Nicholas Polson
Booth Graduate School of Business, University of Chicago
Abstract
| In this paper, we survey asset allocation in finance from a Bayesian decision- theoretic perspective. Our investor wishes to maximize the expected long-run growth of the market returns. We show how Stein’s lemma helps deriving the Kelly criteria for optimal bet size and Merton’s allocation rule for risky stocks. We therefore provide an equivalence between these two criteria. Bayesian inference naturally determines the inputs needed for optimal asset allocation, namely, the expected excess return and volatility of the risky asset. Extensions to exchangeable returns where the investor learns about the probability of success illustrate that risk-averse investors are still will- ing to hold a small proportion of a risky asset even though the odds are unfavorable at the current time. Specifically, the option value of future learning leads the investor to a positive allocation. We conclude with directions for future research. |