Price-Dividend Ratio Factor Proxies for Long-Run Risks
Ravi Jagannathan Kellogg School of Management, Northwestern University and NBER, Indian School of Business and Shanghai Advanced Institute of Finance Downloaded from https://academic.oup.com/raps/article/5/1/1/1915590 by guest on 05 October 2021 Srikant Marakani Department of Economics and Finance, City University of Hong Kong
We show that several asset pricing models that rely on long-run risks imply that the state of the economy can be captured by factors derived from the price-dividend ratios of stock portfolios. We find two factors with small growth and large value tilts are important for this purpose, thereby relating the Fama-French model and the Bansal-Yaron and Merton intertemporal asset pricing models. As predicted by the model, these price-dividend ratio factors track consumption volatility and predict future consumption and stock dividends, and the covariance of returns with their innovations explains the cross-section of average returns of several stock portfolios. (JEL G19)
Introduction We show that long-run risk factors in the model introduced by Bansal and Yaron (2004) can be estimated through principal component analysis of the covariance matrix of log price-dividend ratios of a collection of stocks. Previous studies obtain the long-run risk factors by projecting the future consumption growth and its volatility on the market price-dividend ratio and the real risk-free rate (Bansal, Yaron, and Kiku 2007; Constantinides and Ghosh 2011; Ferson, Nallareddy, and Xie 2013). However, both con- sumption growth and the real risk-free rate are measured with considerable error. As we show using Monte Carlo simulations, this error could be large enough to result in the rejection of the long-run risk model too often even when it holds. Our approach shows a remarkable improvement as long as a
For their valuable comments and suggestions, we would like to thank Ravi Bansal, George Constantinides, Du Du, Dana Kiku, Ernst Schaumburg, Jonathan Parker, Robert Korajczyk, Annette Vissing-Jørgensen, Arvind Krishnamurthy, Tatjana Xenia-Puhan, Bernard Dumas, seminar participants at INSEAD, the City University of Hong Kong, the Indian School of Business, the Western Finance Association 2011 Annual Meeting, and the 2012 City University International Conference on Corporate Finance, and the editor, Wayne Ferson. Earlier versions of the paper appeared under the titles “Long run risks, the factor structure of price-dividend ratios and the cross-section of stock returns” and “Long-run risks and P/D factors.” Supplementary data can be found on The Review of Asset Pricing Studies web site. Send correspondence to Ravi Jagannathan, Department of Finance, Kellogg School of Management, Northwestern University and NBER, Indian School of Business and Shanghai Advanced Institute of Finance. E-mail: [email protected].
ß The Author 2015. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please email: [email protected] doi:10.1093/rapstu/rav003 Advance Access publication March 24, 2015 Review of Asset Pricing Studies / v 5 n 1 2015
reasonable number of portfolios are used to estimate the long-run risk factors. Our approach enables an answer to one of the important critiques of the long- run risk model raised by Marakani (2009), Beeler and Campbell (2012) and Constantinides and Ghosh (2011), among others, that the log market price- dividend ratio does not predict dividend or consumption growth. Fama and French (1993) construct a set of twenty-five stock portfolios by sorting stocks based on their size and book-to-market ratios. We argue that results in the literature suggest that the log P/D ratios of these portfolios are likely to show wide variation in their exposure to the long-run risk factors, Downloaded from https://academic.oup.com/raps/article/5/1/1/1915590 by guest on 05 October 2021 making them a suitable choice from an econometric point of view. We there- fore extract two price-dividend ratio factors using time-series observations on the price-dividend ratios of these twenty-five stock portfolios. The first factor is of a level type with a small-growth firms tilt and the other has a form similar to large-value minus small-growth firms tilt as seen from Table 2. The two factors also predict future aggregate consumption and dividends, and track consumption volatility over time. The finding that the two P/D factors from the Fama-French portfolios are related to future consumption and dividends and their volatilities establishes a tighter link between Fama and French (1993), Merton (1973), and Bansal and Yaron (2004). Fama and French (1993) interpret the SMB and HML factors as innov- ations to state variables in the Merton (1973) intertemporal capital asset pricing model. We show that the class of long-run risk models that we consider can be viewed as versions of the Merton (1973) model.1 The Fama and French interpretation implies that the price-dividend ratio factors whose innovations are similar to SMB and HML. We find this to be the case with the P/D factors extracted from the twenty-five Fama-French portfolios. We further find that the factor innovation betas explain the cross-section of aver- age excess returns on the twenty-five assetsandotherassetsaswell.These observations are consistent with the predictions of the long-run risk models andhelptorelatethewidelyusedFamaandFrench(1993)modelandthe intertemporal asset pricing models of Merton (1973) and Bansal and Yaron (2004). An important insight that follows from our analysis is that the cross- section of P/D ratios of stocks contains information about state variables relevant for valuing securities with risky payoffs. To evaluate the robustness of our findings, we also extract two price- dividend ratio factors from a different collection of stock portfolios: ten stock portfolios formed by sorting stocks on their dividend yield. We find that they perform as well as the state variables in Petkova (2006) or the two
1 Petkova (2006) uses the short-term interest rate, yield spread, credit spread, aggregate dividend yield as state variables that describe the investment opportunities set, and finds that HML and SMB factor returns are correlated with innovations to these state variables, consistent with the Fama and French (1993) three-factor model being a version of the ICAPM. Our approach is more direct. When the long-run risk model holds, and the HML and SMB factors are innovations to state variables summarizing the state of the economy, then the price-dividend ratios on the underlying stock portfolios should predict future consumption and dividends and track consumption volatility.
2 Price-Dividend Ratio Factor Proxies for Long-Run Risks
factors constructed from the twenty-five portfolios discussed earlier in jointly predicting future consumption and dividends, and tracking consumption volatility. The betas on the factor innovations are also able to explain the cross-section of average returns of the various test assets, thereby providing robust support for the wide class of long-run risk models. These findings support the view that the P/D factors are the relevant state variables in the Merton (1973) model as well.2 Our conclusions are robust to the recent critique of factor models by Downloaded from https://academic.oup.com/raps/article/5/1/1/1915590 by guest on 05 October 2021 Kleibergen (2010) and the lookahead bias critique of Ferson, Nallareddy, and Xie (2013). We analyze our results usingtherobustteststatisticsde- velopedbyKleibergen(2009)inAppendixBandfindthattheyperform well along that dimension. We also develop lookahead bias-free versions of the factors and find that they behave in the expected manner (see Tables 11, 12, and 13). Our asset pricing results are also robust to the critique of Lewellen, Nagel, and Shanken (2010) as our cross-sectional regression inter- cepts are generally very small and close to zero. The importance of the small intercept has been particularly emphasized by Jagannathan and Wang (2007). The fact that the expected model implied relation between the P/D factors and macroeconomic variables holds, even though the latter do not have any mech- anical relationship with the size and book-to-market ratio factors, gives fur- ther credence to the point that our results are robust to the critique of Lewellen, Nagel, and Shanken (2010). We find that the predictability of consumption growth does not extend to the period following the financial crisis and the Great Recession. This may be due to a structural break in the mean of consumption growth after the global financial crisis. We present evidence for this, but the hypothesis only can be properly verified in the future as time unfolds.
1. The Long-Run Risk Model The long-run risk model introduced by Bansal and Yaron (2004) is ex- pressed as pffiffiffiffiffi Dct + 1 ¼ + Xt + Vt t + 1; ð1Þ pffiffiffiffiffi Xt + 1 ¼ Xt + ’x Vtet + 1; ð2Þ
2 Merton (1973) used time separable utility function and did not consider investors’ preferences over the timing of resolution of uncertainty. Campbell (1993) showed that the Merton (1973) ICAPM relation will continue to hold in a model economy populated by a representative investor with Epstein-Zin utility function with preference over timing of uncertainty resolution. In that model, with conditional homoscedasticty, the state variables predict expected future returns on the aggregate wealth portfolio. Campbell, Giglio, Polk, and Turley (2013) generalize the results to an economy with stochastic volatility. In contrast, we establish the relationship between the state variables in the Merton (1973) ICAPM relation and the state variables in the Bansal and Yaron (2004) type long runriskmodels.
3 Review of Asset Pricing Studies / v 5 n 1 2015
pffiffiffiffiffi
Ddl;t + 1 ¼ l;d + lXt + ’l;d V ul;t + 1; 1 l M; ð3Þ
Vt + 1 ¼ V + ðVt V Þ + wt + 1; ð4Þ 3 where c is the log per capita consumption, dl is the log dividend of asset l, and the shocks t + 1; et + 1 and wt + 1 are independent standard normals. The shock ul;t + 1 is a vector of normally distributed shocks with covariance