Market Expectations in the Cross Section of Present Values

Bryan T. Kelly, Seth Pruitt
2012 Social Science Research Network  
Returns and cash flow growth for the aggregate U.S. stock market are highly and robustly predictable. Using a single factor extracted from the cross-section of book-tomarket ratios, we find an out-of-sample return forecasting R 2 of 13% at the annual frequency (0.9% monthly). We document similar out-of-sample predictability for returns on value, size, momentum, and industry portfolios. We present a model linking aggregate market expectations to disaggregated valuation ratios in a latent factor
more » ... ystem. Spreads in value portfolios' exposures to economic shocks are key to identifying predictability and are consistent with duration-based theories of the value premium. * Kelly is with Booth School of Business, University of Chicago, and Pruitt is with the Board of Governors of the Federal Reserve System. The view expressed here are those of the authors and do not necessarily reflect the views of the Federal Reserve System or its staff. 1 See Cochrane (2005) and Koijen and Van Nieuwerburgh (2011) for surveys of return and cash flow predictability evidence using the aggregate price-dividend ratio. Similar results obtain from forecasts based on the aggregate book-to-market ratio. 1721 obey an exact one-factor model as in the CAPM, μ i,t = μ i,0 + c i,μ μ t , and individual expected ROE obeys a one-factor model, g i,t = g i,0 + c i,g g t + e i,t . This special case is similar to the formulation of Polk, Thompson, and Vuolteenaho (2006) . 3 In Vuolteenaho's (2002) book-to-market identity, cash flow growth enters as ROE. We later discuss how this system relates to the Campbell and Shiller (1988) price-dividend identity, where cash flows enter in the form of dividend growth. 4 This remains true despite the absence of measurement error in the aggregate book-to-market expression, as pointed out by Fama and French (1988) . 8 We assume that all model parameters are constant. When we estimate the model using Fama-French size-and value-sorted portfolios, we find an impressive degree of stability in estimated parameters between the first and second half of the sample. This is not the case when the crosssection involves individual stocks. Our framework may be generalized to incorporate time-varying parameters, or may be implemented using rolling window parameter estimates, as in our stocklevel analysis in Section III.A.3. 9 That F t is a first-order process is without loss of generality since any higher order vector autoregression can be written as a VAR(1). 10 Vuolteenaho (2002) represents this identity in terms of excess returns. We use his identity exactly, though we represent it in terms of returns rather than excess returns.
doi:10.2139/ssrn.1752543 fatcat:qo72ykpdlbejjam6skevyfbqk4