Essays in consumption and portfolio choice

Abstract

This thesis analyzes optimal consumption and portfolio strategy by considering three different extensions to the classic work by Merton (1971). The first chapter considers consumption and strategic asset allocation when expected returns are predictable for Epstein-Zin preferences. The second chapter focuses on the role of imperfect information in the consumption and portfolio choice problem and presents a tractable solution to the strategic asset allocation problem in incomplete markets. The third chapter considers the role of human capital in consumption and portfolio choice and presents normative evidence of hump-shaped life-cycle investment in risky assets, in line with empirical findings on asset allocation strategies. In Chapter 1 (co-authored with John Campbell, George Chacko, and Luis Viceira) we derive an approximate solution to a continuous-time intertemporal portfolio and consumption choice problem. The problem is the continuous-time equivalent of the discrete-time problem studied by Campbell and Viceira (1999), in which the expected excess return on a risky asset follows an AR(1) process, while the riskless interest rate is constant. We show also how to obtain continuous-time parameters that are consistent with discrete-time econometric estimates. The continuous-time solution is numerically close to that of Campbell and Viceira and has the property that conservative long-term investors have a large positive intertemporal hedging demand for stocks. In Chapter 2, we relax the assumption on preferences made in Chapter 1 and consider how imperfect information about expected excess returns on the risky asset shifts the asset allocation strategy. I present a model of consumption and portfolio choice with imperfect information.

(cont.) I solve analytically the consumption and portfolio choice problem for an investor learning about the current value of time-varying expected returns. When prices are the only observables, the investor optimally estimates the current expected returns using the realized returns. Because of this, the market is observationally complete for an imperfectly informed investor. The observational completeness of the market allows me to find analytical, closed-form solutions to the investor's consumption and portfolio choice problem. I show how learning affects both the covariance and the consumption smoothing component of the hedging portfolio. Applying the model to monthly return data, I show a significant reduction in hedging demands due to imperfect information. In contrast to portfolio choice assuming expected returns are observed, in some cases the reduction implies the agent will optimally hold a negative hedging portfolio. I solve in closed-form for the model implied R2 for the return forecast regression, in other words the predictable fraction of return variance, and discuss the relationship between the reduction in hedging demands and the reduction in the model implied R2 for the return forecast regression. Little work has been done in regards to the role of labor income when investment opportunities are stochastic. Chapter 3 considers the consumption and portfolio choice problem of an investor when interest rates are time-varying and labor income growth might be sensitive to changes in interest rates. We obtain closed-form solutions to the consumption and portfolio choice for an investor with both inelastic and elastic labor supply ...