Demographics and the Econometrics of the Term Structure of Stock Market Risk

The term structure of the stock market risk, defined as the per period conditional variance of cumulative returns, is measured in the strategic asset allocation literature (e.g. Campbell and Viceira (2002), (2005)) via multi-step ahead predictions from a VAR model of the joint process for one-period returns and their predictor, the dividend-price ratio. In this paper we modify the dynamic dividend growth model to allow for a time varying linearization point driven by the age structure of population. This specification leads to a decomposition of the dividend-price prices into an high volatility little persistence noise component, and a low volatility high persistence information component. The dividend-price ratio is mean reverting toward the time-varying mean and its deviations from it have a predicting power for returns that increases with the horizon. As a result of these two effects, the forward solution of the model delivers a negative sloping term structure of stock market risk. Direct regressions of returns at different horizons on the relevant predictors are much better suited to capture this feature than VAR based multi-period iterated forecasts. This evidence is very little affected by parameters' uncertainty and is robust to the existence of "imperfect predictiors", as a parsimoniuos parameterization is very precisely estimated and no-projections for future variables are needed in the direct regression approach.