in the expected value premium. It also examines the relation between the premium and various macroeconomic variables. Section 5 provides a variety of robustness checks and Section 6 offers a summary and interpretation of our results. 2 Research Design This section describes the empirical methods we use to construct the expected value premium. Section ?? discusses the basic idea and Section ?? presents implementation details including the construction of our sample. 2.1 The Basic Idea The method we use to construct expected returns follows closely that of Blanchard (1993), who studies movements in the expected equity premium. The basic idea is to use dividend growth rates to estimate expected rates of dividend growth, which can then be combined with expected dividend-price ratios to obtain expected returns. To be precise, let Rt+1 be the realized stock return from time t to t+1, i.e., 1+Rt+1 = (Dt+1 +Pt+1 )/Pt , where Pt is the stock price known at time t, and Dt+1 is the real dividend paid over the period from t to t+1; Dt+1 is unknown until the beginning of time t+1. If we assume that the dividend-price ratio is stationary, we can solve for Pt as the present value of future dividends discounted by the sequence of realized rates of return. We next divide both sides by Dt , take conditional expectations at time t, and linearize to obtain the 7 expected return at time t, denoted as Et [Rt+1 ] Et [Rt+1 ] = Et ∙ ¸ Dt+1 + Et [Agt+1 ], Pt (1) where Agt+1 is the long-run growth rate of dividends defined as the annuity value of the growth rate of future dividends Agt+1 ¸ ∞ ∙ ¸i r̄ − ḡ X 1 + ḡ ≡ gt+i+1 , 1 + r̄ i=0 1 + r̄ ∙ (2) with ḡ and r̄ being the average growth rate of real dividends and the average real stock return, respectively. Finally, gt+1 denotes the growth rate of real dividends from time t to t+1. The interpretation of equation (??) is straightforward—the expected return conditional on time t is the sum of the expected dividend-price ratio and the expected long-run growth rate of dividends, both conditional on time t. Accordingly, the expected value premium equals the sum of the dispersion in the expected dividend-price ratio and the dispersion in the expected long-run growth rate of dividends between value and growth. 2.2 Implementation We now discuss the details of estimating expected returns based on equations (??) and (??) for value and growth portfolios. Data We obtain relevant data from three main sources. The first source is the Center for Research in Securities Prices (CRSP) monthly stock file that contains information on stock prices, shares outstanding, dividends, and returns for NYSE, AMEX, and Nasdaq stocks. The 8 second source is the COMPUSTAT annual research file that provides accounting information for publicly traded U.S. firms. To alleviate the potential survivorship bias due to backfilling data, we require that firms be on COMPUSTAT for two years before using the data. The third source is Moody’s book equity information used in Davis, Fama, and French (2000), available from Kenneth French’s web site.2 Our sample period begins in 1941 and ends in 2002. In earlier periods, only a few firms have data on dividends once we classify them into value and growth portfolios. Potential problems with disclosure regulations also affect our choice of the starting date of the sample period. We construct value and growth portfolios by sorting on book-to-market ratios. We implement both a one-way sort on book-to-market to obtain five quintile portfolios and a two-way, two-by-three sort on size and book-to-market to obtain six portfolios (e.g., Fama and French (1993)). Our timing in portfolio construction differs slightly from that commonly used in the literature. Instead of in June, we form portfolios in December of each year t. We use book equity from the fiscal year ending in calendar year t−1 divided by market equity at the end of December of year t. This method avoids any look-ahead bias that might arise as accounting information from the current fiscal year is often not available at the end of the calendar year. Portfolio ranking is effective from January of year t+1 to December of year t+1. This portfolio timing is lined up with the timing of dividend growth which occurs from the beginning to the end of the calendar year. The different timing convention that we use is not a source of concern, however. In fact, using slightly more lagged information on book value makes it harder to find an ex ante value premium. We repeat the analysis using the original book-to-market and size portfolios constructed by Fama and French, and we find 2 http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data-library.html 9 similar results. Our definition of book equity follows that of Cohen, Polk, and Vuolteenaho (2003). In particular, book equity is defined as stockholders’ equity plus balance sheet deferred taxes (item 74) and investment tax credit (item 208 if available) plus post-retirement benefit liabilities (item 330 if available) minus the book value of preferred stock. Depending on data availability, we use redemption (item 56), liquidation (item10), or par value (item 130), in this order, to represent the book value of preferred stock. Stockholders’ equity is equal to Moody’s book equity (whenever available) or the book value of common equity (item 60) plus the par value of preferred stock. If neither is available, stockholders’ equity is calculated as the book value of assets (item 6) minus total liability (item 181). Estimating Expected Returns To estimate the expected returns for value and growth portfolios, we have to construct the time series of their dividend-price ratios and dividend growth rates. For each portfolio, we construct the real dividend-price ratio from the time series of value-weighted realized stock returns with and without dividends and the time series of the consumer price index from the U.S. Bureau of Labor Statistics. In particular, ¡ ¢ X (CPIt /CPIt+1 ), where Rt+1 is the nominal return with dividends Dt+1 /Pt = Rt+1 − Rt+1 X from time t to t + 1, Rt+1 is the nominal return without dividends over the same period, and CPIt is the level of the consumer price index. The real dividend growth is calculated as ¢ Dt+1 /Pt ¡ X Rt + 1 (CPIt−1 /CPIt )−1. The resulting real dividend growth rates are quite gt+1 = D t /Pt−1 volatile even at the portfolio level. To trim the outliers, we replace any annual observations of dividend growth higher than 50% with 50% and those lower than −50% with −50%. Next, we construct the long-run dividend growth rate, Agt+1 , given by equation (??), for 10 each portfolio. We estimate r̄ as the sample average of the realized real equity returns, and ḡ as the sample average of the real dividend growth rates. Agt+1 is an infinite sum of future real dividend growth rates. In practice we use a finite sum of 100 years of future growth. We assume that the future real dividend growth rates beyond 2002 equal the average dividend growth rate during the 1980—2002 period. We also use the full-sample average and find the results to be quite stable. The focus on the 1980—2002 period intends to pick up the recent trend of dividend growth. Finally, we regress Agt+1 and Dt+1 /Pt on a set of conditioning variables. The fitted values from these regressions provide the two components of the expected returns. Their sum gives us the time series of expected portfolio returns. The set of conditioning variables includes four aggregate variables and one portfoliospecific variable. Our choice of the four aggregate conditioning variables is standard from the time series predictability literature. These variables include: the aggregate dividend yield, computed as the sum of dividend payments accruing to the CRSP value-weighted portfolio over the previous 12 months, divided by the contemporaneous level of the index (e.g., Fama and French (1988)); the default premium, defined as the yield spread between Moody’s Baa and Aaa corporate bonds from the monthly database of the Federal Reserve Bank of Saint Louis (e.g., Keim and Stambaugh (1986) and Fama and French (1989)); the term premium, defined as the yield spread between a long-term and a one-year Treasury bond from Ibbotson Associates (e.g., Campbell (1987) and Fama and French (1989)); and the one-month Treasury bill rate from CRSP (e.g., Fama and Schwert (1977) and Fama (1981)). Previous studies find that the log book-to-market spread, defined as the log book-to- 11 market of portfolio ten minus the log book-to-market of portfolio one from ten deciles sorted on book-to-market, can predict future value-minus-growth returns (e.g., Asness, Friedman, Krail, and Liew (2000); Cohen, Polk, and Vuolteenaho (2003)). Theoretical explanation of this predictability is provided in Gomes, Kogan, and Zhang (2003) and Zhang (2003). Therefore, we also use the log book-to-market spread to predict the long-run dividend growth rate and the dividend-price ratio of value strategies. We obtain data on the returns and the year-end book-to-market ratios of all book-to-market deciles from Kenneth French’s web site. From January to December of year t, the book-to-market of a portfolio is calculated by dividing its book-to-market ratio at the end of December of year t−1, where book value and market value are both measured at the end of December, by its compounded gross return from the end of December of year t−1 to the current month of year t. 3 Preliminary Analysis This section presents some preliminary analysis on estimating the expected value premium. Table ?? reports descriptive statistics for returns, growth rates, dividend yields, both realized and expected, for value and growth portfolios. We report the results for the full sample from 1941 to 2002 and the subsample from 1963 to 2002. When we use the one-way sort on book-to-market, we denote the resulting five portfolios as Low, 2, 3, 4, and High. Portfolios Low and High represent the extremes in terms of book-to-market. The difference between the returns of High and Low is denoted as p5-1 and it represent the value-minusgrowth strategy for the one-way sort of the assets. When we use the two-way sort on size and book-to-market, we denote the resulting six portfolios by two letters—LS, LB, MS, MB, HS, and HB. For example, portfolio LS 12 contains stocks with the bottom 30% book-to-market ratios and the bottom 50% market capitalizations. The value-minus-growth strategy for the two-way sort of the assets is defined as 1/2*(HS+HB)-1/2*(LS+LB) and it is denoted as HML. Note that this is not the HML factor used by Fama and French (1993) due to our different timing convention in forming portfolios. Later in the paper we repeat the analysis using their original factor and find similar results. 3.1 Average Returns The first two rows of all panels in Table ?? show that value-minus-growth strategies are profitable in our samples. For example, the average realized return of portfolio p5-1 is 5.8% per year (t-statistic 2.88) in the full sample, and 4.6% per year (t-statistic 2.10) in the subsample. Similarly, the average realized annual return of HML is 6% in the full sample and 5.9% in the subsample; both are highly significant. 3.2 Growth Rates Rows three and four in all panels of Table ?? show that the realized real dividend growth rate of value portfolios is on average higher than that of growth portfolios, albeit the difference is not significant. The real dividend growth rate, gt+1 , of portfolio High-minus-Low is on average 4.5% per year in the full sample. Controlling for size increases the number further to 5.6% for HML. Moreover, the middle two rows of all panels show that the expected long-run real dividend growth, Et [Agt+1 ], follows largely the same pattern. Except for p5-1 in the subsample, the value portfolio has significantly higher expected long-run growth than the growth portfolio. The average expected long-run dividend growth of HML is 3.5% per year (t-statistic 19.90) in the full sample, and 2.8% (t-statistic 21.00) in the subsample. 13 Importantly, our evidence does not contradict the conventional wisdom that growth stocks have higher proportions of growth opportunities and grow faster than value stocks. The reason is that our evidence is obtained from portfolios rebalanced annually, while the conventional wisdom is based on portfolios with fixed sets of firms without rebalancing. To illustrate this point, we study the event-time evolution of profitability (defined as the earnings-lagged book equity), the rate of dividend payment (defined as the dividend-lagged book equity), and the real dividend growth rate for value and growth stocks during 21 years around the portfolio formation year. Our test design follows closely that of Fama and French (1995). We define value and growth portfolios both from book-to-market quintiles and from six size and book-to-market portfolios. The sets of stocks in the value and growth portfolios are fixed throughout the event years. The sample we use is from 1941 to 2002. We back out data on dividends from valueweighted portfolio returns with and without dividends. Since data on earnings is not available for the pre-COMPUSTAT years we follow Cohen, Polk, and Vuolteenaho (2003) and use the clean-surplus relation to compute earnings from data on book equity and dividends, i.e., earnings(t) =book value(t)−book value(t − 1)+dividends(t). To be consistent, we use this method to compute earnings in later years even when earnings data from COMPUSTAT is available. Figure ?? reports the results. First, Panels A and D confirm the main result in Fama and French (1995, Figure 1) that growth firms are persistently more profitable than value firms. Panels B and E show that growth firms also have higher rates of dividends than value firms. The dispersion in dividend rates appears even more persistent than the dispersion in profitability, especially for the two-way sort. More importantly, Panels C and F show that 14 the real dividend growth rates of growth stocks are higher than the real dividend growth rates of value stocks. This dispersion is large at the portfolio formation year. It remains positive for almost ten years for the one-way sort. However, for the two-way sort the dispersion is much more short-lived and converges in about three years. However, when the portfolios are rebalanced annually, the firms in the growth portfolio next year are not the same as the firms in the growth portfolio this year. There is no particular reason to expect the dividend growth of growth portfolios to be higher than the dividend growth of value portfolios, given that growth rates are measured using different sets of firms. Consistent with this observation, Figure ?? plots the time series of the annual realized real dividend growth rates for portfolios five and one in the book-to-market quintiles (Panel A), portfolio five-minus-one (Panel B), portfolios High and Low from the six portfolios sorted on size and book-to-market (Panel C), and HML (Panel D). Panels B and D show that the real dividend growth rates for the value-minus-growth strategies are frequently negative. 3.3 Expected Returns Not surprisingly, Table ?? reports that the average expected dividend-price ratio, Et [Dt+1 /Pt ], is higher for value firms than for growth firms. Given that the expected long-run dividend growth and the expected dividend-price ratio are both higher for value firms, their expected returns are even higher than the expected returns of growth firms. The last two rows of Panels A and B show that the expected return of p5-1 is 3.7% per year (t-statistic 14.91) in the full sample, and 2.8% (t-statistic 12.05) in the subsample. Similarly, the last two rows of Panels C and D show that the expected return on HML is 5.1% (t-statistic 40.89) in the full sample, and 5.1% (t-statistic 31.73) in the subsample. To sum up, the expected value premium is significantly positive on average. 15 An interesting result that emerges from Table 1 is that the expected return for each portfolio in the one-way and two-way sorts is substantially lower than the average realized return of the portfolio. Such a result has been documented before for the excess return on the market portfolio. For example, Fama and French (2002) report that for the sample period 1951-2002 the expected equity premium is 4.32% per year, while the average realized equity premium is 7.43% per year. Our evidence suggests that this result holds in the cross-section of portfolios sorted by size and book-to-market. However, the expected value premium within each sorting procedure is not far away from the average realized return. This indicates that the difference between the expected return and the average realized return cancels out at the cross-sectional level. We next study the time series of the expected p5-1 return, the expected HML return, their respective expected long-run dividend growth rates, and their expected dividend-price ratios. Figure ?? plots the sample paths. Panels A and C show that the expected p51 and HML returns are positive throughout the sample. Both series of expected returns display positive spikes during most of the recessions in the sample. They also seem to covary positively with the default premium, a well-known countercyclical variable commonly used to predict the business cycle and the excess return of the market (e.g., Jagannathan and Wang (1996)). Therefore, this informal analysis suggests that the expected value premium is also countercyclical. Panels A and C also suggest that the expected value premium increased in the period 1950-1980 and decreased after that. Panels B and D of Figure ?? show that the expected dividend growth rates and the expected dividend-price ratios of p5-1 and HML covary negatively with each other. There has been a noticeable decline in the expected long-run dividend growth from the early 1940s 16 to the early 1980s, but an increase thereafter. The expected dividend-price ratios display the opposite long-term movements. As a result, these graphs do not show an obvious trend in the expected value premium, although the expected p5-1 return appears to decline slightly over time. Finally, Table ?? reports the results of autocorrelations and MacKinnon (1994) unit root tests for the expected p5-1 return, the expected HML return, and their respective components—the expected dividend-growth rate and the expected dividend-price ratio. The table shows that the two separate components are more persistent than the expected value premium itself. The unit root tests fail to reject the unit-root null for the expected dividendprice ratios of both p5-1 and HML, but the null is rejected for the expected dividend growth rates and the expected value premium. 3.4 The Equity Premium The method we use to derive the expected value premium is the dynamic extension of the method used in Fama and French (2002) to compute the equity premium. It is therefore interesting to compare the properties of the equity premium constructed our way to those documented in Fama and French. First, our estimates are close to those obtained by Fama and French (2002). During the 1951—2000 period studied by Fama and French, our estimates of the expected long-run real dividend growth rate, the expected real dividend yield, the expected real equity return, and the average realized real market return are 0.84%, 4.07%, 4.91%, and 10.21%, respectively. These numbers are reasonably close to their counterparts in Fama and French—1.05%, 3.70%, 4.75%, and 9.62%, respectively. The differences are likely due to the way we use to construct our sample. Second, consistent with Fama and French (2002), the equity premium that we estimate 17 is much lower than the average realized real equity return. The expected equity premium from 1941 to 2002 is 4.25% per year, compared to the realized real equity premium of 7.76% per year for the same period. More importantly, our estimates also show that the equity premium has declined over time. The time series plot in Figure ?? shows that the equity premium reaches its peak of about 10% in the early 1950s, declines over the next two decades to about 2.5% in the mid 1970s, climbs up to about 5% in the mid 1980s, then declines over the next one and half decades to about 1% in the early 2000s. Using the equity premium in a trend regression yields a negative slope of -0.077% (t-statistic -8.46) in the 1941—2002 sample. Although the slope is only an insignificant -0.021% (t-statistic -1.65) in the post-1963 sample, it increases in magnitude to -0.142% (t-statistic -7.73) in the sample after 1980. 4 The Expected Value Premium We now study the dynamics, including both trend and cyclical movements, of the expected value premium in more details. 4.1 Trend Dynamics We use two methods to isolate the cyclical component of the expected value premium from the low-frequency, trend component. The first method is to regress the expected value premium on a time trend ValuePremiumt = a + b t + εt , (3) where the fitted component including the intercept is defined as the trend component and the residual is defined as the cyclical component. The second method is to pass the expected 18 value premium through the Hodrick-Prescott (1997) (HP) filter that separates the trend and the cyclical components of the premium. The results from regression (??) indicate that the expected p5-1 return exhibits a downward trend in the 1941—2002 and the 1963—2002 samples, but the expected HML return does not. The expected HML return exhibits a downward trend in the 1980—2002 sample, but the expected p5-1 return does not. Specifically, the slope coefficient, b, is -0.078% for the expected p5-1 return (t-statistic -8.01) in the 1941—2002 sample, -0.052% (t-statistic -2.83) in the post-1963 sample, and -0.091% (t-statistic -1.86) in the 1980—2002 sample. The slope is -0.010% (t-statistic -1.47) for the expected HML return in 1941—2002, -0.011% (t-statistic -0.76) in 1963—2002, and -0.097% (t-statistic -3.12) in the 1980—2002 sample. Using the HP filter yields somewhat different results. Figure ?? plots the trend and cyclical components of the expected p5-1 return and the expected HML return. Panel B shows a downward movement in the HP-filtered, low frequency component of the expected p5-1 and HML returns. Panel A shows the patterns for the low frequency movements of p5-1 and HML in the case of the time-trend regression (estimated using the full sample). As pointed out before, there is a downward trend for p5-1 and no clear trend for HML. Overall, the evidence based on the time-trend regression and the HP filter indicates a downward trend in the low-frequency movements of the expected value premium. 4.2 Cyclical Dynamics Panels C and D of Figure ?? trace the cyclical components of the expected p5-1 and HML return. Panel C is based on the residuals from the time-trend regression, while Panel D is based on the HP filter. Both panels plot the NBER recession dummy which takes the value of one in recessions and zero otherwise. The graphs show that the expected value premium 19 is countercyclical—the expected value premium rises in recessions and drops in expansions. We use two additional methods to study the cyclical properties of the expected value premium. As an informal test, we first report the lead-lag cross-correlation structure of the expected value premium with a list of cyclical indicators. We then supplement the cross-correlations with a more formal VAR analysis. Cross Correlations Table ?? reports the cross-correlations. The list of cyclical indicators includes the default premium, the NBER recession dummy, the real investment growth rate, and the real consumption growth rate. Among the four variables, the default premium and the recession dummy are countercyclical, while the real investment and consumption growth rates are procyclical. The middle column in Panel A of Table ?? shows that the contemporaneous correlation between the expected p5-1 return and the default premium is 0.49 and that between the expected p5-1 return and the recession dummy is 0.50. Both correlations are significant. Further, the contemporaneous correlation between the expected p5-1 return and real investment growth is -0.36 and that between the expected p5-1 return and real consumption growth is -0.32 (both are significant). The middle column in Panel B shows that using the expected HML return yields similar results. To sum up, the evidence suggests that the expected value premium is countercyclical. The middle columns of the two panels also show that the countercyclical property of the expected value premium derives mostly from a similar property of the expected dividendprice ratio. The dividend price ratios of p5-1 and HML have significantly positive correlations with the default premium. Their correlations with the other cyclical variables are not 20 significant. In contrast, the expected dividend growth rates of p5-1 and HML exhibit only weak comovements with the business cycle, relative to the expected dividend-price ratio. VAR Analysis We next supplement the lead-lag correlations with a more formal VAR analysis. The VAR contains one measure of the expected value premium (either the expected p5-1 or the HML return) and one cyclical indicator. We use two cyclical variables separately in the VAR—the investment growth and the real consumption growth. Using other cyclical variables yields similar results (not reported). The lag in the VAR is one, which is chosen according to the Akaike information criterion. In some specifications, we also include the one-month T-bill rate in the VAR in an effort to isolate the business cycle shock from the monetary policy shocks. Table ?? reports the results. Panel A shows that the coefficients of real investment growth in the VAR are negative and significant (in the full sample period for portfolio p5-1 they are marginally significant). The result holds with and without controlling for the T-bill. Panel B shows that the coefficients of real consumption growth rate are all negative; they are all significant for both the long and the short sample periods. These results suggest that the expected value premium responds negatively to aggregate shocks. A positive shock to real consumption growth or real investment leads to lower expected value premia. To interpret the magnitudes of the VAR coefficients and to quantify the business cycle sensitivity of the expected value premium, we study the impulse response functions implied by the estimated VARs. Figure 6 plots these impulse response functions of the expected value premium in the presence of a one standard deviation shock to the explanatory variable. Panels A—C report the response of the expected value premium to a one-standard deviation 21 positive shock to real investment growth, while Panels E—H report the results relative to real consumption growth. In all cases, the premium responds negatively to good news about investment and consumption. 4.3 Predictive Regressions Previous studies (e.g., Asness et al. (2000) and Cohen, Polk, and Vuolteenaho (2003)) document that the realized value premium is predictable using the log book-to-market spread, suggesting that the expected value premium is time-varying. We investigate this issue further within our empirical framework. Specifically, we regress the value premium defined as the sum of the long-run dividend growth, Agt+1 , and the dividend-price ratio, Dt+1 /Pt , on a set of conditioning variables including the aggregate dividend yield, the default premium, the term premium, the log book-to-market spread, and the one-month T-bill rate. To study the predictability of the two separate components of the value premium, we also regress Agt+1 and Dt+1 /Pt on the same set of conditioning variables. These regressions have been used to construct the expected dividend growth and the expected dividend-price ratio. To adjust for the small-sample bias in the slopes and their standard errors (e.g., Stambaugh (1999)), we use the simulation method of Nelson and Kim (1993). Table ?? reports the results. The first three rows of all panels show that the value premium is indeed predictable. The adjusted R2 clusters around 30% except for the HML return in the 1941—2002 sample that has an adjusted R2 of 15.60%. Although not reported in the table, the null hypothesis that all the slopes are jointly zero is strongly rejected in all cases. The results suggest that the aggregate dividend yield has reliable predictive power with positive slopes, except for the HML return in the period from 1941 to 2002. Further, the term premium has significant predictive ability for the expected value premium 22 with negative slopes in all cases and across both sample periods. Consistent with previous studies, we find that the log book-to-market spread is largely a positive predictor of the value premium, except for predicting the p5-1 return in the post-1963 sample (Panel B). However, our results also show that its predictive power is weak, given that all corresponding p-values are close to 0.20. The default premium and the short-term rate do not have significant predictive ability for the expected value premium in the presence of the other conditioning variables. The rest of Table ?? reports the results of predicting the two separate components of the value premium including the dividend growth and dividend-price ratio. The set of conditioning variables does an overall better job in predicting the separate components than the value premium itself. This is reflected in much higher adjusted R2 s; in some cases the goodness-of-fit coefficients are more than doubled. Moreover, in some cases, the conditioning variables have different signs when predicting the two components, consistent with the results in Figure ?? that the expected dividend growth and the expected dividend-price ratio are negatively correlated. Specifically, the short rate is a significantly positive predictor of the long-run dividend growth, and a significantly negative predictor of the dividend-price ratio. A similar result holds for the term premium variable. 5 Robustness This section reports a set of robustness checks such as incorporating stock repurchases into the computation of the payout, using an alternative set of instruments to model expectations, and using a different set of portfolios to measure the value premium. 23 5.1 Stock Repurchases Fama and French (2001) document that the proportion of firms paying dividends has fallen dramatically over the years regardless of their levels of earnings. Grullon and Michaely (2002) show that dividends have been the dominant form of payout in earlier periods, but repurchases have become more important in recent years. In light of this evidence, we add net stock repurchases as part of the dividends. We replicate the results on ḡt+1 , Et [Agt+1 ], Et [Dt+1 /Pt ], and Et [Rt+1 ] in Table ??, the time series plots in Figure ??, and the VAR analysis in Table ?? and Figure 6. Table 6 reports the descriptive statistics for returns, dividend growth rates, and dividend yields, both realized and expected, for value and growth portfolios. Including stock repurchases in the payout makes all numbers in the table larger than their counterparts in Table ??. The value-minus-growth strategies are even more profitable in the case of repurchases—for example, the average realized return of p5-1 is 6.4% per year in the full sample and 5.7% per year in the subsample. Both values are significant. A similar result holds for the average realized return of HML. The expected value premium remains positive and significant—for example, the average expected return of p5-1 is 4.5% per year in the full sample and 4.2% per year in the subsample. The average expected return of HML is higher— it is 5.5% per year for 1941—2002 and 5.7% for 1963—2002. The table also shows that value portfolios have significantly higher expected long-run dividend growth rates and expected dividend-price ratios than growth portfolios. Figure 7 plots the trend and cyclical components of the expected p5-1 and HML returns, taking into account stock repurchases. Panel B shows that there is no obvious downward or upward movement in the HP-filtered, low-frequency component of both HML and p524 1. Panel A, however, shows a downward trend for the p5-1 portfolio using the time trend regression method. There is a slight upward trend for HML in Panel A. Table 7 reports the results from the VAR analysis of the expected value premium in the case of stock repurchases. In Panel A, the coefficients of real investment growth in the VAR are negative and significant. The result holds with and without controlling for monetary policy. Panel B shows that the coefficients of real consumption growth rate are all negative; they are all significant for both the long and the short sample periods. These results suggest that the expected value premium responds negatively to aggregate shocks. Finally, Figure 8 presents the impulse response functions implied by the estimated VAR in Table 7. Panels A—C report the response of the expected value premium to a one-standard deviation positive shock to real investment growth, while Panels E—H report the results relative to real consumption growth. In all cases, the expected value premium responds negatively to good news about investment and consumption. In summary, when stock repurchases are included in the computation of the expected value premium, the results are qualitatively very similar to the ones reported for our base case. The expected value premium is still significantly positive and countercyclical. The new result that emerges is that there does not exist a clear trend pattern in the movement of the expected value premium. 5.2 Alternative Instruments We also study the robustness of our benchmark results with respect to alternative sets of instruments. We first exclude the log book-to-market spread from the list of conditioning variables. The results look qualitatively very similar to the ones reported for our base case (they are not reported for the sake of brevity, but are readily available upon request). 25 Alternatively, we include Lettau and Ludvigson’s (2001, 2004) cay and cdy variables in the set of conditioning variables used to predict the dividend growth and the dividend-price ratio of value and growth. The new results indicate that there is a significant downward trend in the expected HML return once we use the HP filter. This is consistent with our previous findings based on the benchmark case. The impulse response functions from the VAR analysis indicate that, once we control for monetary policy, the value premium responds negative to good news about investment and consumption in the first year, but the response is positive in the second year. 5.3 Alternative Portfolios Finally, we use the portfolios already constructed by Fama and French to measure the expected value premium and its components. These portfolios include the group of 6 constructed by a 2x3 sort on size and book-to-market, as well as the 25 portfolios constructed by a 5x5 sort on size and book-to-market. The results reported before are robust to the choice of these portfolio. They are not reported for the sake of brevity, but are readily available upon request. 6 Summary and Interpretation In this paper we use fundamentals (dividends) to estimate the expected value premium. We show that over the period from 1941 to 2002, the expected value premium is positive and significant. Its magnitude is 5.1% per year based on the expected HML return. In addition, we document that the expected value premium is countercyclical—it rises in recessions and decreases in expansions. Furthermore, the expected value premium tends to be positively correlated with countercyclical variables like the default spread and negatively correlated 26 with procyclical variables like the growth in real consumption. We also report that the expected value premium increases with negative macroeconomic shocks and decreases as a result of positive macroeconomic shocks. There is some evidence that the expected value premium has decreased over time. What might explain the time variation in the expected value premium? Why is the expected value premium be countercyclical? Why do the dividend growth rates of value firms respond more to shocks to aggregate economic conditions? The rational asset pricing model of Zhang (2003) provides a unified explanation for the cyclical properties of the value premium and the spread in dividend growth between value and growth. Using a neoclassical framework, Zhang (2003) argues that the expected value premium is countercyclical. There are two key features in Zhang’s model. First, costly reversibility implies that it is more costly for firms to cut their productive assets than to expand them (e.g., Abel and Eberly (1994)). Second, a countercyclical price of risk implies that shareholders’ discount rates are higher in bad times than in good times (e.g., Fama and French (1989) and Campbell and Cochrane (2000)). Specifically, firms usually invest at a lower rate than the long run average rate in recessions. Value firms, having lower profitabilities than growth firms, will start to disinvest. Without costly reversibility, value firms will have enough flexibility to scale down. With costly reversibility, disinvestment implies higher adjustment costs which prevents value firms from scaling down as much as they would have otherwise. A countercyclical price of risk further complements and propagates the effects of costly reversibility. When the price of risk is countercyclical, firms’ discount rates are higher in recessions. Higher discount rates lead to lower conditional expectation of the firm value as 27 the net present value of its future dividends. As future prospects become gloomier, value firms would scrap even more capital than in the case with a constant price of risk. Because costly reversibility prevents value firms from disinvesting, these firms are burdened with more unproductive assets in bad times. Growth firms, on the other hand, are relatively immune to the effects of costly reversibility and a countercyclical price of risk in recessions. Growth firms have more productive assets, and hence have fewer incentives to scale down in recessions. 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Zhang, Lu, 2005, The value premium, Journal of Finance 60, 67—103. 30 30 Et [Rt+1 ] Et [Dt+1 /Pt ] Et [Agt+1 ] gt+1 Rt+1 Et [Rt+1 ] Et [Dt+1 /Pt ] Et [Agt+1 ] gt+1 Rt+1 0.085 2.89 0.009 0.33 0.003 3.54 0.032 10.66 0.035 10.36 LS 0.071 3.12 0.013 0.59 0.017 14.85 0.031 17.55 0.048 23.63 Low 0.090 4.59 0.026 1.22 0.019 16.15 0.048 28.63 0.067 27.54 3 0.105 4.58 0.036 1.53 0.028 32.58 0.054 28.01 0.082 35.67 4 0.129 4.60 0.058 2.12 0.031 12.14 0.054 30.08 0.085 21.69 High 0.073 3.29 0.014 0.69 0.018 15.19 0.033 18.97 0.051 25.22 LB 0.123 4.47 0.050 2.07 0.041 44.34 0.042 16.87 0.083 28.45 MS 0.080 3.96 0.015 0.72 0.008 5.47 0.048 28.23 0.056 19.86 MB 0.157 5.12 0.087 3.45 0.062 33.75 0.040 25.51 0.102 32.67 HS 0.120 4.56 0.048 1.99 0.030 19.64 0.057 29.86 0.087 27.13 HB Panel C: 1941–2002, two-way sort 0.075 3.60 0.016 0.60 0.017 17.70 0.041 22.22 0.058 24.36 2 Panel A: 1941–2002, one-way sort 0.060 4.24 0.056 2.07 0.035 19.90 0.016 9.90 0.051 40.89 HML 0.058 2.88 0.045 1.42 0.014 4.65 0.023 15.10 0.037 14.91 p5-1 0.066 1.83 0.005 0.14 0.001 1.156 0.017 13.77 0.018 8.78 LS 0.058 2.01 0.016 0.53 0.019 11.06 0.023 29.97 0.041 20.64 Low 0.077 3.58 0.023 0.79 0.014 11.59 0.042 27.47 0.056 31.94 3 0.103 4.41 0.039 1.30 0.025 24.64 0.050 21.17 0.075 29.53 4 0.104 4.03 0.036 1.04 0.019 13.18 0.050 23.14 0.069 23.21 High 0.059 2.12 0.015 0.51 0.020 11.51 0.025 31.06 0.045 20.81 LB 0.113 3.57 0.053 1.52 0.039 30.08 0.031 21.42 0.070 29.99 MS 0.066 3.00 0.011 0.41 0.001 1.12 0.042 25.33 0.044 20.00 MB 0.143 4.43 0.077 2.49 0.054 40.33 0.034 21.82 0.088 39.60 HS 0.101 4.11 0.033 1.13 0.023 25.60 0.054 22.51 0.077 24.49 HB Panel D: 1963–2002, two-way sort 0.058 2.33 0.013 0.34 0.016 11.69 0.033 30.36 0.049 23.19 2 Panel B: 1963–2002, one-way sort 0.059 3.81 0.045 1.22 0.028 21.00 0.023 14.74 0.051 31.73 HML 0.046 2.10 0.020 0.48 0.000 0.12 0.028 14.60 0.028 12.05 p5-1 This table reports the sample averages of the realized return, Rt+1 , the realized dividend growth, gt+1 , the expected long-run dividend growth, Et [Agt+1 ], the expected dividend yield, Et [Dt+1 /Pt ], and the expected return, Et [Rt+1 ] for various value and growth portfolios. The corresponding t-statistics are reported in the rows below the sample averages. The results for both the full sample from 1941 to 2002 and for the subsample from 1963 to 2002 are reported. Panels A and B contain the results for five quintiles sorted on book-to-market, while Panels C and D contain the results for six portfolios based on a two-by-three sort on size and book-to-market. In Panels A and B, p5-1 denotes the difference between portfolio High and portfolio Low in the five book-to-market quintiles. In Panels C and D, portfolios are denoted by two letters, for example, portfolio LS contains stocks with the bottom 30% book-to-market ratios and the bottom 50% market capitalization. Significant average realized and expected returns for p5-1 and HML and their t-statistics are highlighted. Table 1 : Descriptive Statistics for The Realized Returns, Realized Dividend Growth, Expected Long-run Dividend Growth, Expected Dividend Yield, and Expected Returns of Value and Growth Portfolios Table 2 : Autocorrelations and Unit Root Tests for the Expected Value Premium and Its Two Components (1941—2002) This table reports autocorrelations of orders 1, 2, 3, 4, 5, and 10, MacKinnon unit root test statistics, and their corresponding p-values for the expected return of portfolio 5-1 (Panel A), the expected return of HML (Panel B), and their respective two components—the expected long-run dividend growth rate, Et [Agt+1 ] and the expected dividend-price ratio, Et [Dt+1 /Pt ]. Panel A: p5-1 Autocorrelations (order) Et [Agt+1 ] Et [Dt+1 /Pt ] Premium Unit-Root Test 1 2 3 4 5 10 Statistic p-value 0.811 0.873 0.638 0.731 0.720 0.473 0.675 0.608 0.368 0.615 0.583 0.295 0.599 0.574 0.323 0.496 0.235 0.275 -2.889 -1.992 -5.180 0.047 0.290 0.000 Panel B: HML Autocorrelations (order) Et [Agt+1 ] Et [Dt+1 /Pt ] Premium Unit-Root Test 1 2 3 4 5 10 Statistic p-value 0.740 0.916 0.534 0.576 0.808 0.188 0.513 0.728 0.028 0.468 0.705 -0.066 0.459 0.688 0.010 0.440 0.423 0.070 -3.740 -1.705 -6.058 0.004 0.428 0.002 31 32 Real gCON Real gINV Cycle DEF Real gCON Real gINV Cycle DEF Real gCON Real gINV Cycle DEF 0.43 0.00 -0.08 0.56 -0.01 0.93 -0.14 0.29 -0.32 0.02 0.06 0.64 0.01 0.92 0.03 0.85 0.09 0.50 -0.13 0.32 -0.01 0.92 -0.07 0.61 -5 -3 -2 -1 0 1 2 3 4 0.13 0.32 0.03 0.83 0.18 0.18 0.17 0.19 0.42 0.00 0.28 0.03 -0.14 0.27 0.07 0.62 -0.39 0.00 0.20 0.13 0.25 0.06 0.23 0.08 -0.34 0.01 0.15 0.27 0.24 0.07 0.15 0.26 -0.27 0.03 0.14 0.28 -0.02 0.91 0.09 0.48 -0.27 0.04 0.13 0.30 -0.16 0.21 -0.10 0.42 -0.38 0.00 - 0.03 0.80 -0.11 0.40 -0.12 0.38 -0.58 0.00 -0.15 0.26 -0.04 0.74 0.03 0.81 -0.54 0.00 -0.08 0.54 0.04 0.76 0.14 0.28 -0.46 0.00 -0.02 0.86 0.05 0.70 0.14 0.31 0.49 0.28 -0.22 -0.29 -0.13 0.00 0.03 0.10 0.02 0.33 0.50 0.12 -0.34 -0.24 -0.03 0.00 0.37 0.01 0.06 0.83 -0.36 -0.35 -0.15 0.15 0.18 0.00 0.01 0.26 0.25 0.19 -0.32 -0.54 -0.26 0.13 0.21 0.01 0.00 0.04 0.32 0.11 Expected Dividend Growth, Et [Agt+1 ] -0.03 0.83 -0.03 0.82 0.13 0.34 0.20 0.13 0.47 0.00 -0.10 0.45 -0.02 0.86 -0.12 0.38 0.45 0.00 -0.14 0.29 -0.05 0.71 -0.11 0.42 0.46 0.00 -0.11 0.40 0.03 0.82 -0.02 0.88 0.59 0.00 -0.03 0.84 -0.00 0.99 0.01 0.92 0.77 0.92 0.69 0.49 0.41 0.00 0.00 0.00 0.00 0.00 0.19 0.27 0.07 -0.05 -0.08 0.14 0.04 0.62 0.69 0.55 -0.04 -0.20 -0.23 -0.09 0.03 0.75 0.12 0.08 0.48 0.82 -0.04 -0.26 -0.36 -0.22 -0.01 0.74 0.04 0.01 0.09 0.96 Expected Dividend-Price Ratio, Et [Dt+1 /Pt ] -0.36 0.01 0.19 0.15 0.26 0.05 0.23 0.08 0.05 0.71 -0.01 0.94 0.22 0.10 0.22 0.10 Expected Value Premium, Et [Agt+1 ] + Et [Dt+1 /Pt ] -4 Panel A: p5-1 -5 -3 -2 -1 0 1 2 3 4 -0.22 0.10 -0.28 0.03 -0.24 0.06 -0.31 0.02 -0.31 0.02 -0.25 0.06 0.07 0.63 0.04 0.74 -0.48 0.00 -0.08 0.54 0.08 0.57 0.18 0.18 -0.33 0.01 0.05 0.72 0.01 0.92 0.07 0.61 -0.21 0.11 -0.15 0.26 0.21 0.12 0.24 0.08 0.43 0.49 0.52 0.49 0.50 0.60 0.70 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 -0.08 -0.16 -0.19 -0.12 0.01 0.16 0.93 0.56 0.23 0.14 0.36 0.93 0.21 0.07 -0.02 -0.14 -0.16 -0.07 -0.00 0.00 0.58 0.86 0.29 0.24 0.58 0.97 0.98 0.04 -0.10 -0.18 -0.16 -0.04 -0.02 -0.03 0.78 0.45 0.19 0.23 0.74 0.91 0.84 0.77 0.00 0.17 0.18 -0.12 0.35 -0.18 0.16 0.60 0.00 0.02 0.89 -0.14 0.28 -0.26 0.05 0.44 0.00 -0.06 0.65 -0.03 0.83 -0.14 0.30 0.38 0.00 -0.06 0.67 0.05 0.71 0.03 0.83 Expected Dividend-Price Ratio, Et [Dt+1 /Pt ] -0.42 -0.34 -0.38 -0.38 -0.27 -0.17 -0.19 -0.42 -0.57 0.00 0.01 0.00 0.00 0.04 0.20 0.14 0.00 0.00 0.03 -0.01 0.17 0.18 0.14 0.15 0.13 -0.11 -0.22 0.82 0.96 0.20 0.17 0.29 0.24 0.30 0.41 0.09 0.04 0.00 0.34 0.31 0.26 -0.07 -0.26 -0.14 0.00 0.77 0.99 0.01 0.02 0.04 0.62 0.04 0.28 0.99 0.12 -0.01 0.30 0.29 0.15 0.05 -0.21 -0.20 0.05 0.40 0.96 0.02 0.03 0.25 0.70 0.10 0.13 0.71 Expected Dividend Growth, Et [Agt+1 ] 0.36 0.00 0.18 0.16 -0.34 0.01 -0.49 0.00 Expected Value Premium, Et [Agt+1 ] + Et [Dt+1 /Pt ] -4 -0.05 0.13 0.10 0.02 0.08 0.28 0.39 0.69 0.33 0.47 0.88 0.53 0.03 0.00 0.06 -0.07 0.08 0.09 0.05 0.16 0.41 0.68 0.62 0.56 0.51 0.68 0.21 0.00 0.14 0.04 0.19 0.11 0.14 -0.16 -0.28 0.32 0.77 0.15 0.43 0.28 0.23 0.03 0.12 -0.05 0.16 0.11 0.08 0.04 -0.24 0.39 0.72 0.24 0.43 0.56 0.77 0.06 5 Panel B: HML 0.42 0.00 0.02 0.90 0.05 0.72 0.03 0.85 -0.34 0.01 0.02 0.89 -0.00 0.98 0.02 0.86 -0.08 0.55 0.07 0.61 0.21 0.11 0.22 0.10 5 This table reports the lead-lag correlations between the expected value premium, expected dividend growth, and expected dividend-price ratio of portfolios p5-1 and HML and a list of cyclical indicators including the default premium, DEF, the NBER recession dummy, Cycle, real investment growth, gINV , and real consumption growth, gCON . Panel A reports the results for portfolio 5-1, and Panel B does the same for HML. p-values are reported in the rows below the correlations. Table 3 : Lead-Lag Correlations between the Expected Value Premium, Expected Dividend Growth, and Expected Dividend-Price Ratio and Cyclical Indicators (1941–2002) 33 Expected HML Return Expected p5-1 Return -0.008 0.071 -0.016 0.021 no T-bill -0.007 0.066 -0.017 0.020 with T-bill 1941–2002 -0.031 0.015 -0.042 0.029 no T-bill -0.024 0.006 -0.041 0.026 with T-bill 1963–2002 Panel A: Real gINV -0.158 0.000 -0.239 0.000 no T-bill -0.122 0.000 -0.231 0.000 with T-bill 1941–2002 -0.255 0.000 -0.342 0.001 no T-bill -0.143 0.005 -0.295 0.004 with T-bill 1963–2002 Panel B: Real gCON This table reports the results from a first-order VAR that includes the expected value premium and one of two cyclical indicators–real investment growth, gINV , and real consumption growth, gCON . The table reports the equation for the expected value premium for the 1941–2002 and 1963–2002 samples. We also report the results with and without controlling for monetary policy as captured by the one-month T-bill rate. The lag in the VAR is one, which is chosen based on the Akaike information criterion. p-values associated with Newey-West t-statistics adjusted for heteroscedasticity and autocorrelation of up to six lags are reported in the rows below the coefficients. Table 4 : VAR Analysis 34 0.055 0.038 0.016 Agt+1 bias p Dt+1 /Pt bias p -0.002 0.000 0.221 0.005 -0.001 0.036 0.003 -0.001 0.128 div intercept Premium bias p 0.001 -0.001 0.346 0.028 Dt+1 /Pt bias p 0.007 -0.001 0.071 0.007 -0.002 0.034 0.017 0.045 div Agt+1 bias p Premium bias p intercept 0.001 -0.001 0.252 -0.017 0.001 0.002 -0.016 0.001 0.002 term 0.006 0.002 0.290 0.006 -0.001 0.310 0.012 0.001 0.213 ls 0.008 -0.001 0.004 -0.004 0.000 0.183 0.004 -0.001 0.099 def 0.002 -0.001 0.150 -0.008 0.000 0.008 -0.006 0.000 0.049 term -0.003 0.002 0.263 0.014 0.000 0.076 0.011 0.003 0.180 ls Panel C: 1941–2002, HML 0.013 -0.001 0.000 0.003 0.000 0.385 0.015 0.000 0.015 def Panel A: 1941–2002, p5-1 0.009 0.000 0.007 -0.006 -0.001 0.112 0.003 -0.001 0.212 rf 0.007 0.000 0.044 -0.020 0.000 0.006 -0.013 0.001 0.025 rf 0.395 0.794 0.156 adj. R 2 0.581 0.540 0.301 adj. R 2 0.008 0.058 0.066 intercept 0.011 0.028 0.039 intercept -0.006 -0.001 0.118 0.023 -0.001 0.000 0.017 -0.003 0.002 div -0.006 -0.002 0.226 0.024 -0.003 0.001 0.018 -0.005 0.010 div 0.004 0.000 0.099 -0.020 0.001 0.001 -0.016 0.001 0.012 term -0.013 0.001 0.101 0.002 0.002 0.490 -0.011 0.003 0.249 ls 0.007 -0.001 0.009 -0.005 -0.001 0.207 0.002 -0.002 0.255 def 0.004 -0.001 0.063 -0.013 0.000 0.001 -0.009 0.000 0.035 term -0.011 0.002 0.057 0.023 0.001 0.042 0.012 0.003 0.260 ls Panel D: 1963–2002, HML 0.008 -0.001 0.021 -0.002 -0.001 0.425 0.005 -0.002 0.206 def Panel B: 1963–2002, p5-1 0.013 0.000 0.005 -0.019 -0.002 0.008 -0.006 -0.001 0.294 rf 0.015 0.001 0.010 -0.030 -0.002 0.007 -0.015 0.000 0.103 rf 0.452 0.721 0.309 adj. R2 0.575 0.485 0.315 adj. R2 This table reports predictive regressions for the value premium, Agt+1 + Dt+1 /Pt , and its two components–the long-run dividend growth rate, Agt+1 , and the dividend-price ratio, Dt+1 /Pt . We report results for both portfolio 5-1 from the one-way sort on book-to-market and HML from the two-way sort on size and book-to-market. There are five regressors, (i) dividend yield, div, computed as the sum of dividends accruing to the CRSP value-weighted portfolio over the previous 12 months divided by the current index level; (ii) default premium, def, which is the yield spread between Baa and Aaa corporate bonds; (iii) term premium, term, computed as the yield spread between ten-year and one-year government bonds; (iv) log book-to-market spread, ls, defined as the log book-to-market of decile ten minus that of decile one from ten book-to-market portfolios; and (v) one-month Treasury bill, rf. All regressors are standardized to have zero mean and unit variance. We report intercepts, slopes, bias in slopes, adjusted R2 s, and p-values adjusted for small-sample problems using Nelson and Kim (1993) methods. Table 5 : Predictive Regressions for the Value Premium and Its Two Components–the Long-Run Dividend Growth Rate and the Dividend-Price Ratio 35 Et [Rt+1 ] Et [Dt+1 /Pt ] Et [Agt+1 ] gt+1 Rt+1 Et [Rt+1 ] Et [Dt+1 /Pt ] Et [Agt+1 ] gt+1 Rt+1 0.090 3.10 0.035 1.19 0.029 19.67 0.038 15.58 0.067 43.64 LS 0.073 3.22 0.032 1.31 0.036 21.75 0.036 24.68 0.072 44.90 Low 0.097 4.92 0.048 2.09 0.041 81.97 0.055 40.58 0.096 91.64 3 0.111 4.84 0.050 1.92 0.039 61.09 0.061 38.82 0.100 71.03 4 0.137 4.90 0.080 2.77 0.054 46.70 0.064 43.64 0.117 50.45 High 0.076 3.41 0.029 1.27 0.031 19.71 0.038 26.48 0.069 39.04 LB 0.131 4.76 0.074 2.79 0.064 62.56 0.051 26.94 0.115 98.70 MS 0.086 4.26 0.033 1.37 0.024 60.71 0.055 40.19 0.079 58.78 MB 0.166 5.40 0.109 4.06 0.088 139.33 0.050 50.42 0.138 118.80 HS HB 0.127 4.82 0.064 2.59 0.044 47.01 0.066 42.03 0.110 47.63 Panel C: 1941–2002, two-way sort 0.080 3.83 0.029 1.03 0.024 24.72 0.047 34.71 0.071 40.28 2 Panel A: 1941–2002, one-way sort 0.063 4.43 0.054 2.22 0.036 24.58 0.020 11.69 0.055 52.55 HML 0.064 3.19 0.048 1.47 0.017 8.08 0.028 18.18 0.045 27.09 p5-1 0.074 2.05 0.039 1.02 0.036 26.64 0.026 22.51 0.062 48.34 LS 0.060 2.10 0.044 1.30 0.043 23.90 0.030 29.62 0.073 32.04 Low 0.086 3.99 0.054 1.76 0.043 90.52 0.053 31.95 0.095 68.91 3 0.110 4.72 0.062 1.71 0.042 72.73 0.060 28.80 0.102 51.73 4 0.117 4.56 0.068 1.89 0.051 59.91 0.064 34.11 0.115 48.08 High 0.063 2.25 0.038 1.15 0.037 19.79 0.032 29.51 0.069 27.80 LB 0.123 3.90 0.086 2.25 0.069 98.13 0.043 33.24 0.111 88.47 MS 0.074 3.36 0.039 1.17 0.023 42.71 0.053 30.58 0.076 46.92 MB 0.155 4.80 0.112 3.30 0.088 148.01 0.049 39.48 0.137 116.08 HS HB 0.111 4.56 0.058 1.90 0.044 51.17 0.065 32.46 0.109 41.20 Panel D: 1963–2002, two-way sort 0.065 2.59 0.034 0.83 0.026 18.74 0.042 34.82 0.068 30.94 2 Panel B: 1963–2002, one-way sort 0.064 4.07 0.047 1.47 0.030 23.57 0.027 19.27 0.057 57.38 HML 0.057 2.59 0.024 0.61 0.008 5.23 0.034 22.36 0.042 36.72 p5-1 This table reports the sample averages of the realized return, Rt+1 , the realized dividend growth, gt+1 , the expected long-run dividend growth, Et [Agt+1 ], the expected dividend yield, Et [Dt+1 /Pt ], and the expected return, Et [Rt+1 ] for various value and growth portfolios. The computation of dividends includes net stock repurchases. The corresponding t-statistics are reported in the rows below the sample averages. The results for both the full sample from 1941 to 2002 and for the subsample from 1963 to 2002 are reported. Panels A and B contain the results for five quintiles sorted on book-to-market, while Panels C and D contain the results for six portfolios based on a two-by-three sort on size and book-to-market. In Panels A and B, p5-1 denotes the difference between portfolio High and portfolio Low in the five book-to-market quintiles. In Panels C and D, portfolios are denoted by two letters, for example, portfolio LS contains stocks with the bottom 30% book-to-market ratios and the bottom 50% market capitalization. Significant average realized and expected returns for p5-1 and HML and their t-statistics are highlighted. Table 6 : Including Repurchases: Descriptive Statistics for The Realized Returns, Realized Dividend Growth, Expected Long-run Dividend Growth, Expected Dividend Yield, and Expected Returns of Value and Growth Portfolios 36 Expected HML Return Expected p5-1 Return -0.009 0.012 -0.014 0.006 no T-bill -0.009 0.013 -0.014 0.009 with T-bill 1941–2002 -0.034 0.000 -0.035 0.000 no T-bill -0.030 0.000 -0.034 0.000 with T-bill 1963–2002 Panel A: Real gCON -0.149 0.000 -0.177 0.000 no T-bill -0.142 0.000 -0.178 0.000 with T-bill 1941–2002 -0.203 0.000 -0.210 0.000 no T-bill -0.159 0.000 -0.195 0.000 with T-bill 1963–2002 Panel B: Real gCON This table reports the results from a first-order VAR that includes the expected value premium and one of two cyclical indicators–real investment growth, gINV , and real consumption growth, gCON . The computation of dividends includes net stock repurchases. The table reports the equation for the expected value premium for the 1941–2002 and 1963–2002 samples. We also report the results with and without controlling for monetary policy as captured by the one-month T-bill rate. The lag in the VAR is one, which is chosen based on the Akaike information criterion. p-values associated with Newey-West t-statistics adjusted for heteroscedasticity and autocorrelation of up to six lags are reported in the rows below the coefficients. Table 7 : Including Repurchases: VAR Analysis 37 −10 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 −10 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 −6 −4 −2 0 2 4 6 −8 −6 −4 −2 0 2 4 6 Panel D: Et+1 /Bt , two-way sort −8 8 8 S/H B/H S/L B/L Value Stocks Growth Stocks Panel A: Et+1 /Bt , one-way sort 10 10 0.01 −10 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.02 −10 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 −6 −4 −2 0 2 4 6 −8 −6 −4 −2 0 2 4 6 Panel E: Dt+1 /Bt , two-way sort −8 8 8 S/H B/H S/L B/L Value Stocks Growth Stocks Panel B: Dt+1 /Bt , one-way sort 10 10 0.9 −10 0.95 1 1.05 1.1 1.15 0.9 −10 0.95 1 1.05 1.1 1.15 −8 −8 −4 −2 0 2 4 6 −6 −4 −2 0 2 4 6 Panel F: gt+1 , two-way sort −6 Panel C: gt+1 , one-way sort 8 8 S/H B/H S/L B/L Value Stocks Growth Stocks 10 10 This figure plots the event time evolution of dividend growth rates and the ratios of dividend and lagged book equity for value and growth portfolios. We construct value and growth portfolios using a one-way sort on book-to-market into five quintiles and using a two-by-three sort on size and book-to-market into six portfolios as Fama and French (1993). Panel A plots profitability defined as earnings divided by lagged book value, Et+1 /Bt , for portfolios five (value) and one (growth) from the quintiles, and Panel D does the same for four portfolios including small-high (S/H), big-high (B/H), small-low (S/L), and big-low (B/L) from the six portfolios sorted on size and book-to-market. Panel plots the dividend-lagged book equity, Dt+1 /Bt , for portfolios five and one from the quintiles, and Panel E does the same for S/H, B/H, S/L, and B/L. Panel C plots the real dividend growth rates, gt+1 , for portfolios five and one from the quintiles, and Panel F does the same for S/H, B/H, S/L, and B/L. Figure 1 : Event-Time Evolution of Profitability, Real Dividend/Lagged Book Equity, and Real Dividend Growth for Value and Growth Portfolios (1941–2003) Figure 2 : Times Series of the Annual Realized Real Dividend Growth Rates of Value and Growth Portfolios (1941—2002) This figure plots the sample paths of the annual realized real dividend growth rates of value and growth portfolios. We construct value and growth portfolios using a one-way sort on book-to-market (into five quintiles) and using a two-by-three sort on size and book-to-market (into six portfolios). Panel A plots the annual real dividend growth rates for portfolios five and one from the quintiles, and Panel B plots that for portfolio five-minus-one, p5-1. Panel C plots the annual real dividend growth rates for portfolios High and Low defined from the six portfolios after controlling for size as in Fama and French (1993). Panel D does the same for HML. In Panels A and C, the solid lines represent the value portfolios, and the broken lines represent Dt+1 /Pt the growth portfolios. The real dividend growth is measured as gt+1 = D (RtX + 1)(CPIt−1 /CPIt ) − 1, t /Pt−1 where RtX is the nominal value-weighted portfolio return without dividend from year t−1 to t, and CPIt is the X consumer price index at year t. The dividend yield is constructed as Dt+1 /Pt = (Rt+1 −Rt+1 )(CPIt /CPIt+1 ), where Rt+1 is the nominal value-weighted portfolio return with dividend from year t to t+1. Panel B: p5-1 Panel A: Portfolios 5 and 1 0.5 Dividend Growth Diff. between Value and Growth Stocks Value Stocks Growth Stocks 0.6 0.4 0.3 0.4 0.2 0.2 0.1 0 0 −0.1 −0.2 −0.2 −0.4 −0.3 −0.4 −0.6 −0.5 1950 1960 1970 1980 1990 2000 1950 Panel A: Portfolios High and Low 1960 1970 1980 1990 2000 Panel B: HML 0.5 Value Stocks Growth Stocks Dividend Growth Diff. between Value and Growth Stocks 0.4 0.4 0.3 0.2 0.2 0.1 0 0 −0.2 −0.1 −0.2 −0.4 −0.3 −0.4 −0.5 −0.6 1950 1960 1970 1980 1990 2000 38 1950 1960 1970 1980 1990 2000 Figure 3 : Times Series of the Expected Value Premium and Its Two Components—the Expected Long-Run Dividend Growth and the Expected Dividend-Price Ratio (1941—2002) This figure plots the times series of the expected value premium, Et [Rt+1 ], and its two components—the expected long-run dividend growth, Et [Agt+1 ], and the expected dividend-price ratio, Et [Dt+1 /Pt ]. Panel A plots the expected return of portfolio five-minus-one, p5-1, and Panel B plots its two components—the expected long-run dividend growth and the expected dividend-price ratio. Panel C plots the expected HML return, and Panel D plots its two components—the expected long-run dividend growth and the expected dividend-price ratio. In Panels A and C, we also plot the scaled default spread defined as the Baa yield over the Aaa yield scaled by two. In all panels, the shadowed rectangles represent the NBER recession dummy, which takes the value of one in recessions and zero otherwise. Panel A: p5-1: Expected Return Panel B: p5-1: Et [Agt+1 ] and Et [Dt+1 /Pt ] 0.12 The Expected Value Premium Scaled Default Spread Expected Dividend Growth Expected Dividend Price Ratio 0.06 0.1 0.04 0.08 0.02 0.06 0 0.04 −0.02 0.02 −0.04 0 1950 1960 1970 1980 1990 2000 1950 Panel C: HML: Expected Return 1960 1970 1980 1990 2000 Panel D: HML: Et [Agt+1 ] and Et [Dt+1 /Pt ] 0.09 0.08 Expected Dividend Growth Expected Dividend Price Ratio 0.08 The Expected Value Premium Scaled Default Spread 0.07 0.07 0.06 0.06 0.05 0.04 0.05 0.03 0.04 0.02 0.03 0.01 0.02 0.01 0 1950 1960 1970 1980 1990 2000 39 −0.01 1950 1960 1970 1980 1990 2000 Figure 4 : Time Series of the Expected Equity Premium (1941—2002) This figure plots the time series of the constructed expected equity premium. The Expected Market Equity Premium 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 1950 1960 1970 40 1980 1990 2000 Figure 5 : Trend and Cyclical Components of the Expected Value Premium (1941—2002) This figure reports trend and cyclical components of the expected value premium including both that from a one-way sort on book-to-market (broken line) and that from a two-way sort on size and book-to-market (solid line). Panel A reports the time trend and Panel B reports the trend components from a Hodrock and Prescott (HP) filter. Panel C reports the cyclical component after the time trend is removed from the expected value premium, and Panel D reports the cyclical component from the HP-filter. In all panels, the shadowed rectangles represent the NBER recession dummy, which takes the value of one in recessions and zero otherwise. Panel A: Time Trend Panel B: HP-filtered Trend 0.1 Two−way sort One−way sort Two−way sort One−way sort 0.06 0.09 0.055 0.05 0.08 0.045 0.04 0.07 0.035 0.03 0.06 0.025 0.02 0.05 0.015 0.01 1950 1960 1970 1980 1990 2000 0.04 1950 Panel C: Cyclical Component with Time Trend 1960 1970 1980 1990 2000 Panel D: HP-filtered Cyclical Component 0.05 0.04 Two−way sort One−way sort Two−way sort One−way sort 0.04 0.03 0.03 0.02 0.02 0.01 0.01 0 0 −0.01 −0.01 −0.02 −0.02 −0.03 1950 1960 1970 1980 1990 2000 41 −0.03 1950 1960 1970 1980 1990 2000 42 −5 −4 −3 −2 −1 0 1 0 x 10 −3 1 2 3 4 5 6 7 8 9 Panel A: p5-1: gINV , no T-bill 0 x 10 −3 1 2 3 4 5 6 7 8 9 Panel E: p5-1: gCON , no T-bill −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 10 10 0 1 2 3 4 5 6 7 8 9 −4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 0 −3 x 10 1 2 3 4 5 6 7 8 9 Panel F: p5-1: gCON , with T-bill −2.5 10 10 −3 0 1 2 3 4 5 6 7 8 9 Panel C: HML: gINV , no T-bill x 10 −7 −6 −5 −4 −3 −2 −1 0 1 0 −3 x 10 1 2 3 4 5 6 7 8 9 Panel G: HML: gCON , no T-bill −5 −4 −2 −2 −1 0 1 −3 −3 x 10 −1.5 −1 −0.5 0 0.5 Panel B: p5-1: gINV , with T-bill 10 10 0 −3 x 10 1 2 3 4 5 6 7 8 9 10 −6 −5 −4 −3 −2 −1 0 1 0 −3 x 10 1 2 3 4 5 6 7 8 9 10 Panel H: HML: gCON , with T-bill −4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 Panel D: HML: gINV , with T-bill This figure plots the impulse response functions for the expected return of p5-1 and the expected HML return in the presence of a one-standarddeviation positive shock to real investment growth, gINV (Panels A–D), and to real consumption growth, gCON (Panels E–H). We report the results with and without controlling for the one-month T-bill rate in the VAR. In all panels, a two-standard-error band is also plotted. Figure 6 : Impulse Response Functions for the Expected Value Premium After A One-Standard-Deviation Positive Shock to Real Investment Growth or the Real Consumption Growth Figure 7 : Including Repurchases: Trend and Cyclical Components of the Expected Value Premium (1941—2002) This figure reports trend and cyclical components of the expected value premium including both that from a one-way sort on book-to-market (broken line) and that from a two-way sort on size and book-to-market (solid line). The computation of dividends includes net stock repurchases. Panel A reports the time trend and Panel B reports the trend components from a Hodrock and Prescott (HP) filter. Panel C reports the cyclical component after the time trend is removed from the expected value premium, and Panel D reports the cyclical component from the HP-filter. In all panels, the shadowed rectangles represent the NBER recession dummy, which takes the value of one in recessions and zero otherwise. Panel A: Time Trend Panel B: HP-filtered Trend 0.065 0.08 Two−way sort One−way sort Two−way sort One−way sort 0.075 0.06 0.07 0.055 0.065 0.06 0.05 0.055 0.045 0.05 0.045 0.04 0.04 0.035 0.035 0.03 1950 1960 1970 1980 1990 2000 0.03 Panel C: Cyclical Component with Time Trend 1950 1960 1970 1980 1990 2000 Panel D: HP-filtered Cyclical Component 0.04 Two−way sort One−way sort 0.05 Two−way sort One−way sort 0.03 0.04 0.02 0.03 0.01 0.02 0 0.01 −0.01 0 −0.02 −0.01 −0.02 1950 1960 1970 1980 1990 2000 43 −0.03 1950 1960 1970 1980 1990 2000 44 0 x 10 −3 1 2 3 4 5 6 7 8 9 Panel A: p5-1: gINV , no T-bill −3 1 2 3 4 5 6 7 8 9 10 −4 −2.5 −2.5 −4 −2 −2 −3 −1.5 −1.5 −3.5 −1 −1 −3 −0.5 −0.5 −3.5 0 1 0.5 0 0 1 2 3 4 5 6 7 8 9 0 −3 x 10 1 2 3 4 5 6 7 8 9 Panel F: p5-: gCON , with T-bill −2.5 0 x 10 10 −2 −1.5 −1 −0.5 0 −3 x 10 Panel B: p5-1: gINV , with T-bill 0.5 0.5 1 Panel E: p5-1: gCON , no T-bill −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 10 10 0 −3 x 10 1 2 3 4 5 6 7 8 9 −5 −4 −3 −2 −1 0 1 0 x 10 −3 1 2 3 4 5 6 7 8 9 Panel G: HML: gCON , no T-bill −4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 Panel C: HML: gINV , no T-bill 10 10 0 −3 x 10 1 2 3 4 5 6 7 8 9 10 −5 −4 −3 −2 −1 0 1 0 −3 x 10 1 2 3 4 5 6 7 8 9 10 Panel H: HML: gCON , with T-bill −4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 Panel D: HML: gINV , with T-bill This figure plots the impulse response functions for the expected return of p5-1 and the expected HML return in the presence of a one-standarddeviation positive shock to real investment growth, gINV (Panels A–D), and to real consumption growth, gCON (Panels E–H). The computation of dividends includes net stock repurchases. We report the results with and without controlling for the one-month T-bill rate in the VAR. In all panels, a two-standard-error band is also plotted. Figure 8 : Including Repurchases: Impulse Response Functions for the Expected Value Premium After A One-Standard-Deviation Positive Shock to Real Investment Growth and Real Consumption Growth