Recent research in empirical finance has documented that expected excess returns on bonds and stocks, real interest rates, and risk shift over time in predictable ways. Furthermore, these shifts tend to persist over long periods of time. Starting at least with the pioneering work of Samuelson (1969) and Merton (1969, 1971, 1973) on portfolio choice, financial economists have argued that asset return predictability can introduce a wedge between the asset allocation strategies of short-and longterm investors. This document examines asset allocation when expected returns and interest rates are time-varying, and investors have mean-variance preferences and long investment horizons.

This paper provide the technical backbone of the empirical results shown in “The Term Structure of the Risk-Return Tradeoff”(Campbell and Viceira, 2004). The paper is organized as follows. Section 2 derives multi-period expected returns, variances and covariances in a model where log (or continuously compounded) return dynamics are described by a homoskedastic VAR (1) process. Section 2 also discusses several important extensions of this VAR (1) model. Section 3 and Section 4 derives conditional mean-variance frontiers at different investment horizons. Section 5 illustrates the general results shown in Sections 2, 3, and 4 using a simple example. The section is particularly useful to understand how return predictability can create nonlinear patterns in variances and covariances across investment horizons. Finally Section 6 concludes.