Predicting Portfolio Return Volatility at Medium Horizons

Abstract

Commercially available factor models provide good predictions of short-horizon (e.g. one day or one week) portfolio volatility, based on estimated portfolio factor loadings and responsive estimates of factor volatility. These predictions are of significant value to certain short-term investors, such as hedge funds. However, they provide limited guidance to long-term investors, such as Defined Benefit pension plans, insurance companies, sovereign wealth funds, endowments, and individual owners of Defined Contribution pension plans. Because return volatility is variable and mean-reverting, the square root rule for extrapolating short-term volatility predictions to medium-horizon (one year to ten years) risk predictions systematically overstates (understates) medium-horizon risk when short-term volatility is high (low). In this paper, we propose a computationally feasible method for extrapolating to medium-horizon risk predictions in one-factor models that substantially outperforms the square root rule.