Estimating Long-Term Expected Returns: More Bad News for Equity Premia

A QWAFAFEW discussion arranged by Mark Kritzman & led by:

Eric  Jacquier

Abstract

Assessing future long-term (compound) expected returns is crucial to many aspects of portfolio management. Long-term expected returns obtain by compounding the one-period expected return. However, compounding an estimate of the one-period expected return (such as an arithmetic average) does not yield a desirable estimate of the compound expected return. It can vastly overestimate the long-term expected return. First, we review how to correct for this biases. Second we show that even bias-corrected estimates are very inefficient, we write an efficient estimate. These estimators can be written as combinations of the well-known arithmetic and geometric averages. The needed corrections are akin to downward penalties in estimated return. The longer the forecasting horizon, the higher the volatility, the more severe the penalties.

Then, we show how the optimal allocation of a long-term risk-averse investor must account for estimation risk, and implies a risk-adjusted forecast of the long-term expected return. More risk averse investors  implicitly use lower long-term expected returns forecasts in their optimal allocation. This third estimate is consistent with each investor’s risk tolerance. It is economically better motivated than its purely statistical counterpart, but results in  equally severe downward penalties in the single period rate of return to  use for long-term forecasting. Overall, all these estimators contradict the conventional wisdom that with longer horizons, one can invest more in the risky asset. A robustness analysis shows that the simplifying  assumptions made to derive simple, usable formulas, only have a second order  effect on the problem.  

Bio

 Eric  Jacquier’s research is in empirical asset pricing and financial econometrics, especially quantitative portfolio and risk management. He studies the forecasting of risk parameters, such as betas and volatilities, crucial for derivative pricing, and risk and portfolio management.  He is a specialist of Bayesian methods in finance, and his work with Nick Polson and Peter Rossi pioneered the use of Markov Chain Monte Carlo methods in Finance.

Eric Jacquier is a visiting Professor of Finance at Boston University. His MBA is from UCLA, and his  PhD in Finance and Statistics from the University of Chicago Booth School. Before BU, he taught at  Chicago, Cornell, Wharton, Boston College, Montreal and MIT. He also consults and conducts executive education courses.

Please RSVP: hugh@QWAFAFEW.org

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