LONG-TERM BONDS: Conclusion 2

Our constrained solution enables us to study the welfare effects of bond indexation in a realistic framework. When portfolio constraints are in place, and both nominal and indexed bonds are available to investors, more conservative investors hold in their portfolios relatively more indexed bonds than nominal bonds. These investors benefit substantially from the consumption insurance provided by long-term indexed bonds.

We have also studied the demand for bonds when equities are available as an alternative investment. We find that the ratio of bonds to stocks in the optimal portfolio increases with risk aversion, very much in line with popular investment advice but contrary to the mutual fund theorem of static portfolio analysis. However the demand for long-term bonds is only large when these bonds are indexed, or when inflation uncertainty is low as it has been in the Volcker-Greenspan monetary policy regime since 1983.

Our approach can be extended in several ways. We can explore alternative term-structure models, adding factors or allowing for changing interest-rate volatility A particularly tractable possibility is a discrete-time version of the Cox, Ingersoll, and Ross (1985) model, in which interest-rate volatility rises with the level of the interest rate. Since term premia and bond return variances move in proportion to one another, this model delivers constant portfolio allocations.
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We can consider the effect of investors’ horizons more explicitly by solving a finite-horizon version of our model, or by varying the time discount factor 8. In a model with a constant probability of death each period, an investor with a high death probability has a low 8. Our model predicts that this investor has a high optimal consumption-wealth ratio, a low value for the log-linearization parameter p, and an optimal portfolio that is close to the optimal portfolio for a myopic single-period investor.

We can allow for multiple consumption goods, and consider assets that are indexed to the price of one of these goods. A house, for example, can be regarded as an asset that delivers a constant flow of housing services, in the same way that an indexed bond delivers a constant flow of consumption. This perspective might explain why conservative investors are willing to own houses despite the short-run variability of house prices (Flavin and Yamashita 1998).

Our analysis also has interesting implications for the design of pension plans and annuities. Our results suggest that conservative investors should favor indexed defined-benefit plans, while more risk-tolerant investors may be willing to accept some inflation or equity risk in their retirement income in exchange for higher average payments.

Our ultimate goal is to build a more fully realistic model of portfolio choice by combining the results in several of our recent papers. This paper explores the effects of interest-rate risk on long-term portfolio choice, while Campbell and Viceira (1999) studies time-variation in the equity premium, and Viceira (1997) considers uninsur-able risk in labor income. A complete model accounting for all these effects offers the exciting prospect that financial economists will at last be able to offer realistic but scientifically grounded investment advice.