LONG-TERM BONDS: Introduction

Long-term bonds have been issued for centuries, and they remain extremely common financial instruments. It is natural to suppose that bonds have been popular because they meet the needs of an investor clientele. Investment advisers and financial journalists, for example, often say that bonds are appropriate for long-term investors who seek a stable income.

Curiously, modern financial economics has little to say about the demand for longterm bonds. In the early postwar period Hicks (1946), following Keynes (1930) and Lutz (1940), argued that investors would naturally prefer to hold short-term bonds and would only hold long-term bonds if compensated by a term premium. Modigliani and Sutch (1966) countered that some investors might have a preference for longterm bonds (a long-term “preferred habitat”), and such investors would require a premium to go short, not a premium to go long. However Modigliani and Sutch were vague about the characteristics of investors that would lead to a long-term preferred habitat. They took it as a given that some investors would desire stable wealth at a long rather than a short horizon there.

Since the 1960’s there has been a vast increase in the sophistication of bond pricing models, but little further progress has been made in understanding the demand for long-term bonds. Recent authors, building on the seminal contributions of Va-sicek (1977) and Cox, Ingersoll, and Ross (1985), have related term premia to the covariances of bond returns with an exogenously specified stochastic discount factor, but have not asked what bond portfolios are optimal for different types of investors.

One reason for this gap in the literature may be that it is extremely hard to characterize optimal portfolio strategies for long-term investors. Samuelson (1969) and Merton (1969, 1971) obtained some explicit results under the assumption that real asset returns are independently and identically distributed over time; but this assumption implies that real interest rates are constant, so in the absence of inflation uncertainty—or with full indexation of bond payments to inflation—bond returns are nonrandom and all bonds are perfect substitutes for cash. Fischer (1975), Bodie, Kane, and McDonald (1985), and Viard (1993) have nonetheless used this assumption to study bond demand.

In Fischer’s model there is one nominal bond with a fixed nominal interest rate, and one indexed bond with a fixed real interest rate. The maturity of these bonds need not be specified, since bonds of all maturities are perfect substitutes for each other. Bo die, Kane, and McDonald use historical data to estimate the variance-covariance matrix of real returns on nominal bonds, assuming that this matrix and mean real bond returns are constant over time. In their model random inflation allows imperfect substitutability among nominal bonds of different maturities, but constant real interest rates imply that long-term and short-term indexed bonds are perfect substitutes. Viard uses the same framework as Bodie, Kane, and McDonald and derives some further analytical results.