A Note on the Economics and Statistics of Predictability: A Long Run Risks Perspective

The Wharton School, University of Pennsylvania and NBER


Asset return and cash flow predictability is of considerable interest in financial economics. In this note, we show that the magnitude of this predictability in the data is quite small and is consistent with the implications of the long-run risks model.

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    ABSTRACT: We show that volatility movements have first-order implications for consumption dynamics and asset prices. Volatility news affects the stochastic discount factor and carries a separate risk premium. In the data, volatility risks are persistent and are strongly correlated with discount-rate news. This evidence has important implications for the return on aggregate wealth and the cross-sectional differences in risk premia. Estimation of our volatility risks based model yields an economically plausible positive correlation between the return to human capital and equity, while this correlation is implausibly negative when volatility risk is ignored. Our model setup implies a dynamics capital asset pricing model (DCAPM) which underscores the importance of volatility risk in addition to cash-flow and discount-rate risks. We show that our DCAPM accounts for the level and dispersion of risk premia across book-to-market and size sorted portfolios, and that equity portfolios carry positive volatility-risk premia.Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at
    Full-text · Article · May 2012 · The Journal of Finance
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    Preview · Article · Dec 2012
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    ABSTRACT: This paper investigates the empirical evidence of long-run risk and its implications for the equity premium puzzle. We find that the long-run risk model is generally weakly identified and that standard inferences tend to underestimate the uncertainty of long-run risk. We extend the LM-type test of Ma and Nelson (2010) that remains valid under weak identification to the bivariate VARMA-GARCH model of consumption and dividend growth. The results cast doubt on the validity of long-run risk as an explanation for the equity premium puzzle. We also evaluate the approach of Bansal, Kiku and Yaron (2007a), which extracts long-run risk by regressing consumption growth and its volatility on predictive variables. The results using the Bonferroni Q-test of Campbell and Yogo (2006) suggest that consumption and dividend growth are generally unpredictable by price-dividend ratio and risk-free rate. This casts doubt on the validity of the BKY approach.
    Preview · Article · Feb 2013 · Journal of money credit and banking