Consider a futures contract on a pure discount bond. A pure discount bond provides its holder with a single payment upon maturity.

In particular, if the 120-day pure discount bond costs $95 and the interest cost associated with financing a $95 loan for 30 days is $1, then the total cost associated with the buy-and-hold strategy is $96.

The actual return associated with a 120-day pure discount bond 30 days from now, however, is uncertain: The price may turn out to be $96, but it could also be $94 or $98.

Note that the rate we refer to is the rate of return associated with a 90-day pure discount bond that pays $100 at maturity.

The value of the pure discount bond [p.sub.0](t) satisfies [p.sub.0](t) = [(1 + r).sup.-1][p.sub.0](t + 1), for t = 0, 1 .

Any bond with a large final payment is partly a pure discount bond with a significant portion of its return coming in the form of capital gains or losses over time.

where [v.sub.t] is the value of currency (the reciprocal of the price level, measured in goods per dollar), and [[Rho].sub.jt] is the yield to maturity on a j-period pure discount bond.(7) Equation 2 tells how to convert the yield to maturity [[Rho].sub.jt] on a j-period nominal pure discount bond into the real price of a promise, sold at time t, to one dollar at time t + j.

Consider an obligation that can be expressed as a T-year pure discount bond. At time zero, the random present value of one unit payable at time T is

In the case of a T-year pure discount bond and random force of interest {[y.sub.s]},

The Appendix provides the recursive calculations relating [V.sub.1] to [V.sub.0], which generalize the T-year pure discount bond case described in the introduction.

I consider debt in the form of

pure discount bonds with stochastic maturity.