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1、7Interest Rate Forwards and FuturesSuppose you have the opportunity to spend $1 one year from today to receive $2 two years from today. What is the value of this opportunity? To answer this question, you need toknow the appropriate interest rates for discounting the two cash flows. This comparison i
2、san example of the most basic concept in finance: using interest rates to compute presentvalues. Once we find a present value for one or more assets, we can compare the values ofcash flows from those assets even if the cash inflows and cash outflows occur at different times. In order to perform thes
3、e calculations, we need information about the set of interest rates prevailing between different points in time. We begin the chapter by reviewing basic bond conceptscoupon bonds, yields to maturity, and implied forward rates. Any reader of this book should understand these basic concepts. We then l
4、ook at interest rate forwards and forward rate agreements, which permit hedging interest rate risk. Finally, we look at bond futures and the repo market.7.1 BOND BASICSTable 7.1 presents information about current interest rates for bonds maturing in from 1 to3 years. Identical information is present
5、ed in five different ways in the table.Although the information appears differently across columns, it is possible to take the information in any one column of Table 7.1 and reproduce the other four columns.1 In practice, a wide range of maturities exists at any point in time, but the U.S.government
6、 issues Treasury securities only at specific maturitiestypically 3 months, 6 months, and 1, 2, 5, 10, and 30 years.2Government securities that are issued with less than 1yeartomaturityandthatmakeonlyasinglepayment,atmaturity,arecalledTreasurybills. Notesandbondspaycouponsandareissuedatapriceclosetot
7、heirmaturityvalue(i.e.,they are issued at par). Notes have 10 or fewer years to maturity and bonds have more than 101. Depending upon how you do the computation, you may arrive at numbers slightly different from those in Table 7.1. The reason is that all of the entries except those in column 1 are r
8、ounded in the last digit, and there are multiple ways to compute the number in any given column. Rounding error will therefore generate small differences among computations performed in different ways.2. Treasury securities are issued using an auction. In the past the government also issued bonds wi
9、th maturities of 3 and 7 years. Between 2002 and 2005 the government issued no 30-year bonds.195196Chapter 7. Interest Rate Forwards and FuturesTABLE 7.1Five ways to present equivalent information about default-free interest rates. All rates but those in the last column are effective annual rates.(1
10、)(2)(3)(4)(5) Continuously Years toZero-CouponZero-CouponOne-Year ImpliedParCompounded MaturityBond YieldBond PriceForward RateCouponZero Yield16.00%0.9433966.00000%6.00000%5.82689% 26.500.8816597.002366.484236.29748 37.000.8162988.007056.954856.76586years to maturity. The distinctions between bills
11、, notes, and bonds are not important for ourpurposes;wewillrefertoallthreeasbonds.Treasuryinflationprotectedsecuritiesarebondsfor which payments are adjusted for inflation. Finally, the most recently issued government bonds are called on-the-run; other bonds are called off-the-run. These terms are u
12、sed frequently in talking about government bonds since on-the-run bonds generally have lower yields and greater trading volume than off-the-run bonds. Appendix 7.A discusses some of the conventions used in bond price and yield quotations. In addition to government bonds there are also STRIPS. A STRI
13、PSSeparate Trad- ingofRegisteredInterestandPrincipalofSecuritiesisaclaimtoasingleinterestpayment or the principal portion of a government bond. These claims trade separately from the bond. STRIPS are zero-coupon bonds since they make only a single payment at maturity. “STRIPS” should not be confused
14、 with the forward strip, which is the set of forward prices available at a point in time. We need a way to represent bond prices and interest rates. Interest rate notation is, unfortunatelyandinevitably, cumbersome, becauseforanyratewemustkeeptrackofthree dates: the date on which the rate is quoted,
15、 and the period of time (this has beginning and ending dates) over which the rate prevails. We will let rt(t1, t2) represent the interest rate fromtimet1totimet2, prevailingondatet.Iftheinterestrateiscurrenti.e., ift = t1and if there is no risk of confusion, we will drop the subscript.Zero-Coupon Bo
16、ndsWebeginbyshowingthatthezero-couponbondyieldandzero-couponbondprice,columns (1) and (2) in Table 7.1, provide the same information. A zero-coupon bond is a bond that makes only a single payment at its maturity date. Our notation for zero-coupon bond prices will mimic that for interest rates. The price of a bond quoted at time t0, with the bond to be purchased at t1and maturing at t2, is Pt0(t1, t2). As with interest rates, we will drop the subscript when t0= t1. The 1-year zero-coupon bo
