Portfolio and Consumption Choice for Long-Term Investors

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9809545 Campbell The choice of an optimal portfolio of assets is a classic problem in financial economics. In a single-period setting the problem is well understood, and analytical solutions for optimal portfolio weights are available in important special cases. When mean-variance analysis is appropriate, for example, optimal portfolio weights are known functions of the first and second moments of asset returns. In a multi-period setting the problem is far less tractable. Explicit solutions for portfolio weights are available in the special cases where a long-term investor has no labor income and either has log utility or faces constant investment opportunities; but these cases are tractable precisely because they reduce to the familiar single-period problem. The seminal work of Samuelson and Merton in the late 1960's showed that in more general cases portfolio choice is influenced by long-term investors' desire to hedge against random shocks to labor income and investment opportunities, but it has been very hard to go beyond this general insight to find explicit solutions for portfolio weights as functions of state variables. This gap in the literature is particularly unfortunate because it is clear that the tractable special cases do not adequately describe reality. Labor income is more important than financial income for most investors who are not yet retired. The assumption that investors have log utility is inconsistent with the large rewards for bearing risk that are observed in equity and bond markets. The assumption that investment opportunities are constant is inconsistent with a substantial body of evidence that real interest rates and risk premia move over time and are related to the state of the economy. A number of important policy questions can only be answered if one has a solution to the long-run portfolio and consumption choice problem. For example, the recent issue of indexed bonds by the US Treasury makes available for the first time a long-term investment vehicle that is riskless in real terms. How does this affect the welfare of conservative long-term investors? The Secretary of the Treasury has argued that the availability of indexed bonds should increase savings. For what preference parameters is this true? How large is the effect? There is growing momentum for reform of the Social Security system. Many privatized systems involve investing retirement savings in risky assets which offer a higher average rate of return. Under what conditions does this improve the welfare of system participants? This project aims to increase our understanding of long-run portfolio choice by deriving approximate analytical solutions to several variants of the intertemporal portfolio choice problem. Each variant concentrates on a single aspect of the problem: time-varying real interest rates, time-varying risk premia, or uninsurable risk in labor income.