Derivatives: Valuation and Risk Management

By David A. Dubofsky; Thomas W. Miller Jr. | Go to book overview

CHAPTER 10

Treasury Bill and Eurodollar Futures

This chapter covers the pricing and hedging applications of short-term interest rate futures contracts, with a particular focus on Eurodollar and Treasury bill futures. Chapters 3, 4, and 5 contain important background material concerning forward contracts (FRAs), how they are used to hedge, and how they are priced. Because FRAs are very similar to Eurodollar and T-bill futures, you should review these three chapters before reading this chapter.

Here, we study institutional details of short-term interest rate futures, including unique features concerning their pricing and their use in risk management. In general, arbitrage ensures that forward interest rates computed from spot interest rates equal futures interest rates. Futures contracts are resettled daily, but most market participants agree that this fact has little or no impact on price differences between futures prices and the forward prices. Trading frictions such as transactions costs (bid-ask spreads and commissions) and restrictions on short-selling debt instruments will create a range of futures prices that can exist without any arbitrage opportunities. The additional costs associated with short selling a spot instrument, which is required when one is performing reverse cash-and-carry arbitrage, can be built into any theoretical futures pricing model.

To begin, we will look at the spot market for Treasury bills.


10.1 THE SPOT TREASURY BILL MARKET

A Treasury bill is a pure discount debt instrument sold by the U.S. government. At maturity, the owner of a T-bill receives its face value, which is usually $10,000, although other denominations as high as $1 million are also issued. Maturities as of the issue date are either three months, six months or one year.1 Three-month T-bills are auctioned every Monday (except on holidays and on days of unexpected acts of nature).2 T-bills are usually quoted on a discount yield basis. For example, Figure 10.1 is a reprint of price data on T-bills from The Wall Street Journal. The columns labeled “Bid” and “Asked” are discount yields. The discount yield, DY, is defined as follows:

(10.1)

where F represents the face value, P is the price, and t is the days to maturity.

There are two problems with selecting the discount yield to serve as a rate of return measure. First, a periodic rate of return is computed as (F'P) /P, not (F'P) /F. Second, the discount yield annualizes this expression incorrectly by using a 360-day year, not a 365-day year. Both these conventions cause the discount yield to be smaller than the true rate of return.

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