Portfolios and risk premia for the long run

TL;DR

This paper introduces a comprehensive method to explicitly derive long-term optimal portfolios and risk premia in complex diffusion models with multiple assets and state variables, accommodating market incompleteness and various risk factors.

Contribution

It provides explicit formulas for long-run portfolios and risk premia in models with multiple assets and state variables, solving associated differential equations.

Findings

Explicit formulas for long-run portfolios and risk premia.

Framework encompasses stochastic interest rates, volatility, and correlation risk.

Finite-horizon performance of optimal strategies is analyzed.

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.