Portfolios and risk premia for the long run

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 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 an elliptic operator. Multiple state variables lead to a quasilinear partial differential equation which is solvable for many models of interest. The paper derives the long-run optimal portfolio and the long-run optimal pricing measures depending on relative risk aversion, as well as their finite-horizon performance.

Published in at http://dx.doi.org/10.1214/11-AAP767 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Equivalent and absolutely continuous measure changes for jump-diffusion processes
• Sensitivity analysis of utility-based prices and risk-tolerance wealth processes
• On the structure of solutions of ergodic type Bellman equation related to risk-sensitive control
• On the two-times differentiability of the value functions in the problem of optimal investment in incomplete markets

Cited by in corpus (2)

• Portfolio Selection with Small Transaction Costs and Binding Portfolio Constraints
• Long Term Optimal Investment in Matrix Valued Factor Models