Long Memory and the Term Structure of Risk

This paper explores the implications of asset return predictability on long-term portfolio choice when return forecasting variables exhibit long memory. We model long memory using the class of fractionally integrated time series models. Important predictor variables for U.S. data, like the dividend-price ratio and nominal and real interest rates, are non-stationary with orders of integration around 0.8. These time series properties lead to substantial increases of the estimated long-term risk of stocks, bonds and cash compared to earlier estimates obtained from a stationary VAR. Long-term risk increases because the fluctuations in the predictor variables imply that expected returns themselves become a significant source of long-term risk. We find that results are sensitive to the specification of the prediction equation of excess stock returns. The inclusion of the short-term nominal interest rate among the predictor variables has the most profound impact. Jointly with the dividend-price ratio it has significant predictive power, but contrary to the dividend-price ratio the nominal interest rate does not induce mitigating effects through mean reversion.