Predictable Variation in Stock Returns and Cash Flow Growth: What Role Does Issuance Play?

Transcription

1 Predictable Variation in Stock Returns and Cash Flow Growth: What Role Does Issuance Play? Gregory W. Eaton 1 and Bradley S. Paye 1 1 Terry College of Business, University of Georgia, Athens, GA 30602, USA September 22, 2014 JEL Classification: G1, C13 Keywords: Stock return predictability, cash flow growth predictability, dividend yield, net payout yield, stock issuances, stock repurchases. Abstract We assess the predictive content of yields based on alternative cash flow measures, focusing on the role of equity issuance. For stock returns, it is preferable to incorporate (net) issuance via the net payout yield, which implicitly restricts slope coefficients associated with different cash flow components, rather than as a separate forecasting variable. In contrast to results for dividend growth, issuance and net payout growth are predictable using the corresponding yields both in- and out-of-sample. We show that long-term investors hedging demand for stock is greatly reduced when net payout, rather than dividends, serves as the cash flow measure. We thank Jacob Boudoukh, Alexander Butler, John Campbell, Indraneel Chakraborty, Andrew MacKinlay, Thomas Quistgaard Pedersen, James Weston and seminar participants at Rice University, Southern Methodist University, and the University of Georgia for helpful comments. Paye acknowledges support from CREATES- Center for Research in Econometric Analysis of Time Series (DNRF78), funded by the Danish National Research Foundation, as well as a 2013 summer research grant from the University of Georgia. A previous version of this paper circulated under the title Net Cash Disbursements to Equity Holders: Implications for Stock Return Predictability and Long-Horizon Consumption and Portfolio Decisions. Gregory Eaton: geaton@uga.edu; Bradley Paye: bpaye@uga.edu.

2 Predictability in Stock Returns and Cash Flow Growth: What Role Does Issuance Play? Abstract We assess the predictive content of yields based on alternative cash flow measures, focusing on the role of equity issuance. For stock returns, it is preferable to incorporate (net) issuance via the net payout yield, which implicitly restricts slope coefficients associated with different cash flow components, rather than as a separate forecasting variable. In contrast to results for dividend growth, issuance and net payout growth are predictable using the corresponding yields both in- and out-of-sample. We show that long-term investors hedging demand for stock is greatly reduced when net payout, rather than dividends, serves as the cash flow measure.

3 Introduction The dividend yield is among the most common variables used to forecast stock returns. The intuition behind this variable is simple: when prices are high relative to dividends, we expect low future returns, and vice versa. The extent of stock return predictability associated with the dividend yield remains controversial; however, due to econometric issues that complicate inference in predictive regressions. 1 Dividends represent only one facet of cash flows between firms and investors. Firms increasingly rely on share repurchases as an alternative means of returning cash to shareholders. 2 Equity issuance also constitutes an important component of aggregate cash flows between firms and shareholders. Grullon, Paye, Underwood, and Weston (2011) find that a nontrivial fraction of firms are recyclers, in the sense that these firms pay dividends or repurchase shares, but issue equity in amounts that exceed total payout. This evidence of equity recycling at the firm level understates the extent of equity recycling at the aggregate level, where equity issuance by some firms offsets dividend payments and repurchasing activity by other firms. Miller and Modigliani (1961) establish that, in perfect and complete capital markets, dividend policy does not affect firm value. Firms can adjust dividends to any level with offsetting changes in shares outstanding. Consequently, it is not obvious that dividends represent the most appropriate measure of payout to signal whether current prices are high or low. Existing evidence concerning relative predictive power among alternative yield definitions is inconclusive. Boudoukh, Michaely, Richardson, and Roberts (2007) examine two alternative yields: the total payout yield, which incorporates dividends and share repurchases, and the net 1 Early studies reporting evidence that the dividend yield forecasts stock returns include Rozeff (1984), Shiller (1984), Keim and Stambaugh (1986), Campbell and Shiller (1988b), and Fama and French (1988). See Shiller (1981), Campbell and Shiller (1988a), Campbell and Ammer (1993), and Cochrane (1991, 1992, 1994, 2005, 2008, 2011) regarding the connection between return predictability and the nature of movements in the pricedividend ratio. Many papers focus on inference issues in predictive regressions involving financial ratios such as the dividend yield. A sampling of relevant studies includes Goetzmann and Jorion (1993), Nelson and Kim (1993), Stambaugh (1999), Tourus, Valkanov, and Yan (2004), Campbell and Yogo (2006), and Ang and Bekaert (2007). 2 Fama and French (2001) document a substantial decrease in the proportion of firms that pay dividends between the 1970s and the late 1990s. Grullon and Michaely (2002) and Skinner (2008) provide evidence that the decline in the propensity to pay dividends is accompanied by increasing substitution from dividends to repurchases following the SEC s enactment of safe harbor provisions covering repurchases in Allen and Michaely (2003) review these changes in the regulatory environment and the ensuing evolution of payout policy. Brav, Graham, Harvey, and Michaely (2005) provide survey evidence consistent with the substitution hypothesis. 1

4 payout yield, which incorporates dividends, repurchases and stock issuances. They conclude that both outperform the traditional dividend yield in predicting stock returns. 3 Results are particularly strong for the net payout yield: Boudoukh et al. (2007) report an R 2 -value in excess of 20% for a predictive regression based on this yield using annual data. Some controversy surrounds this finding, however. Referring to the result, Cochrane (2008) states The stunning 23.4% R 2 -value comes from one large outlier in the early 1930s. (p. 1567) Welch and Goyal (2008) consider net issuance relative to market capitalization as a separate return forecasting variable. They find that this variable is signficant in-sample, but underperforms the historical average out-of-sample. Overall, there does not appear to be consensus regarding whether aggregate (net) issuance predicts stock returns; and, if so, whether issuance information should be incorporated via a net payout yield, or as a separate forecasting variable. 4 This paper provides new evidence concerning the predictive content associated with yields based on alternative measures of cash flow between firms and shareholders. Variance decompositions imply that yield fluctuations forecast future returns, cash flow growth, or both. With respect to stock return forecasts, we show that it is preferable to incorporate (net) issuance information via the net payout yield, which implicitly restricts slope coefficients associated with different cash flow components, rather than as a separate forecasting variable. In contrast to existing results for dividend growth, we find that issuance and net payout growth are predictable using the corresponding yields, both in- and out-of-sample. Most variation in the issuance yield forecasts issuance growth, while roughly equal portions of variation in the net payout yield correspond to expected returns and cash flow growth, respectively. We also demonstrate that the choice of cash flow measure matters economically in the context of long-horizon consumption and portfolio decisions. In particular, the hedging demand for stock 3 See Ackert and Smith (1993), Robertson and Wright (2006) and Kim and Park (2013) for related contributions. 4 Baker and Wurgler (2000) find that a variable related to issuance activity the equity share of new issues forecasts aggregate returns, and interpret their results as indicative of managers ability to time market returns via their issuing activity. Butler, Grullon, and Weston (2005) argue that apparent predictive power from the equity share of new issues reflects pseudo-market timing. They find that the predictive ability of the equity share of new issues vanishes once the Great Depression and Oil Crisis of the early 1970s are removed from the sample. Although the issuance yield we study is positively correlated with the equity share of new issues, the correlation is not overly large (around 0.4). Moreover, the issuance yield does not exhibit unusual behavior around the Oil Crisis of the 1970s. A key difference between the variables is that the issuance yield incorporates market prices (in the denominator), providing a natural adjustment to market shocks absent from the equity share of new issues. 2

5 is greatly reduced when net payout, rather than dividends, serves as the cash flow measure. Following Boudoukh et al. (2007), we construct aggregate annual measures of dividends, stock repurchases and issuances over the period Using these payout measures, we define a variety of payout yields, including the conventional dividend yield, the total payout yield, net payout yield, issuance yield and net issuance yield. The latter two yields enable us to provide evidence regarding whether the (net) issuance yield improves return forecasts when used independently, or alternatively as a separate predictor alongside the dividend or total payout yield. Predictive regressions using the net payout yield are sensitive to the inclusion of data from the years , a period when stock issuance was extraordinarily high relative to prices. When these years are omitted from the sample, the R 2 for the regression falls to a value much closer to the corresponding R 2 -values for the dividend yield and total payout yield regressions. For example, over the sample period , the R 2 -values for the dividend yield, total payout yield, and net payout yield regressions are 8.59%, 8.90% and 9.50%, respectively. Issuance is the component of net payout that exhibits high sensitivity to the inclusion of in the sample. When these years are included, the issuance yield alone produces an R 2 of over 16%. Upon excluding from the sample, the R 2 of the issuance yield falls to around 2% and the variable becomes insignificant. The extreme issuance years of coincide with the Great Depression and a major financial crisis. It is possible that predictive power associated with issuance activity concentrates in such crises. By extending the sample considered by Boudoukh et al. (2007) through 2012, we include data from the financial crisis of The issuance yield does not increase dramatically prior to the crisis. This casts doubt on the hypothesis that the issuance yield reliably forecasts low stock returns associated with financial crises. Although the R 2 -value associated with the net payout yield falls after excluding from the sample, we continue to find strong statistical evidence that both the total payout yield and net payout yield forecast returns, consistent with Boudoukh et al. (2007). 5 shed further light on the role of issuance and net issuance in forecasting returns, we examine multivariate regressions that decompose the net payout yield into components, e.g., the total 5 Butler, Cornaggia, Grullon, and Weston (2011) provide complementary evidence at the firm level regarding the relation between the level of net financing and future stock returns. To 3

6 payout yield and the issuance yield. Basing a predictive regression on the net payout yield imposes an implicit constraint on the slope coefficients associated with the components of net payout. We cannot reject the validity of these implicit restrictions in the data for sample periods that exclude This provides a statistical rationale for combining payout components via the net payout yield to complement economic justifications: the net payout yield imposes a form of shrinkage on the slope coefficients associated with different cash flow components. Consistent with this intuition, forecasts based on the net payout yield perform better out-of-sample than forecasts based on models in which the net issuance yield enters separately alongside the traditional dividend yield. The Campbell and Shiller (1988a) linearized present value identity implies that variation in the dividend yield must forecast stock returns, dividend growth, or both. Cochrane (2008) argues that the lack of predictability in dividend growth provides strong implicit evidence that the dividend yield forecasts returns. In contrast to results for dividends, Bansal and Yaron (2007) and Larrain and Yogo (2008) find that the net payout yield does forecast growth in net payout. We conduct in- and out-of-sample predictive regressions for cash flow growth under various definitions of cash flow. In addition, we provide empirical variance decompositions regarding the fraction of yield variation corresponding to changes in expected returns versus changes in expected cash flow growth. Consistent with previous literature, there is little evidence that the dividend yield or total payout yield forecast cash flow growth. 6 In contrast, we find strong evidence that the issuance yield forecasts (negatively) future growth in stock issuances. We confirm previous evidence that the net payout yield forecasts net payout growth, and our results highlight that issuance activity drives predictable variation in net payout growth. Welch and Goyal (2008) document a breakdown in the performance of many stock return forecasting variables following the 1970s. This is a particularly interesting period over which to analyze alternative yield measures, because it coincides with the emergence of share repurchases as a viable alternative to dividends. Our evidence does not indicate a similar deterioration of predictive ability for net payout and issuance growth. Bias-corrected slope coefficients in predictive regressions for net payout and issuance growth over the period are just 6 Chen (2009) finds stronger evidence for predictable variation in dividend growth when annual dividends are constructed without reinvestment of monthly dividends in the stock market. 4

7 as large (in absolute value) as estimates over the full historical sample. In addition, cash flow growth forecasts based on the net payout and issuance yields tend to outperform the historical average benchmark out-of-sample. Plots of cumulative differences in squared forecasting errors show that forecasts based on these yields underperform the benchmark during the 1960s and 1970s, and then outperform the benchmark thereafter. This pattern of results for net payout and issuance growth is essentially opposite that observed for many stock return forecasting variables analyzed by Welch and Goyal (2008). Long-horizon forecasting coefficients imply that 50 72% (depending on the method used) of variation in the net payout yield corresponds to cash flow growth, consistent with results in Bansal and Yaron (2007). Evidence of predictable variation in net payout growth does not undermine the case for stock return predictability, as the remaining variation in the net payout yield corresponds to variation in expected returns. It is primarily the volatile issuance component of net payout that accounts for predictable variation in cash flow growth. Variance decomposition results for the issuance yield are essentially opposite those for the dividend yield. The vast majority of variation in the issuance yield corresponds to changes in expectations of issuance growth. Previous studies demonstrate that issuance activity is procyclical and varies with stock market conditions. 7 We show that high issuance activity relative to prices predicts lower future issuance growth, and vice versa. This result is consistent with evidence of waves in corporate financing events: peaks of issuance waves are followed by troughs, so high current issuance activity (relative to prices) predicts low future issuance growth. Once the extreme issuance years of are removed from the sample, differences in forecasting performance among the dividend yield, total payout yield, and net payout yield are smaller, and the question of which yield is superior is not decisively resolved. (The net payout yield achieves higher out-of-sample R 2 -values, for example, but differences are not statistically significant.) In light of this evidence, it is tempting to conclude that the particular choice of yield is not important in practice. To the contrary, we show that there are significant economic differences between the alternative yields from the perspective of long-horizon consumption and portfolio decisions. Our analysis builds upon analytical results derived by Campbell and Viceira 7 Lowry (2003) finds that IPO volume is higher when the aggregate market-to-book ratio is higher. Dittmar and Dittmar (2008) show that equity issuances and repurchases are both procyclical, but issuance activity increases earlier in the business cycle relative to repurchasing activity. 5

8 (1999) for optimal long-horizon portfolio and consumption decisions when expected returns are time-varying. We extend the calibration analysis performed by Campbell and Viceira (1999) based on the dividend yield to the total payout yield and net payout yield, and document the extent to which changing the yield alters agents optimal consumption and portfolio policies. For individuals with identical preferences, the calibration results reveal significant differences across the three yields with respect to optimal long-horizon portfolio and consumption policies. Most notably, there is a large difference in the extent of hedging demand, in the sense of Merton (1969). The intuition behind this result is as follows. Shocks to both the dividend yield and total payout yield are strongly negatively correlated with contemporaneous shocks to returns. In a predictive regression context, the yield captures the future investment opportunity set available to investors, and the strong negative correlation with returns generates an important hedging demand for stock, as demonstrated by previous studies including Campbell and Viceira (1999). In contrast, shocks to the net payout yield and returns exhibit only weak contemporaneous correlation, due to the fact that much variation in the net payout yield is driven by volatile issuance activity. Consequently, the hedging demand for stock is greatly reduced. This result has normative implications concerning the extent to which financial advisors should emphasize the hedging potential of stock for clients with long investment horizons. The relationship between corporate payout yields and future returns and payout growth depends a great deal on how payout is defined. The stylized facts concerning predictable variation in stock returns and cash flow growth change considerably when net payout serves as the cash flow measure. Under this measure, both stock returns and cash flow growth are predictable. Implied discount rates are less persistent relative to analogs based on the dividend yield. Finally, the hedging component of long-horizon investors demand for risky stock is much smaller when the net payout yield drives variation in expected returns. 6

9 1 Alternative payout yields and cash flow measures 1.1 Data sources and data construction Stock return data are sourced from the University of Chicago s Center for Research in Security Prices (CRSP) covering the period Consistent with many studies in the stock return predictability literature, we measure aggregate stock returns using the value-weighted return, including dividends, for the CRSP universe. Our primary measure of the annual dividend yield is imputed from CRSP market returns by taking the capitalized series of returns over the uncapitalized series, i.e., DY t+1 = D t+1 /P t+1 = (R t+1 /Rx t+1 ) 1, where R t+1 and Rx t+1 denote gross annual CRSP index returns with and without dividends, respectively. 8 Dividend growth is then computed as D t+1 D t = DY t+1 DY t (Rx t+1 ) = D t+1 P t+1 P t D t P t+1 P t. (1) Imputing the dividend yield from annual returns implicitly assumes that dividends received within the year are reinvested at the return R until the end of the year. Several studies, including Ang (2012), Chen (2009), and Engsted and Pedersen (2010), document that the extent of dividend growth predictability is sensitive to whether or not dividends are assumed to be reinvested. Following Chen (2009), we compute an alternative dividend yield as DY t+1 = Dt+1 12 /P t+1, where Dt+1 12 denotes the simple sum of monthly dividends during the corresponding year. This convention assumes that dividends received during the year are consumed rather than reinvested. The annual return without reinvestment is defined as R t+1 = (P t+1 +D 12 t+1 )/P t, and annual (gross) dividend growth is D 12 t+1 /D12 t. Stock repurchases and issuances represent additional cash flows between firms and shareholders that are central to the questions addressed in this paper. We construct annual time series of aggregate stock repurchases and issuances following the approach of Boudoukh et al. (2007) and use these to compute alternative yield measures including the total payout yield, the net payout yield, the issuance yield, and the net issuance yield. 9 We also calculate annual 8 The literature occasionally distinguishes between the dividend-to-price ratio D t/p t and the dividend yield D t/p t 1. In this paper, we consider only measures of the form D t/p t, or analogous quantities for alternative payout yields, and we use the term dividend yield as opposed to the more cumbersome dividend-to-price ratio. 9 It is also possible to define a repurchases yield; however, because repurchases are negligible prior to the 7

10 growth rates for total payout, net payout, and stock issuances. All growth rates are computed for the period except for net payout growth, for which the sample period is due to negative net payouts in several years prior to Total payout and net payout implicitly involve dividends. Consequently, yields and growth rates associated with these quantities are computed both with and without reinvestment for dividends. The Appendix provides details regarding the construction of yields and growth rates associated with the various cash flow measures. Engsted and Pedersen (2010) show that results for long-horizon dividend growth predictability in US data crucially depend on whether payout is measured in real or nominal terms. They attribute the difference in results to the fact that the dividend yield negatively predicts long-term inflation in US post-war data. Our empirical analysis emphasizes variables measured in real terms, and we adjust payout growth rates for inflation as described in the Appendix. Below, we list and briefly describe the variables used in the empirical analysis: Market returns The real excess return (R e ) on the value-weighted CRSP portfolio is computed as the index return, including dividends, less the return on a 90-day Treasury bill available from CRSP. r denotes the real log return and r e is the log excess return. Dividend yield The dividend yield (DY ) for the value-weighted CRSP portfolio is imputed using annual index returns including and excluding dividends, respectively. dividend yield is denoted dy. The log Total payout yield The total payout yield (T P Y ) is the sum of the dividend yield and the repurchase yield, where the latter is defined as aggregate repurchases divided by year-end market capitalization. The log total payout yield is denoted tpy. Net payout yield The net payout yield (T P Y ) is the dividend yield minus the net issuance yield, where the net issuance yield is the dollar value of issuances minus repurchases divided by year-end market capitalization. We construct two versions of the log net payout yield. First, following Boudoukh et al. (2007), we define npy ln(0.1 + NP Y ) 1980s and trend upward thereafter, such a yield does not have desirable statistical properties for predictive regressions. Of course, repurchases appear as a component in net payout and net issuance yields. 8

11 to obtain a log net payout yield for the full sample period that includes two years (1929 and 1930) in which NP Y < 0. Alternatively, we define npy ln(np Y ), where the series is available for the period Issuance yield The issuance yield (IY ) is defined as aggregate issuances divided by year-end market capitalization. The log issuance yield is denoted iy. Net issuance yield The net issuance yield (NIY ) is the dollar value of issuances minus repurchases divided by year-end market capitalization. Because the net issuance yield is positive for some years in our sample and negative for others, we construct a log net issuance yield as niy ln(0.1 + NIY ). Dividend growth Dividend growth ( D) is the annual percentage change in the dividend level. Log dividend growth is d ln(d t+1 /D t ). Total payout growth Total payout growth ( T P ) is the annual percentage change in the total payout level. Log total payout growth is tp ln(t P t+1 /T P t ). Net payout growth Net payout growth ( NP ) is the annual percentage change in the net payout level. Log net payout growth is np ln(np t+1 /NP t ). Issuance growth Issuance growth ( I) is the annual percentage change in the issuance level. Log issuance growth is i ln(i t+1 /I t ). Alternative series based on the convention of no reinvestment are denoted using a tilde. For example, the alternative dividend yield assuming no reinvestment of intrayear dividends is denoted DY, and the corresponding log dividend yield is dy. Log net payout growth using a measure of dividends without reinvestment is denoted np, and so forth. 1.2 Time series properties of returns, yields and payout growth Table 1 presents summary statistics for the time series of annual excess returns, payout yields, and payout growth rates for variables computed assuming reinvestment of dividends. The Supplementary Appendix contains analogous statistics for variables assuming no reinvestment of dividends, which are qualitatively similar. As expected, the average total payout yield is 9

12 higher than the average dividend yield due to the addition of repurchases, while the average net payout yield is lower. Issuances average approximately 1.4% of market capitalization. Although the level of volatility across the yields is similar, the net payout yield is noisier than the dividend yield and total payout yield, in the sense that its signal-to-noise ratio (mean-tostandard deviation) is lower. Both the issuance yield and net issuance yield exhibit considerable excess kurtosis values, indicative of potential outliers. The sample autocorrelations in Table 1 reveal differences in persistence across yields. It is well-known that the dividend yield is highly persistent (AC(1) of 0.90). Using the augmented Dickey-Fuller (ADF) test, we fail to reject the null of a unit root at the 1% level, but we do reject the null at the 5% threshold. The alternative yields are less persistent. The first-order sample autocorrelation for the total payout yield is approximately 0.77, while those for the net payout yield, issuance yield, and net issuance yield range between We reject the null of a unit root at the 1% level for each of these yields. The summary statistics for the payout growth measures show that, irrespective of the specific payout definition, payout growth is highly volatile. The sample kurtosis values for dividend and total payout growth are roughly consistent with the normal distribution, whereas net payout growth and issuance growth exhibit significant excess kurtosis. The autocorrelation values are small for each growth measure. Figure 1 provides time series plots of the various yields. The top panel shows the traditional dividend yield along with the total payout yield and net payout yield. The bottom panel shows the issuance and net issuance yields. The net payout yield plunges around the Great Depression. The bottom panel of Figure 1 confirms that this plunge is attributable to a large spike in issuance activity between 1928 and This accounts for the high kurtosis values in Table 1 associated with issuance-related quantities. It is notable that issuance does not exhibit a similar spike around the recent financial crisis of , suggesting that extreme issuance activity is not a systematic feature of financial crises. The total payout yield begins to meaningfully differ from the dividend yield around the mid 1980s, following passage of SEC rule 10b-18 providing a safe harbor for firms wishing to repurchase shares. 10 Yet the divergence of the total payout yield remains relatively modest 10 SEC rule 10b-18, passed in 1982, provided a safe harbor for firms initiating share repurchase programs. See Grullon and Michaely (2002) for a detailed discussion of the impact of SEC rule 10b-18 on share repurchase 10

13 until the mid 2000s, when there is a surge in repurchasing activity. Aside from the extreme issuance years around the Great Depression and the mid-2000s when repurchases rise rapidly, the dividend yield and net payout yield comove closely. The fact that the net payout yield and dividend yield are similar from the mid-1980s (when share repurchase programs became more common) through the 1990s implies that firms repurchased and issued equity in roughly similar aggregate amounts during this period. This finding is consistent with the positive correlation between aggregate issuing and repurchasing activity documented by Dittmar and Dittmar (2008). The similar time paths of the two variables suggests that, a priori, we should not expect a dramatic difference between the two yields in terms of forecasting performance. Figure 2 illustrates differences in payout growth rates driven by whether or not annual dividends are constructed assuming reinvestment. The top panel compares the time series d and d. Consistent with Chen (2009), there are clear differences in the dynamic pattern for the two alternative series. Dividends represent a component in more general payout measures such as total payout and net payout. The bottom panel of Figure 2 compares the (log) net payout growth series np and ñp, which differ only with respect to how dividends are measured. It is clear that the relative importance of the dividend measurement convention for net payout growth is considerably smaller than for dividend growth. Relative to most existing literature regarding predictable patterns in stock returns and cash flow growth, this paper focuses on alternative cash flow measures such as net payout and issuances. Issuances do not include dividends and consequently results for this cash flow measure are not impacted by the dividend measurement convention. The similarity between np and ñp depicted in Figure 2 suggests that tests for predictability in net payout growth are not likely to critically depend on the convention for measuring dividends. This proves to be the case in the data. To conserve space, most results using the alternative dividends measure appear in the Supplementary Appendix. 2 Predictive regressions for stock returns and cash flow growth This section assesses whether alternative payout yields possess forecasting power for stock returns and cash flow growth using traditional predictive regressions. Section 2.1 discusses inference issues in one-period-ahead predictive regressions for returns and cash flow growth. programs. 11

14 Section 2.2 summarizes results from univariate and multivariate one-step-ahead predictive regressions for stock returns. Section 2.3 covers predictive regressions for cash flow growth. 2.1 Inference issues in predictive regressions involving financial ratios A predictive regression for (excess) stock returns takes the form: R e t+1 = α + β X t + ɛ t+1, (2) where Rt+1 e denotes the real excess return on the market and X t represents a vector of variables used to forecast returns. The null hypothesis of interest is β = 0 (no predictability). Under standard assumptions, OLS based on Eq. (2) is consistent for β; however, the OLS estimate can be substantially biased in finite samples (Stambaugh (1999)). For example, suppose that X t is scalar-valued and follows a first-order autoregressive process: X t+1 = θ + φx t + η t+1, (3) with φ < 1. Stambaugh (1999) shows that the bias of the estimated slope coefficient in the predictive regression of Eq. (2) is: E[ ˆβ β] σ ɛη σ 2 η ( 1 + 3φ T ), (4) where ˆβ is the OLS estimate of β, σ ɛη = Cov(ɛ, η),and ση 2 = Var(η). Eq. (4) implies that ˆβ is biased upward when φ > 0 and σ ɛη < 0, as is the case for the financial ratios considered in this paper. Consequently, standard t-tests of the null of no predictability reject too often. The Stambaugh bias is particularly important for financial ratios, because these ratios tend to be highly persistent and exhibit strong (negative) contemporaneous correlation with returns. Our empirical analysis addresses the small sample bias in predictive regressions by applying corrected slope coefficients and associated standard errors proposed in Amihud and Hurvich (2004) and Amihud, Hurvich, and Wang (2009). The approach to bias-correction in these papers involves augmented regressions applicable to a multiple-predictor generalization of the model analyzed by Stambaugh (1999). The traditional predictive regression is augmented 12

15 with proxies for the residual series in a Gaussian VAR (1) model for the predictors. To conserve space, we refer the reader to Amihud and Hurvich (2004) and Amihud et al. (2009) for details. Slope coefficients in predictive regressions for cash flow growth are also subject to the Stambaugh bias. The main difference between the stock return and cash flow growth cases is that the contemporaneous correlation σ ɛη between shocks to the yield and shocks to cash flow growth tends to be positive. For example, a positive shock to issuance growth tends to be associated with a positive shock to the issuance yield. From Eq. (4), the slope coefficient ˆβ in predictive regressions for cash flow growth will be biased downward when σ ɛη > 0, as is the case in the data. Similar to predictive regressions for returns, standard t-tests of the null of no predictability will reject too often. 2.2 Predictive regressions for stock returns and cash flow growth Univariate predictive regressions for stock returns Table 2 presents results for one-step-ahead predictive regressions of excess returns on alternative yields at an annual frequency. We consider five alternative yields to forecast stock returns: the dividend yield, the total payout yield, the net payout yield, the issuance yield, and the net issuance yield. The regression model is specified either in levels or in logarithms. Panel A presents results for the sample period , which represents an extension of the sample period analyzed in Boudoukh et al. (2007). 11 Stock issuance activity was extraordinarily high around the period To investigate the influence of this period, Panel B presents results for the alternative sample period Finally, Panel C presents results for the post-treasury Accord period Results for the sample period are similar to those reported by Boudoukh et al. (2007). Focusing on the regression results in levels (left-hand side of Table 2), the OLS estimate of the slope coefficient on the dividend yield is As Cochrane (2011) emphasizes, this estimate is economically large: an increase in aggregate dividends of 1% implies an increase in the expected market excess return of approximately 3.5%. When statistical inference is based on conventional standard errors, the dividend yield is a statistically significant predictor of 11 Boudoukh et al. (2007) focus on log returns and log yields, and analyze the sample period , along with the subperiod We obtain results very similar to theirs for identical sample periods. 13

16 stock returns (t-statistic of 2.79). The associated regression R-squared is 6.81%. Consistent with previous literature, correcting estimates for the Stambaugh bias weakens the evidence for predictability. The Amihud and Hurvich (2004) bias-corrected slope coefficient falls to approximately 2.7 (still an economically significant quantity) and the corrected t-statistic falls to The evidence for predictability is stronger for the total payout and net payout yields. The estimated slope coefficients for these variables are 4.75 and 5.42, respectively. Corrections for the Stambaugh bias are more modest, particularly for the net payout yield. This is not surprising, because the net payout yield is much less persistent than the dividend yield (see Table 1). The corrected estimates provide strong statistical support for predictability, particularly for the net payout yield. Consistent with results reported by Boudoukh et al. (2007), the R 2 -value for the net payout yield forecasting regression is nearly 20%, which is more than double that for the total payout yield and approximately three times the R 2 for the dividend yield regression. Forecasting regressions for the issuance yield and the net issuance yield suggest that issuance activity predicts returns: both variables are statistically significant and the associated slope coefficients are economically significant. In summary, the results in Panel A suggest that issuance activity forecasts stock returns, and incorporating issuance activity via the net payout yield leads to dramatically improved stock return forecasts relative to the traditional dividend yield. Results in Panel B demonstrate that most of the apparent predictive power of issuance activity is driven by outlier issuance behavior in 1929 and When the sample period begins in 1932, the issuance yield and net issuance yield are no longer statistically significant and the regression R 2 -value drops dramatically for both variables. Forecasting results for the net payout yield are also altered by omitting from the sample. The R 2 -value for the regression drops from approximately 20% to roughly 9.5%, and the bias-corrected estimate of the slope coefficient falls from 5.22 to In contrast, regression results for the dividend yield and total payout yield are not materially affected by this slight alteration of the sample period. These results illustrate that the period is only unusual with respect to issuance activity and stock returns In 1929 and 1930 the issuance yield spikes to over 6%. Market returns in the subsequent years (1930 and 1931) are approximately -29% and -43%, respectively. The dividend yield was 3.8% and 4.8% in 1929 and 1930, 14

17 Although our equity issuance data are subject to measurement error, the extreme issuance activity of is not an artifact of measurement error. Baker and Wurgler (2000) collect data on equity and debt issuance from an alternative source, the Federal Reserve Bulletin, covering the period Their data also indicate a large jump in equity issuance activity in Because this period coincides with a major financial crisis, it is possible that extreme issuance activity and low subsequent stock returns are systematically associated with financial crises. Regarding this possibility, it is important to note that our sample period also includes data from the financial crisis of and its aftermath. There is no major increase in stock issuance around the financial crisis of , and predictive regressions based on the issuance or net issuance yield that exclude , but include the recent financial crisis, deliver insignificant slope coefficients and low R 2 -values. Results in Panel C, covering the sample period , are qualitatively similar to those in Panel B with respect to the (absence of) predictive ability for the issuance and net issuance yields. Slope coefficients and R 2 -values for the dividend, total payout, and net payout yields fall relative to the sample period. Bias-corrected estimates for the dividend and total payout yields are no longer statistically significant. These results are consistent with previous studies documenting a breakdown in predictive power for payout yields and many other return forecasting variables over recent decades (see, e.g., Welch and Goyal (2008)). Interestingly, the net payout yield remains significant at the 10% level based on the Amihud and Hurvich (2004) bias-corrected t-statistic. The right-hand portion of Table 2 contains results for regressions in log form, i.e., where the dependent variable is the log excess market return and the forecasting variable is the natural logarithm of the corresponding financial ratio. For comparability with Boudoukh et al. (2007), we report results for the log net payout yield constructed as npy (see Section 1). Overall, there is little qualitative difference between the results of predictive regressions in log form from those in levels. The results in Panels B and C show that the R 2 -value for the log net payout yield drops dramatically when the years are excluded from the sample, and slope coefficients on the log issuance yield and net issuance yield are insignificant for these sample periods. 13 respectively. Neither value is unusual by historical standards. 13 The R 2 for the log issuance yield regression over the period (Panel A) is significantly lower than 15

18 The net payout yield remains a statistically significant predictor of stock returns even after excluding the years from the sample. The bias-corrected slope coefficient of 3.70 over the period is economically significant. Consequently, our results remain consistent with conclusions drawn by Boudoukh et al. (2007): alternative yields provide more accurate stock return forecasts. Conditioning on the net payout yield, rather than the dividend yield, also alters the dynamics of discount rates. In univariate linear return forecasting regressions, the model-implied expected return inherits the dynamics of return forecasting variable. Because the net payout yield is considerably less persistent than the dividend yield (see Table 1), time-varying expected returns under the net payout yield are less persistent than those under the dividend yield. The Supplementary Appendix provides a detailed analysis of impulse responses to shocks for alternative yields. Responses of returns to a net payout yield shock exhibit a half-life of approximately 2 3 years, which is reasonably consistent with macroeconomic shocks in the context of the business cycle Multivariate regressions for stock returns Predictive regressions using alternative yields such as the total payout yield and net payout yield implicitly constrain the manner in which payout components impact future returns. Consider the predictive regression specification: R e t+1 = α + β 1 DY t + β 2 RY t + β 3 IY t + ɛ t+1, (5) where DY, RY, and IY represent the dividend yield, repurchases yield, and issuances yield, respectively. A univariate predictive regression based on the net payout yield implicitly imposes the restriction β 1 = β 2 = β 3 in Equation (5). Similarly, a regression based on the total payout yield imposes a restriction that the slope coefficients on the dividend yield and repurchases yield are equal. By examining multivariate regressions incorporating multiple components of net payout, it is possible to directly test the validity of these restrictions. 14 that based on the level of the issuance yield. The intuitive explanation for this fact is that the log transformation dampens the extent to which is an outlier in terms of issuance activity. 14 Boudoukh et al. (2007) report multivariate regressions involving multiple yields; however, their analysis differs from ours in two key respects. First, they run regressions in which the dividend yield appears along with either the total payout yield or net payout yield, rather than multivariate regressions featuring different components of the net payout yield, as in our analysis. Second, they run predictive regressions in log form, in 16

19 Stock repurchases are negligible prior to the early 1980s, and the repurchase yield exhibits (upward) trending behavior for much of the subsequent two decades. Both features create difficulties with respect to including the repurchases yield RY as an individual predictor in a specification such as Equation (5). Instead, we consider two alternative decompositions of the net payout yield that bundle repurchases with either dividends or issuances: R e t+1 = α + β 1 DY t + β 2 ( NIY t ) + ɛ t+1, or (6) R e t+1 = α + β 1 T P Y t + β 2 ( IY t ) + ɛ t+1. (7) These specifications include the opposite of the issuance yield or net issuance yield in order to facilitate comparison of the associated slope coefficient with that of the total payout or dividend yield. In each case, the null hypothesis of interest is β 1 = β 2. Although this null hypothesis can be tested via a standard Wald test, it is important to account for the Stambaugh bias in conducting inference. Intuitively, the Stambaugh bias is likely to be stronger for β 1, the slope coefficient on the total payout yield (or dividend yield) than for β 2, the slope coefficient on the issuance yield (or net issuance yield). In such a case, the Stambaugh bias generates biased estimates of the difference β 1 β 2. In particular, under the null hypothesis that β 1 = β 2 it is likely that E[ ˆβ 1 ˆβ 2 ] > 0, where ˆβ 1 and ˆβ 2 refer to the OLS estimates of β 1 and β 2, respectively. To account for this possibility, we adopt the bias-corrected estimation and testing approach for multivariate predictive regressions proposed by Amihud et al. (2009). Results are presented in Table 3. We first consider the specification based on Eq. (6), which decomposes the net payout yield into the dividend yield and the net issuance yield. 15 For the sample period, both the dividend yield and the net issuance yield are statistically significant predictors of excess returns. Applying the bias correction reduces the estimate of the slope coefficient on the dividend yield from 5.34 to In contrast, the bias corrected estimate of the slope coefficient for the net issuance yield (approximately 5.5) is virtually identical to the OLS estimate. Both the OLS and bias-adjusted slope estimates for the two yield components are quite close, and a test of the null hypothesis of equal slope coefficients fails to reject. Results under the alternative decomposition of net payout (Eq. (7)) are similar for the OLS estimates, which the connection between coefficients on the net payout yield and its components is more complex. 15 The net issuance yield is multiplied by negative one and is therefore equivalent to the net repurchases yield. 17

20 but differ for bias-corrected estimates. In particular, the bias-corrected slope estimate for the issuance yield is substantially larger than the corresponding bias-adjusted slope estimate for the total payout yield. This finding should be interpreted with caution; however, due to the inclusion of the outlier issuance period of in the sample. Panels B and C consider the sample periods of and , respectively, which omit the extraordinary issuance years of For these sample periods, the Wald test is unable to reject the null hypothesis that the slope coefficients on the two yield components are identical. This conclusion is robust to whether inference is based on standard OLS estimates and standard errors, or upon on the bias-corrected estimates and associated standard errors. In some cases the point estimates of the slope coefficients on the two yield components are quite close. For example, over the sample period (Panel B), the bias-corrected estimates of the coefficients on the dividend yield and the opposite of the net issuance yield are 3.63 and 2.75, respectively. For other cases in which the point estimates are farther apart, the estimates are relative imprecise and consequently the test still fails to reject the null of equal coefficients. Failure to reject the null hypothesis does not imply that the null is true. In other words, it is certainly possible that the population coefficients associated with the different yield coefficients differ. From this perspective, basing a return forecasting on a yield measure that combines payout components, such as the net payout yield, can be viewed as a form of shrinkage. Even if the true slopes associated with the underlying yield components differ, the reduction in estimation error achieved via imposing the constraint of equal slopes may result in more accurate return forecasts. Later in the paper, we address this question explicitly in an out-ofsample return forecasting exercise. 2.3 Predictive regressions for cash flow growth Table 4 presents results of predictive regressions for various cash flow growth measures. Panel A presents results for , the longest sample period such that net payout remains positive. (This period also omits the extreme issuance years of ) Panels B and C present results for and The latter period is of interest primarily because it focuses on years following the establishment of safe harbor provisions covering share 18

21 repurchases. Results for dividend and total payout growth are consistent with previous empirical literature. In particular, there is little evidence of predictability in dividend or total payout growth when dividends and yields are computed assuming that intrayear dividends are reinvested. Consistent with Chen (2009), there is stronger evidence of predictability in cash flow growth for the alternative cash flow measures that assumed that dividends are consumed. The bias-corrected slope coefficient in the predictive regression for these cash flows is negative and statistically different from zero over the period. Since both the regressor and regressand are in logarithms, coefficient estimates can be interpreted as elasticity values. For example, the bias-corrected estimate of β cf for total payout growth over the period is approximately -0.20, so that a 1% increase in the total payout yield tpy (computed assuming intrayear dividends are consumed) corresponds to a 0.20% decrease in expected total payout growth tp the following year. This evidence for predictability diminishes in more recent data, a finding that is consistent with Chen (2009), who documents that the pattern of stock return and dividend growth predictability reverses in the post-war period. In contrast to weak, or at best mixed, evidence of predictability in dividend or total payout growth, we find strong evidence of predictability in issuance growth. The slope coefficient in the predictive regression of issuance growth on the lagged issuance yield is statistically significant across all sample periods examined, even after correcting for finite sample bias using the approach of Amihud and Hurvich (2004). The predictable component of issuance growth is economically significant: bias-corrected point estimates imply that a 10% increase in the issuance yield corresponds to a decrease in expected issuance growth the following year of %, depending on the sample period examined. Given the strong evidence of a predictable component in issuance growth, coupled with the fact that issuance represents a key component of net payout, it is perhaps not surprising that we also find strong evidence of predictability in net payout growth, consistent with earlier findings in Bansal and Yaron (2007) and Larrain and Yogo (2008). Our results show that, although slope coefficients tend to be larger when dividends are measured assuming no reinvestment, the predictable component in net payout growth is economically significant irrespective of how dividends are measured. In addition, the evidence for predictable variation in net payout 19

22 growth survives corrections for finite sample bias. 3 Variance decompositions and links between stock return and cash flow predictability The Campbell and Shiller (1988a) linearized present value identity implies that variation in the dividend yield must reflect news about future dividend growth or future returns. A similar line of reasoning suggests that variation in the alternative yields should reflect news about either future returns or future growth in the corresponding cash flow measure. This section provides evidence regarding what proportion of variation in these alternative yields forecasts future stock returns versus future cash flow growth. Section 3.1 presents a first-order vector autoregression (VAR) model and associated identities that link predictability in stock returns and cash flow growth. Several inference issues associated with such systems are discussed. Section 3.2 presents empirical results VAR system, including implied long-run forecasting coefficients. 3.1 VAR model, approximate identities, and long-run coefficients Let cf t represent the logarithm of an arbitrary cash flow measure, such as total payout or stock issuances. The following represents a generalization of the VAR linking stock return and cash flow growth predictability considered in, e.g., Cochrane (2008): r t+1 = a r + β r yld t + ɛ r t+1 (8) cf t+1 = a cf + β cf yld t + ɛ cf t+1 (9) yld t+1 = a yld + φ yld t + ɛ yld t+1, (10) cf t+1 d t+1 = a cf,d + β cf,d yld t + ɛ cf,d t+1 (11) where yld t represents the corresponding yield, defined as cash flow divided by market capitalization. 16 The standard VAR linking predictability in stock returns and dividend growth 16 A technical caveat is that the cash flow measure of interest must be strictly positive to ensure that the log payout yield yld t and log cash flow growth cf t are well-defined. This is not an issue for payout components such as dividends, total payout (dividends plus repurchases), or issuances. Net payout (dividends plus repurchases less issuances), on the other hand, can be negative. Empirically, negative values for NP Y only occur in the years 1929 and 1930, corresponding with extraordinary stock issuance during these years. In the empirical analysis, 20

23 emerges as the special case of Eqs. (8) (11) in which dividends represent the cash flow measure, so that cf t = d t, yld t = dy t, and Eq. (11) can be dropped. Starting with the well-known Campbell and Shiller (1988a) log-linearization of returns, the Appendix establishes the following approximate identity linking slope coefficients in the system (8) (11): β r 1 ρφ + β cf (1 ρ)β cf,d, (12) where the parameter ρ 1/(1 + D/P ), and D/P represents the dividend yield around which one linearizes (usually taken to be the average dividend yield). The identity shows that the null hypothesis of no predictability (β r = 0) implies restrictions on other slope coefficients of the VAR. 17 For the special case in which dividends represent the cash flow of interest, the (approximate) identity (12) reduces to the expression β r 1 ρφ+β d. Assuming that φ < 1, the assumption β r = 0 implies β d < 0. In other words, the dividend yield can only fail to predict stock returns if higher yields forecast lower future dividend growth. Cochrane (2008) finds that incorporating this restriction provides more powerful tests of the null of no predictability, and leads to rejections of the null in the data. Under the null of no stock return predictability, the generalized formula (12) implies that β cf = ρφ + (1 ρ)β cf,d 1. Estimates of the term (1 ρ)β cf,d tend to be small in the data (around 0.01 for the alternative cash flow measures we consider). Consequently, the null hypothesis of no stock return predictability continues to imply β cf < 0, i.e., higher yields forecast lower future cash flow growth if there is no stock return predictability. Given a specified horizon H, let β (H) r cf, β (H), and β(h) represent slope coefficients in regressions of sums of discounted future values of the corresponding variable on the current yield. For example, the coefficient β (H) r on yld t. The quantities β (H) cf cf,d represents the slope coefficient in a regression of H j=1 ρj 1 r t+j and β (H) cf,d are defined analogously. Applying logic similar to established results for the dividends case, the Appendix derives the following generalized longwe consider sample periods starting in 1931, so that the log net payout yield is well-defined for each period. 17 An analogous identity links the errors terms of the VAR: ɛ r t+1 ɛ cf t+1 ρɛyld t+1 (1 ρ)ɛcf,d t+1. 21

24 horizon identity for alternative cash flow yields: 1 β (H) r β (H) cf + (1 ρ)β (H) cf,d + ρh β H yld. (13) The identity (13) constitutes a variance decomposition for a payout yield that involves a generalized measure of cash flow, such as the total payout yield or issuance yield. The final term in (13) disappears as H under a no bubbles assumption that lim H ρ H (yld t+h ) = 0. Assuming no bubbles, we obtain an identity linking long-run coefficients: where β ( ) r β r /(1 ρφ), β ( ) cf 1 β ( ) r β ( ) cf + (1 ρ)β ( ) cf,d, (14) β cf /(1 ρφ), and β ( ) cf,d β cf,d/(1 ρφ). When dividends represent the measure of cash flow, the final term in (14) drops out, and the quantities β ( ) r and β ( ) d capture the proportion of variation in the yield driven by future returns and future dividend growth, respectively. The generalized decomposition says that variation in an arbitrary cash flow yield can be attributed to three sources: 1) changes in expected returns; 2) changes in expected cash flow growth; or 3) changes in the expected spread between (log) cash flow and dividends. Our empirical analysis sheds light regarding the relative contributions of these sources of variation. Under standard assumptions, equation-by-equation OLS provides consistent estimates of unknown slope parameters in the system (8) (11). Consistent estimates of long-run coefficients follow upon plugging OLS estimates into the population formula, e.g., ˆβ( ) r = ˆβ r /(1 ρ ˆφ), where ˆβ r and ˆφ refer to OLS estimates of the corresponding parameters. A drawback to this approach is that the OLS parameter estimates are biased in finite samples. Indeed, earlier discussion of the Stambaugh bias in Section 2.1 highlights the well-known biases associated with the OLS estimates ˆβ r and ˆφ. The OLS estimate of the cash flow growth forecasting coefficient ˆβ cf is also generally biased in finite samples, since the forecasting variable yld t is persistent and shocks to cash flow growth are likely to be positively correlated with shocks to the yield. Arguments analogous to those highlighted in Section 2.1 imply that ˆβ cf is downward biased for β cf in finite samples. Consequently, standard tests of the null of no predictability in cash flow growth will tend to overreject in finite samples. By similar reasoning, OLS estimates 22

25 of the parameter β cf,d for alternative payout measures are also subject to finite sample bias. We apply a Monte Carlo approach to bias-correct estimates of slope coefficients in the VAR system (8) (11). 18 The specifics of the bias-correction are as follows. First, we obtain the usual OLS estimates of the VAR parameters and the associated sample covariance matrix. Second, assuming these parameters represent the true data generating process (DGP), we simulate new samples from the system, of size equal to the original sample size, assuming that model shocks are i.i.d. multivariate normal with covariance matrix equal to the sample covariance matrix. The identities linking slope coefficients and shocks in the system (8) (11) imply that any one variable in the system is determined once the others are specified. In other words, we must simulate three of the four variables in the system (or two out of three when dividends represent the cash flow measure of interest) and compute the final variable in accordance with generalized Campbell-Shiller (1988) identity (see the Appendix for an explicit expression). Following Cochrane (2008), we simulate shocks for the final three variables in the system (8) (11) and compute the corresponding return shock according to the identity. Shocks are drawn assuming a multivariate normal distribution using the sample covariance matrix based on OLS estimates of system parameters. The initial (demeaned) value of the yield is drawn from the unconditional distribution yld 0 N ( 0, σ 2 (ɛ yld )/(1 φ 2 ) ). For each simulated sample, we compute various estimates of interest, including slope coefficients and long-horizon estimates such as ˆβ ( ) r = ˆβ r /(1 ρ ˆφ) based on the slope coefficients. Let ˆθ denote an estimate of interest based on the original sample, e.g.., the vector of slope coefficients in the system (8) (11), and ˆθ denote a corresponding estimate based on simulated data. The quantity θ = (1/M) M i=1 ˆθ i denotes the average of simulated estimates ˆθ, where M represents the number of simulations. The bias-corrected estimate ˆθ C is then computed as ˆθ C = 2ˆθ θ. 19 Note that bias-corrected estimates of long-horizon coefficients are obtained directly via the simulation procedure. An alternative is to compute implied long-run estimates using bias-corrected estimates of slope parameters in the system (8) (11). The resulting esti- 18 See Engsted and Pedersen (2014) for additional discussion of various bias-correction approaches and a simulation-based comparison of the relative effectiveness of alternative methods. One motivation for adopting a Monte Carlo bias-correction approach is that we are interested in bias-correcting long-run coefficients, which are functions of the underlying VAR slope coefficients. 19 In the econometrics literature, this approach is referred to as constant bias correcting. See, e.g., MacKinnon and Smith (1998). 23

26 mates are not unbiased; however, due to the effects of Jensen s inequality. (In our application, differences between the two approaches tend to be small.) 3.2 Empirical Results Table 5 presents estimates for the VAR system (8) (11) based on alternative payout yields for the full sample period Panel A presents results for the dividend yield, Panel B presents results for the total payout yield, Panel C presents results for the net payout yield, and Panel D presents results for the issuance yield. The first two columns of the table display OLS estimates of the slope coefficient on the corresponding yield for each variable in the system, along with standard errors for these estimates. The OLS slope estimates for the return and cash flow growth equations in the system correspond to predictive regression results discussed earlier in the paper. Similarly, the slope coefficient for the yield equation captures the persistence of the yield, discussed in Section 1.2. The next four columns of Table 5 present standard deviations and correlations for errors in each VAR system. For each system, error standard deviations are on the diagonal and error correlations are on the off-diagonal (both expressed as percentages). Shocks to returns are strongly negatively correlated with shocks to the dividend yield and total payout yield: estimates of both correlations are approximately -63%. Shocks to dividend (total payout) growth are at most only weakly correlated with shocks to the dividend (total payout) yield. Error correlations change dramatically for the VAR systems based on net payout yield and issuances. For these systems, there is strong positive correlation between shocks to cash flow growth and the yield (87% for the net payout yield and 95% for the issuance yield) and at most only weak correlation between shocks to returns and shocks to the yield. Shocks to the dividend or total payout yield are strongly associated with contemporaneous unexpected returns; whereas shocks to the net payout yield and issuance yield are strongly associated with contemporaneous shocks to cash flow growth. The pattern of correlations among shocks proves important in our subsequent analysis of long-run portfolio choice under time-varying returns in Section 5. For the moment, we emphasize that the persistence of the payout yields, coupled with nontrivial correlations between shocks to the yield and shocks to other variables in the system, implies that OLS slope estimates are biased and motivates the bias-corrections we 24

27 perform for long-run coefficients. Columns 7 8 of Table 5 show long-run coefficients implied by the OLS slope estimates for the system. Using the identity (13), the long-run regression coefficients in Table 5 can be interpreted as the proportion of variation in the corresponding yield attributable to variation in expected returns, variation in expected cash flow growth, variation in the expected spread between cash flow and dividends, and rational bubbles. The final three columns present bias-corrected slope coefficients and bias-corrected long-run coefficients. The estimates of β (H) r for the dividend yield are relatively close to one, while the estimates of other long-run forecasting coefficients are close to zero. The coefficient (H) ˆβ cf,d for the dividend yield is not tabulated, since it is mechanically zero. Some of the point estimates in Table 5 imply that slightly more than 100% of dividend yield volatility comes from returns, due to the fact that the sign of the estimated long-run dividend growth-forecasting coefficient is positive, rather than negative as expected. These results are consistent with a large body of empirical research finding that, as Cochrane (2011) puts it, all price-dividend ratio volatility corresponds to variation in expected returns. None corresponds to variation in expected dividend growth, and none to rational bubbles. The story is largely the same for a predictive system based on the total payout yield (Panel B). The major difference relative to the dividend yield results is that cash flow predictability is now in the expected direction: a high total payout yield today forecasts lower total payout growth in the future. The vast majority of variance in the total payout yield (at least 85%) still comes from changing expectations of discount rates. Time-variation in the spread between total payout and dividends accounts for relatively little variation in the total payout yield (approximately 3%). The net payout yield (Panel C) provides a different pattern of results. The long-run cash flow growth forecasting coefficient β (H) cf is approximately 70%, and varies little depending on whether H = 15 or H = and whether or not estimates are bias-corrected. This implies that around 70% of variation in the net payout yield corresponds to changes in future net cash flows between firms and investors. 20 The long-run return-forecasting coefficient β (H) r for the 20 Bansal and Yaron (2007) perform a similar variance decomposition based on net payout. Although their measurement scheme for net payout yield differs from ours, they report that approximately 50% of variation in the net payout yield correponds to variation in expected net cash flow growth, consistent with our results. 25

28 net payout yield is around 30-40%. Consequently, a nontrivial proportion of of variation in the net payout yield also corresponds to discount rates. The remaining components (rational bubbles and the spread between net payout and dividends) account for relatively little of the variation in the net payout yield. Finally, Panel D presents results for the issuance yield. The long-run cash flow growth forecasting coefficients are all close to one, while the long-run return forecasting coefficients are close to zero. Rational bubbles and the spread between issuances and dividends account for relatively little of the variation in the net payout yield. These estimates suggest that the vast majority of variation in the issuance yield corresponds to future growth rates in issuances. Turning attention to the bias-corrected estimates in the final three columns of Table 5, the bias-corrected slope estimates differ meaningfully from the OLS analogs in some cases. As expected, the bias-corrected estimates of φ increase: the persistence of the yields increases after bias correction. Similarly, the estimates of slope coefficients in return and cash flow growth forecasting regressions are altered via corrections to the Stambaugh bias. Nevertheless, the bias-corrected long-run coefficient estimates are qualitatively similar to those based on plugging in OLS estimates. Differences are most pronounced for the dividend yield system, for which bias-correction increases the fraction of variance explain by changing expectations of dividend growth (in the wrong direction ). 4 Out-of-sample results and robustness checks This section provides additional empirical evidence concerning predictable variation in expected stock returns and cash flow growth. We first describe an out-of-sample analysis in which forecasts are computed using only information available in real time. We then summarize a series of robustness checks regarding our main results. To conserve space, tabulations of results for the robustness checks appear in the Supplementary Appendix. 4.1 Out-of-sample analysis Out-of-sample research designs split the data into two subsets, the first set of observations constituting an estimation sample and the second set of observations constituting a hold-out 26

29 sample used to compare performance among candidate models. Forecasts for the hold-out sample are constructed using past information, as though the forecasts were constructed in real time. 21 Out-of-sample research designs are often motivated by concerns about structural change and to provide a measure of robustness to potential data mining. In an influential paper, Welch and Goyal (2008) document that many return forecasting models fail to outperform a simple benchmark forecast the historical average out-of-sample. As a robustness check for our in-sample evidence concerning stock return and cash flow growth, we compute out-of-sample forecasts of returns and cash flow growth using alternative payout yield measures. The benchmark forecast is the historical average (return or cash flow growth). To compute forecasts, we consider both rolling and recursive estimation schemes, with an initial estimation window of 30 years. Let ŷ t+1 denote the one-step ahead return forecast for either excess returns or cash flow growth based on a particular predictive regression. The corresponding sample MSPE for the predictive regression is ˆσ 2 P 1 (y t+1 ŷ t+1 ) 2, (15) where P denotes the number of out-of-sample forecasts. Similarly, let ȳ t+1 denote the one-step ahead forecast based on the historical average, with corresponding sample MSPE equal to ˆσ 0 2. To convey the economic significance of differences in forecast performance, we report the outof-sample R 2 statistic considered by Campbell and Thompson (2008) and Welch and Goyal (2008), defined as ROOS 2 = 1 ˆσ2 ˆσ 0 2. (16) Statistical inference associated with out-of-sample forecast performance is nuanced, due to the fact that forecasts rely on estimated parameters. We consider two alternative tests for differences in out-of-sample forecast performance. The first test is the test proposed by Clark and West (2007) for equal MSPE. The second test is the test for superior predictive ability proposed by Giacomini and White (2006). The null hypothesis in these alternative tests differs 21 Implementations vary in terms of how the estimation sample evolves through time. In some cases, parameter values are estimated once using the initial R observations (fixed sample), in others a moving window of size R is used to produce forecasts (rolling), and in some cases an initial window of size R is expanded as new data become available (recursive). 27

30 in a subtle, but important way. In essence, the Clark and West (2007) test is an out-of-sample test for Granger causality, while the Giacomini and White (2006) test focuses on differences in predictive ability, factoring in the impact of parameter estimation on forecast performance. The latter test is more stringent, in the sense that a variable may Granger cause stock returns (β is nonzero in a predictive regression), but fail to forecast returns more accurately than the historical average in practice, due to the bias-variance tradeoff. The Appendix provides additional discussion and explicit expressions for the associated test statistics (see also the review article by Clark and McCracken (2011)). Table 6 presents results for the out-of-sample analysis of stock return forecasts. We highlight three points regarding the out-of-sample R 2 results. First, forecasts based on the net payout yield achieve the highest out-of-sample R 2 -value among the candidate yields and outperform the historical average under both the rolling and recursive designs. Second, stock return forecasts based on the issuance yield and net issuance yield perform relatively poorly out-of-sample. Third, return forecasts based on the net payout yield, which imposes the restriction of equal slope coefficients on the components of net payout, perform better than forecasts from multivariate models in which the net payout yield is decomposed into components, or both the dividend and net payout yield are included. This pattern of results is consistent with earlier, in-sample results suggesting that it is preferable to incorporate (net) issuance information via the net payout yield, rather than include issuance activity separately alongside the traditional dividend yield in a predictive regression. Out-of-sample R 2 -values and associated MSPE differences are subject to considerable sampling error and the Giacomini and White (2006) test often fails to reject the null of equal predictive ability. In other words, although the out-of-sample performance differences are economically significant, these differences are often not statistically significant at conventional levels. An exception is the net issuance yield under the recursive scheme, which significantly underperforms the historical average Asymptotic results derived by Giacomini and White (2006) require the estimation sample to remain bounded, which is inconsistent with an estimation window that expands forever. We report these test results for comparison with results using a rolling window of fixed length; however, they should be treated with caution. Many of the forecasts based on payout yields underperform the historical average out-of-sample. This is consistent with earlier out-of-sample evidence in Welch and Goyal (2008). Several recent studies find that it is possible to outperform the historical average using more sophisticated forecasting approaches that impose economic constraints on parameter estimates, combine forecasts based on different variables, or incorporate regime switching behavior (see e.g., Guidolin and Timmermann (2007), Ludvigson and Ng (2007), Campbell and Thompson (2008), Rapach, Strauss, and Zhou (2010), Ferreira and Santa-Clara (2011), and Dangl and 28

31 The Clark and West (2007) test rejects the null of no predictability for the dividend yield, total payout yield, and net payout yield. In some cases (e.g., the dividend yield), these rejections occur in spite of the fact that the corresponding variable fails to outperform the historical average out-of-sample. The intuition behind this result is that, under the null of no predictability, the forecast based on the yield is expected to underperform the benchmark due to additional estimation error. In the data, forecasts for these models perform sufficiently well relative to the benchmark (although not necessarily outperforming it) such that we reject the null. The Clark and West (2007) fails to reject the null of no predictability for the issuance yield or net issuance yield. These findings complement in-sample results from univariate regressions (see Table 2) once the period is removed from the sample. Figure 3 provides time series plots of the cumulative difference in mean square error relative to the benchmark for the univariate predictive regressions. When the line slopes upward, the forecasting based on the corresponding yield is more accurate than the benchmark forecast, while for periods in which the line slopes downward the benchmark forecast is more accurate. The issuance yield and net issuance yield consistently underperform the benchmark. The dividend yield, total payout yield, and net payout yield significantly outperform the benchmark during the economically tumultuous 1970s, but underperform the benchmark during the dotcom boom of the 1990s. Differences between these three yields are much more pronounced under a recursive estimation window (bottom panel of Figure 3). Under this estimation scheme, the net payout yield fares better than the dividend or total payout yield during both the 1960s and the 1980s. This suggests that, at least at certain times, incorporating issuance information in a net measure of payout leads to improved out-of-sample forecasts. Table 7 provides results for forecasts of cash flow growth. Forecasts of dividend or total payout growth based on the lagged yield generally fail to outperform the historical average out-of-sample. In contrast, forecasts of growth in net payout or issuances based on the corresponding yield typically outperform the historical average. Similar to the return forecasting results, out-of-sample performance differences are estimated with considerable imprecision, and the Giacomini and White (2006) test often fails to reject the null of equal predictive ability. The Clark and West (2007) test results align closely with in-sample results. The test fails to Halling (2012)). We do not consider these more complex forecasting approaches in this paper, because our primary focus is on relative performance among the alternative yield measures. 29

32 reject the null of no predictability for dividend growth and total payout growth, but rejects the null of no predictability for issuance growth. Results for net payout growth are somewhat dependent on whether the growth measure and yield are stated in simple or logarithmic form, with stronger evidence against the null under the simple growth measure. Figure 4 shows out-of-sample cumulative differences in MSE relative to the historical average for forecasts of cash flow growth. The figure illustrates that differences in forecast performance are much larger for forecasts of net payout and issuance growth relative to dividend and total payout growth. This is because the slope coefficients in the predictive regressions for dividend and total payout growth tend to be close to zero, so that forecasts based on the lagged yield do not differ markedly from the historical average. In contrast, slope coefficients in predictive regressions for net payout and issuance growth using the corresponding lagged yields are economically large. Consequently, the resulting forecasts deviate considerably from the historical average. Yield-based forecasts for net payout and issuance growth tend to underperform the historical average out-of-sample from the 1950s through the 1970s, but outperform the benchmark following from the early 1980s onward. This pattern of results provides an interesting contrast to the typical pattern of results for stock return forecasts, where yield-based forecasts break-down relative to the historical average in recent decades. (See Figure 3 and results in Welch and Goyal (2008).) 4.2 Robustness checks Joint tests of predictability in stock returns or cash flow growth Cochrane (2008) advocates tests for the null of no stock return predictability that jointly exploit information in slope estimates for returns and dividend growth. The idea behind these tests is that, because the the slope coefficients β r and β cf are linked by an (approximate) identity, tests that involve both slope estimates can exhibit increased power. For example, in the standard case in which dividends represent the payout measure of interest, the null of no stock return predictability implies, assuming no bubbles, that the dividend yield must (negatively) forecast future dividend growth. The lack of such a predictive relation in the data, i.e., an insufficiently negative estimate ˆβ cf, signifies evidence against the null of no stock return predictability. The generalized identity (12) permits extension of this idea to alternative payout measures such as 30

33 net payout or stock issuances. Our implementation of joint tests for stock return or cash flow predictability closely follows Cochrane (2008) and Engsted and Pedersen (2010). Implementation details, as well as tabulations of results, appear in the Supplementary Appendix. We omit results from the main paper because they produce little that is new beyond existing literature and our earlier results. The joint test emphatically rejects the null of no stock return predictability using the dividend yield and total payout yield, largely due to the lack of predictability in dividend growth in the data. These results are similar to Cochrane (2008). We also reject the null of no stock return predictability using the net payout yield; however, the rejection is primarily due to the large return forecasting coefficient in the data, rather than the cash flow growth-forecasting coefficient. The most interesting empirical question, from our perspective, is whether the joint test provides strong evidence of stock return forecastability for the issuance yield, because univariate predictive regressions do not (in post-great Depression data). The simulated p-values in these tests are around 8-10%, indicating borderline evidence against the null. As with the net payout yield, it is the empirical estimate of the return forecasting coefficient, rather than the cash flow growth-forecasting coefficient, that drives the relatively low p-values. Finally, joint tests of predictability in cash flow growth produce results similar to standard predictive regressions (see Table 4), i.e., incorporating the point estimate of return-forecasting coefficient does little to alter inference Additional results for dividends measured without reinvestment Results to this point focus on our primary measure of dividends, which implicitly assumes reinvestment of intra-year dividends at the market rate of return. Several studies, including Chen (2009) and Ang (2012) find stronger evidence for predictability in dividend growth for an alternative measure that assumes intra-year dividends are consumed rather than reinvested. The Supplementary Appendix provides descriptive statistics, variance decompositions and out-ofsample forecasting results using the alternative dividend measure without reinvestment (Table 4 provides results for in-sample predictive regressions.) Consistent with earlier studies, we find stronger evidence for predictability in dividend and total payout growth under the alternative measure. For example, a variance decomposition based on the alternative dividend yield over 31

34 the sample period suggests that approximately 45% of variation in the dividend yield corresponds to future dividend growth. Figure 2 shows that the dividend measurement convention does not have a large impact on net payout growth. Not surprisingly in light of this observation, results for net payout growth change little under the alternative dividend measure. Of course, issuance growth is unaffected by the dividend measurement convention Direct long-horizon forecasting regressions An alternative to inferring long-horizon predictability from first-order VAR models is to run direct multi-period predictive regressions. In these regressions, the dependent variable is of the form H j=1 ρj y t+j, where y t represents the variable of interest (e.g., stock returns or log cash flow growth) and H indicates the forecast horizon. The case ρ = 1 corresponds to traditional long-horizon regressions, while ρ = 1/(1 + D/P ) corresponds to discounted longhorizon regressions associated with variance decompositions. The dependent variable in these regressions is serially correlated by construction. This complicates hypothesis tests and the construction of appropriate standard errors. Boudoukh, Richardson, and Whitelaw (2008) develop an analytical approach to standard errors in long-horizon predictive regressions under the null of no predictability. They show that slope coefficients are highly correlated across horizons under the null for persistent predictors. Coefficient estimates and R 2 -values are approximately proportional to the horizon under the null hypothesis of no predictability, due to common sampling error across equations. The Supplementary Appendix provides tabulations of results for direct long-horizon regressions for horizons H of 1 to 5 years following the approach of Boudoukh et al. (2008). To account for small sample biases, we follow Boudoukh et al. (2008) and report simulated p-values under the null of no predictability (see Supplementary Appendix for details). Results for long-horizon stock return regressions are similar to findings reported in Boudoukh et al. (2008). Results for cash flow growth complement our earlier findings based on one-step ahead predictive regressions. In particular, we find little evidence of predictability for dividend or total payout growth, but strong evidence of predictability for net payout and issuance growth. The Supplementary Appendix provides further discussion of results. 32

35 5 Long-horizon portfolio choice: Sensitivity to payout measure Once the issuance outlier period of is removed, the dividend, total payout, and net payout yields achieve comparable in-sample and out-of-sample R 2 -values in return forecasting regressions. Consequently, it is tempting to conclude that the specific choice of yield is not economically important. This section shows that, to the contrary, the choice of yield has important implications for the portfolio and consumption choices of long-horizon investors. 5.1 Long-horizon portfolio and consumption choices with time-varying expected returns To analyze the economic significance of alternative definitions of the payout yield, we consider optimal portfolio and consumption policy rules derived by Campbell and Viceira (1999). Campbell and Viceira (1999) analyze a discrete-time version of a multi-period investment and consumption problem in which an infinitely-lived individual with Epstein-Zin-Weil preferences (an extension of power utility due to Epstein and Zin (1989) and Weil (1989)) finances all consumption via costlessly traded assets in her portfolio. We briefly summarize key assumptions and results from Campbell and Viceira (1999). There are two assets available. The first asset is risky with one-period log return given by r t+1. There is also a risk-free asset f with constant log return equal to r f. The one-period return on wealth from time t to time t + 1 is R p,t+1 = α t (R t+1 R f ) + R f, (17) where R t+1 = exp(r t+1 ), R f = exp(r f ) and α t represents the time t portfolio weight invested in the risky asset. There is a single state variable x t, such that E t r t+1 r f = x t, which evolves according to the AR(1) process: x t+1 = µ + φ(x t µ) + η t+1, (18) where the shock η is conditionally homoskedastic and normally distributed, i.e., η N(0, σ 2 η). The unexpected return on the log risky asset, denoted u t+1, is also conditionally homoskedastic 33

36 and normally distributed, u N(0, σ 2 u), with cov t (η t+1, u t+1 ) = σ ηu < 0. Investor preferences follow the Epstein-Zin-Weil form: U(C t, E t U t+1 ) = { (1 δ)c (1 γ)/θ) t + δ(e t U 1 γ t+1 )1/θ} θ/(1 γ), (19) where δ < 1 is the discount factor, γ > 0 represents the coefficient of relative risk aversion, ψ is the elasticity of intertemporal substitution and the parameter θ (1 γ)/(1 ψ 1 ). Epstein- Zin-Weil preferences separate the elasticity of intertemporal substitution ψ from relative risk aversion γ. Standard time-separable power utility with relative risk aversion γ emerges as the special case in which ψ = γ 1. The investor chooses consumption and portfolio policies to maximize (19) subject to the budget constraint W t+1 = R p,t+1 (W t C t ), where W t is total wealth at the beginning of period t and C t is period t consumption. Campbell and Viceira (1999) derive approximate analytical consumption and portfolio rules for this problem using log-linear approximations to the Euler equation and intertemporal budget constraint. The (approximately) optimal portfolio rule is linear in the state variable x t, and is given by α t = a 0 + a 1 x t, where: a 0 = 1 ( ) ( 2γ b1 γ 1 1 ψ γ ( ) ( 1 b2 γ 1 a 1 = 1 ψ γ γσ 2 u ) σηu σu ) 2 σηu σ 2 u There is no hedging demand when σ ηu = 0. ( b2 1 ψ ) ( γ 1 γ ) σηu σ 2 u 2µ(1 φ) (20) 2φ. (21) Consequently, the first terms in (20) and (21) represent the myopic component of asset demand, while the remaining terms constitute intertemporal hedging demand. The optimal log consumption-wealth ratio is quadratic in the state variable x t and the quantities b 1 and b 2 represent the coefficients on x t and x 2 t for this optimal consumption policy. The parameters characterizing the optimal consumption rule solve a recursive, nonlinear equation system with coefficients that are known constants. Hedging demand also depends upon the scaled deviation of relative risk aversion from one (γ 1)/γ, the consumption coefficients b 1 and b 2, scaled by one minus the elasticity of intertemporal substitution (1 φ), and the parameters µ, φ, and σ 2 u. Campbell and Viceira (1999) derive various properties of the (approximate) solution. Here, 34

37 we mention a subset. First, the coefficient a 1 of (21) is always positive and increases from zero when risk aversion γ is infinitely large to infinitely large values as γ approaches zero. Intuitively, the agent s optimal portfolio policy increases (decreases) the allocation to the risky asset when the expected return on this asset increases (decreases), and the sensitivity of the response to changes in expected returns is smaller the larger the agent s relative risk aversion. Second, certain parameter choices result in myopic rules for portfolio allocation, consumption, or both. Specifically, when ψ 1 and γ = 1, the optimal portfolio policy is myopic, although the optimal consumption rule is not. On the other hand, when ψ = 1 and γ 1, the optimal consumption rule is the known, exact solution of Giovannini and Weil (1989), with c t w t = log(1 δ). The consumption rule is myopic, while the portfolio rule is not. Finally, when ψ 1 and γ 1 (log utility), both the optimal consumption and portfolio rules are myopic. 5.2 Calibration Analysis Calibration results are based on the VAR estimates for the log dividend yield, log total payout yield, and log net payout yield. The VAR model underlying the calibration is: r t+1 = a r + β r yld t + ɛ r t+1 (22) yld t+1 = a yld + φ yld t + ɛ yld t+1,, (23) where (ɛ r t+1, ɛyld t+1 ) N(0, Ω). This VAR model represents a simplified version of (8) (11), in which only the stock return and yield equations appear. We consider a general (log) payout yield, while Campbell and Viceira (1999) focus on the dividend yield. Key parameters defining the stochastic structure of the model can be recovered from the VAR system via: µ = a r + a yld β r /(1 φ), σ 2 η = β 2 r Ω 22, σ 2 u = Ω 11, and σ ηu = β r Ω 12. We calibrate the VAR model using OLS estimates reported in Table 5 over the sample period. (Results based on biascorrected parameter estimates are similar.) For each yield considered, parameter values α r, β r, α yld, and φ can be read directly from Table 5, while calibrated values for the covariance matrix Ω follow from the standard deviation and correlation matrices presented in Table 5. Using the calibrated parameter values, we compute the agent s optimal portfolio allocation and consumption-wealth ratio for a range of potential values for relative risk aversion and 35

38 elasticity of intertemporal substitution. Specifically, we consider relative risk aversion values in the set γ = [1, 2, 4, 10, 20] and elasticity of intertemporal substitution values in the set ψ = [1, 1/2, 1/4, 1/10, 1/20]. Following Campbell and Viceira (1999), we set the discount rate δ to The log risk-free rate is set to the annual mean of the real log risk-free rate for Calibration Results Table 8 presents the optimal portfolio policy intercept and slope for different relative risk aversion (RRA) and elasticity of intertemporal substitution (EIS) values. We follow Campbell and Viceira (1999) and normalize parameters characterizing the optimal portfolio and consumption policies so that the intercepts for these policy rules represent the optimal actions when the expected simple excess return, E t (R t+1 ) R f, is zero. In this case, the risky asset offers no risk premium and a myopic investor would allocate no wealth to it. Consequently, any demand for the risky asset represents intertemporal hedging demand. The expected log excess return x t is equal to σu/2 2 when the expected simple excess return is zero. Parameters reported in the tables are a 0, a 1, b 0, b 1, and b 2, where α t = α 0 + a 1 (x t + σ 2 u/2) (24) and c t w t = b 0 + b 1(x t + σ 2 u/2) + b 2 (x t + σ 2 u/2) 2, (25) with a 0 = a 0 σ 2 u/2, b 0 = b 0 b 1 (σ 2 u/2) + b 2 (σ 4 u/4), and b 1 = b 1 b 2 σ 2 u. Tables 8 and 9 characterize the optimal portfolio policies for alternative payout yield measures. Panel A of Table 8 presents a 0, the optimal allocation to the risky asset when the simple excess return is zero, while Panel B presents a 1, the slope coefficient for the optimal portfolio policy. Panel A in Table 9 presents the average allocation to stocks, as a percentage of wealth, under the optimal portfolio policy. Panel B of Table 9 shows the share of average demand for stocks attributable to the average hedging demand for stocks. In both tables, results are presented for calibrations based on the dividend yield (left-hand portion), total payout yield (middle portion) and net payout yield (right-hand portion). 36

39 Consistent with Campbell and Viceira (1999), Panel A of Table 8 shows that hedging demand is positive whenever γ > There is no hedging demand when γ = 1, because in this case the optimal portfolio rule is myopic. Hedging demand decreases as relative risk aversion increases, and the extent of hedging demand varies only slightly with the elasticity of intertemporal substitution φ. 24 The results in Panel A illustrate significant differences in hedging demand among the three alternative payout yields. As intuition suggests, the extent of hedging demand is much smaller under the net payout yield relative to the dividend yield and total payout yield. As an example, consider the case with γ = 4 and φ = 1/4. An investor with these preferences exhibits an intertemporal hedging demand for stocks of approximately 16.9% when the expected excess return is zero for a calibration based on the total payout yield. The corresponding hedging demand based on the dividend yield and net payout yield are 11.7% and 4.7%, respectively. The fact that hedging demand is significantly larger under the total payout yield relative to the dividend yield might seem surprising, because the extent of negative correlation between contemporaneous shocks to stock returns and the yield is comparable for the two yields (see Table 5). The explanation is that the mean allocation to stock under the total payout yield calibration is higher than that for the dividend yield calibration. Hedging demand as a proportion of total demand is similar for the two yields (see Table 9 and subsequent discussion). Panel B of Table 8 reports the slope of the optimal portfolio policy. As the theoretical properties of the optimal policy rules imply, the slope a 1 of the portfolio rule is positive for all RRA and EIS values, and monotonically decreases as RRA increases for a fixed EIS value. Intuitively, the portfolio policy responds aggressively to changes in expected returns on stocks for lower RRA values, but becomes nearly flat as risk aversion becomes large. The slopes of the optimal portfolio rule are quite insensitive to the elasticity of intertemporal substitution, consistent with properties of the optimal policy derived in Campbell and Viceira (1999). 25 The 23 Campbell and Viceira (1999) show that hedging demand is negative when γ < 1. Although results for cases with γ < 1 are of theoretical interest, we focus on the case γ 1 in this paper, since relative risk aversion in this range appears necessary to explain the equity premium puzzle. 24 This finding is attributable to a property derived by Campbell and Viceira (1999): the optimal portfolio only depends on φ indirectly, via its impact on the optimal expected log consumption-wealth ratio. 25 For all three yields, the slope values in Panel B of Table 8 adhere to another property of the optimal policy rules: hedging demand increases the slope of the portfolio policy. This implies that conservative long-horizon investors who can rebalance each period are more aggressive market timers than conservative short-horizon investors. This assumes that investors know the parameters of the stock return process. See, e.g., Barberis 37

40 slope of the optimal portfolio policy is steeper for the net payout yield relative to the other two yields for lower levels of RRA; however, differences are not dramatic. As risk aversion increases, the slopes across the different payout yields become even closer. In other words, the choice of payout yield influences the portfolio rule primarily via a level effect, and not as much with respect to the sensitivity of the policy to changes in expected returns, particularly for very risk averse individuals. Panel A of Table 9 presents the mean allocation to stocks as a percentage of wealth, given mathematically by a 0 + a 1(µ + σu/2) The average allocation is positive for all levels of RRA and EIS considered. At low levels of RRA, the agent shorts the risk-free asset and holds more than 100% of wealth in risky stocks. The fact that high levels of RRA are needed before the agent allocates less than 100% to stock reflects the well-known equity premium puzzle. There are significant differences in the mean allocation to stock across the three alternative yield calibrations. The pattern of results is somewhat nuanced. For the case γ = 1, in which hedging demand is absent, the largest mean allocation occurs for the net payout yield, and the smallest for the dividend yield. This is driven by the steeper slope of the portfolio policy under the net payout yield at low risk aversion levels. As RRA increases, the mean allocation to stock decreases for all three yields; however, decreases are more pronounced for the net payout yield. This occurs because the slope of the portfolio policy for the net payout yield falls more rapidly relative to the other yields as risk aversion increases. At high RRA levels the mean allocation to stock for the net payout yield is similar to that for the dividend yield, while the mean allocation for the total payout yield remains significantly higher. Panel B of Table 9 shows the share of average total demand for stocks attributable to average hedging demand. Average hedging demand is computed following the approach in Campbell and Viceira (1999). We set x t = µ and subtract from the corresponding total allocation to stock the total allocation when γ = 1, scaled by the level of RRA γ: α t,hedge (µ; γ, φ) = α t (µ; γ, φ) (1/γ)α t (µ; 1, φ). (26) Our results replicate a key finding in Campbell and Viceira (1999): hedging demand accounts for a substantial proportion of total demand for stock for the calibration based on the dividend (2000) for an analysis that accounts for parameter uncertainty. 38

41 yield. This is particularly true at higher levels of risk aversion, where hedging demand accounts for 40-50% of total demand. The proportion of hedging demand is very similar for the total payout yield. This is intuitive, since both yields are persistent and shocks to both yields are strongly negatively correlated with contemporaneous return shocks. The proportion of hedging demand for the net payout yield is much smaller. At higher RRA levels, hedging demand represents only 12-15% of total demand for stock. This occurs because shocks to the net payout yield are only weakly negatively correlated with contemporaneous return shocks. Figure 5 depicts the time series of optimal historical allocations to stock based on calibrations for the dividend yield, total payout yield, and net payout yield. The results plotted in Figure 5 are based on preference parameter choices γ = 4 and ψ = 1/4. The portfolio policies are quite volatile and reveal a high-degree of market timing on the part of the individual. On the whole, the allocations to stock among the three yields comove closely. This is because the underlying yields comove closely at most times (Figure 1), due in turn to the fact that the market price serves as the common denominator for all three yields. Nevertheless, there are important differences among the three yields with respect to the time series of optimal portfolio weights. First, the allocations diverge sharply at certain times. For example, in the early 2000s, prior to the financial crisis, the allocation to stock under the total payout yield and net payout yield are much higher than under the dividend yield. This is because the underlying yields diverge in similar fashion during this time, and consequently predict very different expected returns for risky stock. Second, allocations under the net payout yield are more volatile than under the other yields, and exhibit occasional downward spikes, which are driven by corresponding spikes in (net) issuance. Finally, even when the allocations comove closely, the absolute difference in the allocations can be large, e.g., during the late 1950s when the allocation to stock is in excess of 100% for the dividend yield, but only approximately 50% for the net payout yield. The preceding results pertain to portfolio policies. To conserve space, results and discussion concerning optimal consumption policies appear in the Supplementary Appendix. The key finding is that optimal consumption policies differ meaningfully depending on the definition of payout yield. For example, a time series plot contrasting the optimal consumption-wealth ratio across alternative yield definitions shows that the net payout yield is relatively stable 39

42 over time, with moderate fluctuations around an average level of just under 5%. In contrast, the time series of consumption-wealth ratios for the dividend yield and total payout yield are punctuated by occasional upward spikes that interrupt more stable periods. 6 Conclusion The particular definition of corporate payout used to form a valuation ratio matters economically. When stock repurchases and issuances are incorporated into a net payout yield, we find that a majority of variation in this yield forecasts growth in net payout (primarily via the issuance channel), but that a nontrivial proportion of variation also corresponds to changing expected returns. Consequently, using a broader variation of payout, variation in the yield captures both changes in expected returns and changes in expected (net) cash flow growth. Inand out-of-sample forecasting results suggest that it is preferable to incorporate (net) issuance information via the net payout yield, rather than as a separate forecasting variable. Finally, we show that the particular choice of yield matters economically for dynamic consumption and portfolio decisions, particularly via the extent of hedging demand associated with risky stock, which is much lower under a net measure of payout. We note several interesting directions for future research. First, Campbell, Chan, and Viceira (2003) show how to extend the analysis of Campbell and Viceira (1999) to include multiple forecasting variables, a time-varying risk-free rate, and additional risky assets. This extended framework permits an analysis of long-horizon portfolio and consumption choice with multiple state variables, including various yields or yield components and other common return predictors. Second, optimal long-horizon portfolio and consumption policies depend on model parameters that are unknown to investors. In addition, our results suggest a substantial degree of model uncertainty with respect to the appropriate payout yield to include in predictive regressions for stock returns. Bayesian techniques, including Bayesian model averaging methods, provide a way to formally incorporate uncertainty regarding parameter values and models into return forecasts and long-horizon portfolio choice. It would be interesting to examine the implications of using alternative payout yields in Bayesian implementations of predictive regressions such as Barberis (2000) and Wachter and Warusawitharana (2009, 2013). Finally, 40

43 van Binsbergen and Koijen (2010) model expected returns and expected dividend growth as latent variables that follow an exogenously specified time series process. They combine this setup with a present-value model similar to that used to facilitate variance decompositions and long-run forecasting coefficients in this paper. This approach exploits the entire history of price-dividend ratios and dividend growth to estimate expected returns and expected dividend growth. A similar approach might be applied to improve return and cash flow growth forecasts using alternative cash flow measures such as total payout and net payout. 41

44 Appendix A Details on construction of payout variables We follow Boudoukh et al. (2007) in constructing the payout variables. The sample period is The dividend yield (DY ) is imputed from value-weighted CRSP market returns for the AMEX, NASDAQ, and NYSE universe with and without dividends (VWRETD and VWRETX, respectively) as DY = (1 + VWRETD)/(1 + VWRETX) 1. Aggregate repurchases (RP ) are computed using Compustat data for the period Repurchases are calculated only for common stock, that is, repurchases are the dollar value of the purchase of common and preferred stock (PRSTKC on Compustat) adjusted for any reduction in outstanding preferred stock (PSTKRV). 26 The repurchase yield (RP Y ) is computed as RP Y = RP/MV, where MV is year-end CRSP market capitalization. This yield is set to zero from , since Compustat data on repurchases are unavailable prior to Although repurchases prior to 1971 are unlikely to be literally zero, this serves as a reasonable approximation, since there is minimal repurchasing activity prior to the early 1980s (see, e.g., Grullon and Michaely (2002)). With the dividend yield and repurchase yield in hand, the total payout yield (T P Y ) is computed as T P Y = DY + RP Y. We collect aggregate equity issuances from As with share repurchases, we use Compustat to collect issuance data beginning in 1971 since these data are unavailable on Compustat in prior years. Issuances are the dollar value of the sale of common and preferred stock (SSTK) adjusted for any increase in outstanding preferred stock (PSTKRV). The equity issuance yield (IY ) is then IY = I/MV and the net equity issuance yield (NIY ) is NIY = IY RP Y. Prior to 1971, we compute the net issuance yield using monthly CRSP data on the change in shares outstanding. Specifically, net issuance for the i-th firm in month t is computed as (shrout t cfacshr t shrout t 1 cfacshr t 1 ) (prc t /cfacpr t + prc t 1 /cfacpr t 1 )/2. This figure is aggregated across months and firms to form annual net equity issuance and the 26 Boudoukh et al. (2007) construct an additional, alternative measure based on the change in treasury stock. The treasury stock measure attempts to exclude repurchases potentially earmarked for compensation or payment-in-kind. We rely in this paper on the more inclusive measure; however, changing to the treasury stock measure does not alter our main empirical findings. 42

45 net equity issuance yield. This convention follows previous studies including Stephens and Weisbach (1998), Boudoukh et al. (2007) and Grullon et al. (2011). Finally, we compute the net payout yield (NP Y ) as NP Y = DY NIY. The correlation of our net payout yield data with the net payout yield data used in Boudoukh et al. (2007) over the common sample period of is in excess of We compute aggregate payout growth rates as follows: First, we compute an annual payout level for each yield by multiplying the corresponding annual yield by the CRSP value-weighted index price level excluding distributions. Using the resulting payout level, we calculate growth as the percentage change in year-over-year levels, and log growth as the log of the one-period ahead payout level over current period payout level. All growth rates are computed for the period except for net payout growth, for which the sample period is , due to negative net payouts in 1929 and We adjust growth rates to real terms using CPI data from the U.S. Department of Labor. Specifically, we multiply the one-period ahead payout level by a CPI factor, where the CPI factor is lagged end-of-the-year CPI over current end-of-the-year CPI. For example, real dividend growth is (D t+1 CP Ifactor D t )/D t. We compute aggregate payout growth rates using the CRSP value-weighted index price level, rather than the aggregate market capitalization from CRSP, as the price measure in the yields. We do not use aggregate market capitalization from CRSP because our sample contains a break in the number of firms covered in The break in the number of sample firms is due to the transition from CRSP data to Compustat data in Since aggregate market capitalization is a function of the number of sample firms, it too suffers from a level break in The CRSP value-weighted index price level does not suffer from a level break, since it is invariant to the number of sample firms. However, our results are qualitatively similar regardless of the price measure used to compute payout growth. 27 We thank Michael Roberts for providing these data on his website. 43

46 Appendix B Approximate identities for alternative yields The Campbell and Shiller (1988a) log-linearization expresses the return as: r t+1 ρ(p t+1 d t+1 ) + d t+1 (p t d t ), (27) where lowercase letters represent demeaned logarithms of corresponding capital letters, ρ 1/(1 + D/P ), and D/P represents the dividend yield around which one linearizes (usually taken to be the average dividend yield). To develop generalized versions of the identities linking return and cash flow growth forecasting coefficients, let MV t represent market capitalization and CF t denote an aggregate cash flow measure (e.g., dividends, total payout, etc.). The measure CF t is aggregate dividends in the traditional Campbell-Shiller log-linearization. It is assumed that CF t > 0 for all t. This assumption ensures that natural logarithms are well-defined. The assumption that CF t is positive is innocuous for dividends, total payout (dividends plus repurchases) and issuances, but embeds an important assumption that aggregate issuance is always smaller than total payout when extended to net payout. Introduce the notation yld t cf t mv t, where cf t and mv t are log cash flow and market capitalization, respectively. Starting from an aggregate version of the Campbell-Shiller loglinearization of returns, we have: r t+1 ρ(mv t+1 d t+1 ) + d t+1 (mv t d t ) = ρ(yld t+1 ) + cf t+1 + yld t (1 ρ)(cf t+1 d t+1 ), (28) where the second line follows from the first after some algebra. Projecting both sides of the second line of (28) on yld t gives the adjusted identity (12), where it is implicitly assumed that the log ratio of cash flow to dividends cf t d t is stationary For some of the cash flow measures we consider, e.g., total payout, it is likely that cf t d t is not stationary over the full sample period Note that Eq. (28) and Eq. (29) do not require cf t d t to be stationary. The assumption delivers a time-invariant slope coefficient β cf,d, but in reality this slope coefficient is potentially time-varying. Empirically, variance decompositions estimated using relatively recent data ( ) produce qualitatively similar results (available upon request). 44

47 Solving Eq. (28) for yld t, and recursively substituting forward gives yld t ρ j 1 [r t+j cf t+j + (1 ρ)(cf t+j d t+j )]. (29) j=1 Similar to the traditional Campbell-Shiller decomposition, the validity of the expression on the right-hand side of (29) relies on an assumption of no bubbles, i.e., that lim H ρ H yld t+h = 0. Projecting the left and right-hand sides of (29) onto yld t gives: 1 β lr r βcf lr + (1 ρ)βlr cf,d, (30) where βcf,d lr represents the slope coefficient in a regression of cf lr t d lr t j=1 ρj 1 (cf t+j d t+j ) on yld t. To avoid imposing the no bubbles condition, we can instead substitute forward H times to obtain the following alternative expression for yld t : yld t H ρ j 1 [r t+j cf t+j + (1 ρ)(cf t+j d t+j )] + ρ H yld t+h. (31) j=1 Projecting the left- and right-hand sides of Eq. (31) on yld t gives the identity (13). 45

48 Appendix C Details Regarding Out-of-Sample Performance Tests The null hypothesis in the Clark and West (2007) testing framework is that σ 2 = σ0 2, where σ2 and σ0 2 refer to the population MSPEs associated with the predictive regression and benchmark forecasts, respectively. Under the null hypothesis, the benchmark model generates the data and the out-of-sample MSPE for this model is expected to be smaller than the out-of-sample MSPE for the larger model. Consequently, the unadjusted difference in out-of-sample MSPEs between the two models is not centered around zero. The Clark and West (2007) test statistic takes the form: Clark-West = ˆσ 0 2 ˆσ 2 + P 1 (Rt+1 e R t+1 ) 2. (32) }{{} Adjustment The final term in (32) captures the adjustment for additional noise associated with the larger model s forecast under the null hypothesis. Although the statistic (32) is not asymptotically normal, Clark and West (2007) show that standard normal critical values lead to tests with actual sizes close to nominal size for reasonably large samples. The test is one-sided, since, under the alternative, σ 2 < σ 2 0. Giacomini and White (2006) consider the problem of comparing two alternative forecasting methods. A forecasting method is a broader concept that encompasses not only a model specification, but also the explicit procedure used to obtain forecasts. This procedure includes the parameter estimation scheme and choice of estimation window. The null hypothesis for the Giacomini and White (2006) test is that the two models possess equal (conditional) forecasting ability, and the test incorporates the effects of parameter estimation uncertainty on forecast performance. We focus in this paper on unconditional forecast comparisons. The corresponding Giacomini and White (2006) test statistic is: Giacomini-White = ˆσ2 0 ˆσ2 ˆσ P / P, (33) where ˆσ P is a heteroskedasticity and autocorrelation consistent (HAC) estimator of the asymptotic variance σp 2 = var (ˆσ [ P ] 2 0 ˆσ 2 ). In contrast with the Clark-West test, the Giacomini- White test is two-sided. 46

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53 8 Dividend yield, total payout yield and net payout yield 6 4 Yield (%) 2 0 Dividend yield 2 Total payout yield Net payout yield Issuance yield versus net issuance yield Issuance yield Net issuance yield 4 Yield (%) Figure 1: Time series plots for alternative yields. The first panel plots the dividend yield, total payout yield and net payout yield. The dividend yield is dividend over price. The total payout yield is the dividend yield plus the repurchases yield. The net payout yield is the dividend yield less the net issuance yield, where the net issuance yield is the issuance yield less the repurchase yield. The second panel plots the issuance yield and net issuance yield. See Section I of the paper and the Appendix for details regarding variable construction. 51

54 40 Log dividend growth Year on year growth (%) Dividends reinvested Dividends consumed Year on year growth (%) Log net payout growth Dividends reinvested Dividends consumed Figure 2: Dividend and net payout growth for alternative dividend measures. The top panel plots annual time series of log dividend growth for alternative dividend measures. The series labeled dividends reinvested plots dividend growth for dividends imputed using annual CRSP index returns with and without dividends (dy). This method implicitly assumes that intrayear dividends are reinvested at the annual index return. The series labeled dividends consumed shows dividend growth for the alternative measure that assumes no reinvestment ( dy). The bottom panel plots similar series for net payout growth (np and ñp) for which dividends are computed assuming reinvestment or no reinvestment. Because net payout is negative in 1929 and 1930, the time series begin in See Section 1 and the Appendix for further discussion regarding the treatment of dividends. 52

55 Figure 3: Out-of-sample performance: stock return forecasts. The figure shows the out-of-sample cumulative difference in MSE relative to the historical average, multiplied by 100, for stock return forecasts. The first estimation uses 30 years. Results are presented for forecasts based on the lagged dividend yield, total payout yield, net payout yield, issuance yield, and net issuance yield. The total payout yield is the dividend yield plus the repurchase yield. The net payout yield is defined as the dividend yield less the net issuance yield, where the net issuance yield is the issuance yield minus the repurchase yield. The first panel uses a rolling window of 30 years. The second panel uses a recursive scheme, with an initial estimation sample of 30 years. Shaded areas indicate NBER recession periods. 53

56 Figure 4: Out-of-sample performance: cash flow growth forecasts. The figure shows the out-of-sample cumulative difference in MSE relative to the historical average, multiplied by 100, for forecasts of cash flow growth. The first estimation uses 30 years. Results are presented for dividend growth, total payout growth, net payout growth, and issuance growth. In each case the forecasting model is based on the corresponding lagged yield. For example, for dividend growth, forecasts are based on the lagged (log) dividend yield. The first panel uses a rolling window of 30 years. The second panel uses a recursive scheme, with an initial estimation sample of 30 years. Shaded areas indicate NBER recession periods. 54