Solving Models with External Habit

Habit utility has been the focus of a large and growing body of literature in financial economics. This study investigates ways of accurately and efficiently solving the Campbell and Cochrane (1999) external habit model. Solutions for this model based on a grid of values for the state variable are shown to converge as the grid becomes increasingly fine. Convergence is substantially faster if the price-dividend ratio is computed as a series of ``zero-coupon equity'' claims rather than as the fixed-point of the Euler equation. Fitting the model to the term structure as well as to equity moments (as in Wachter (2005)) also results in faster convergence.

Does the Failure of the Expectations Hypothesis Matter for Long-Term Investors

We consider the consumption and portfolio choice problem of a long-run investor when the term structure is affine and when the investor has access to nominal bonds and a stock portfolio. In the presence of unhedgeable inflation risk, there exist multiple pricing kernels that produce the same bond prices, but a unique pricing kernel equal to the marginal utility of the investor. We apply our method to a three-factor Gaussian model with a time-varying price of risk that captures the failure of the expectations hypothesis seen in the data. We extend this model to account for time-varying expected inflation, and estimate the model with both inflation and term structure data. The estimates imply that the bond portfolio for the long-run investor looks very different from the portfolio of a mean-variance optimizer. In particular, the desire to hedge changes in term premia generates large hedging demands for long-term bonds.

What is the Chance that the Equity Premium Varies over Time? Evidence from Regressions on the Dividend-Price Ratio

We examine the evidence on excess stock return predictability in a Bayesian setting in which the investor faces uncertainty about both the existence and strength of predictability. When we apply our methods to the dividend-price ratio, we find that even investors who are quite skeptical about the existence of predictability sharply modify their views in favor of predictability when confronted by the historical time series of returns and predictor variables. Correctly taking into account the stochastic properties of the regressor has a dramatic impact on inference, particularly over the 2000-2005 period.

Optimal Consumption and Portfolio Allocation under Mean-Reverting Returns: An Exact Solution for Complete Markets

This paper solves, in closed form, the optimal portfolio choice problem for an investor with utility over consumption under mean-reverting re- turns. Previous solutions either require approximations, numerical methods, or the assumption that the investor does not consume over his life time. This paper breaks the impasse by assuming that markets are complete. The solution leads to a new understanding of hedging demand and of the behavior of the approximate log-linear solution. The portfolio allocation takes the form of a weighted average and is shown to be analogous to duration for coupon bonds. Through this analogy, the notion of invest- ment horizon is extended to that of an investor who consumes at multiple points in time

Optimal Consumption and Portfolio Allocation under Mean-Reverting Returns: An Exact Solution for Complete Markets

This paper solves, in closed form, the optimal portfolio choice problem for an investor with utility over consumption under mean-reverting returns. Previous solutions either require approximations, numerical methods, or the assumption that the investor does not consume over his lifetime. This paper breaks the impasse by assuming that markets are complete. The solution leads to a new understanding of hedging demand and the behavior of approximate log-linear solutions. The portfolio allocation takes the form of a weighted average and is shown to be analogous to duration for coupon bonds. Through this analogy, the notion of investment horizon is extended to that of an investor who consumes at multiple points in time

Portfolio and Consumption Decisions Under Mean-Reverting Returns: An Exact Solution for Complete Markets

This paper solves, in closed form, the optimal portfolio choice problem for an investor with utility over consumption under mean-reverting returns. Previous solutions either require approximations, numerical methods, or the assumption that the investor does not consume over his lifetime. This paper breaks the impasse by assuming that markets are complete. The solution leads to a new understanding of hedging demand and of the behavior of the approximate log-linear solution. The portfolio allocation takes the form of a weighted average and is shown to be analogous to duration for coupon bonds. Through this analogy, the notion of investment horizon is extended to that of an investor who consumes at multiple points in time

Solving Models With External Habit

Habit utility has been the focus of a large and growing body of literature in financial economics. This study investigates ways of accurately and efficiently solving the Campbell and Cochrane [1999. Journal of Political Economy 107, 205–251] external habit model. Solutions for this model based on a grid of values for the state variable are shown to converge as the grid becomes increasingly fine. Convergence is substantially faster if the price–dividend ratio is computed as a series of “zero-coupon equity” claims rather than as the fixed point of the Euler equation. Fitting the model to the term structure as well as to equity moments (as in [Wachter, J.A., 2005. A consumption-based model of the term structure of interest rates. Journal of Financial Economics, in press]) also results in faster convergence

Asset Allocation

This review article describes recent literature on asset allocation, covering both static and dynamic models. The article focuses on the bond-stock decision and on the implications of return predictability. In the static setting, investors are assumed to be Bayesian, and the role of various prior beliefs and specifications of the likelihood are explored. In the dynamic setting, recursive utility is assumed, and attention is paid to obtaining analytical results when possible. Results under both full- and limited-information assumptions are discussed

Risk Aversion and Allocation to Long-Term Bonds

As risk aversion approaches infinity, the portfolio of an investor with utility over consumption at time T is shown to converge to the portfolio consisting entirely of a bond maturing at time T. Previous work on bond allocation requires a specific model for equities, the term structure, and the investor\u27s utility function. In contrast, the only substantive assumption required for the analysis in this paper is that markets are complete. The result, which holds regardless of the underlying investment opportunities and the utility function, formalizes the “preferred habitat” intuition of Modigliani and Sutch (Amer. Econom. Rev. 56 (1966) 178)