LONG-TERM BONDS: The Demand for Indexed Bonds

The increase in real-interest-rate persistence increases the risk premia on indexed and nominal bonds, but it also greatly increases the volatility of indexed bond returns so the Sharpe ratio for indexed bonds is lower at 0.15. In the remainder of the paper we present portfolio choice results based on our full-sample estimates for the period 1952-96, but we also discuss results for the 1983-96 period where they are importantly different.

The Demand for Indexed Bonds

Assumptions on investor preferences

The investor is infinitely-lived, lives off her financial wealth and faces the investment environment described above. We assume that her preferences are described by the recursive utility proposed by Epstein and Zin (1989) and Weil (1989):
w6801-7

w6801-8
Two special cases are worth noting. First, as ф approaches one, the exponents in (17) increase without limit. The value function has a finite limit, however, because the ratio Ct/Wt approaches (1 — <5) as shown by Giovannini and Weil (1989). Second, as ф approaches zero, Vt approaches Ct/Wt, A consumer who is extremely reluctant to substitute intertemp orally consumes the annuity value of wealth each period, and this consumer’s utility per dollar is the annuity value of the dollar.

Loglinear approximation of the model

At this point, to simplify the analysis we assume that there are only two bonds available to the investor, a one-period indexed bond and an n-period indexed bond. Given the one-factor structure of our model for indexed bonds, this is equivalent to providing the investor with a complete indexed term structure. Under this assumption, Rp,t+\ is equal to
w6801-9
where an>t is the fraction of the investor’s savings allocated to the n-period indexed bond at time t.