Portfolios and risk premia for the long run

Details Portfolios and risk premia for the long run Portfolios and risk premia for the long run

2012-03-07

arxiv.org/abs/1203.1399v1

Annals of Applied Probability 2012, Vol. 22, No. 1, 239-284

Mathematics

Probability

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

Scientific paper

10.1214/11-AAP767

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.

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