Financial/Actuarial Mathematics Seminar

Special Time: October 17, Friday



Portfolios and Risk Premia for the Long Run

Paolo Guasoni

Department of Mathematics, Boston University

October 17 (Friday), 2008



Abstract

This paper develops a method to derive optimal portfolios and risk premia explicitly in a general diffusion model, for an investor with power utility and in the limit of a long horizon. The market has several risky assets and is potentially incomplete. Investment opportunities are driven by, and partially correlated with, state variables which follow an autonomous diffusion. The framework nests models of stochastic interest rates, return predictability, stochastic volatility and correlation risk. In models with several assets and a single state variable, long-run portfolios and risk premia admit explicit formulas up the solution of an ordinary differential equation, which characterizes the principal eigenvalue of a elliptic operator. Multiple state variables lead to a partial differential equation, which is solvable for most models of interest. For each value of the relative risk aversion parameter, the paper derives the long-run portfolio, its implied risk premia and pricing measure, and their performance on a finite horizon. Two applications to cross-sectional models with predictability, stochastic volatility and stochastic interest rates conclude.


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