1 term structure

# 1 term structure - What Practitioners Need to Know . . . ....

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What Practitioners Need to Know . . . . . About the Term Structure of Interest Rates Mark Kritzman Windham Capital Management This column addresses the term structure of interest rates. I begin by reviewing the various ways in which the term structure is mea- sured. Then I present the major hypotheses that purport to ex- plain the relationship between in- terest rates and term to maturity. Finally, I discuss a simple tech- nique for estimating the term structure. What is the Term Structure of Interest Rates? The term structure of interest rates, sometimes referred to as the yield curve, isolates the differ- ences in interest rates that corre- spond solely to differences in term to maturity, As a first approx- imation, we can measure the term structure by measuring the rela- tionship between the yields to maturity on government debt in- struments and their terms to ma- turity. By focusing on government debt instruments, we control for differences in yield that might arise from credit risk. The yield to maturity of a bond equals the internal rate of return that discounts its cash flows, in- cluding the coupon payments and the repayment of principal, back to the bond s current price. This relationship is described by Equa- tion (1): Eq. 1 P = y) + p = current price, Ci, C2, Cn = coupon pay- ments in periods 1 through n. F = face value, y = yield to maturity' and n = number of dis- counting peri- ods. The yield to maturity does not provide a particularly satisfying yardstick for measuring the term structure of interest rates, for two reasons. First of all, it is an unre- alistic measure of a bond's yield because it assumes that all of a bond's cash flows are reinvested at the same rate. This assumption implies that a one-year instru- ment nine years hence will have the same yield as a 10-year bond today. Obviously, there is no rea- son to expect interest rates to evolve according to this assump- tion. Second, the yield to maturity is deficient because it varies as a function of a bond's coupon rate. If a bond's coupon rate is below its yield to maturity, it will sell at a discount to its face value. Part of its return will thus arise from a capital gain as it gravitates to its face value. Because capital gains receive favorable tax treatment relative to income, bonds that de- rive their return from income only must offer a higher yield to maturity than discount bonds in order to compete on an after-tax basis. Consequently, bonds with the same term to maturity will have yields to maturity that differ according to the fraction of their return that arises from income versus price change. structure of interest rates from the yields on pure discount bonds. These bonds do not pay coupons. Instead, they are ini- tially offered at a discount to their face value, so that their yield is equal to the annualized return resulting from their conversion to face value. The yield on a pure discount bond is referred to as the spot rate of interest. We

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## This note was uploaded on 08/13/2010 for the course FINS 2624 R taught by Professor Yippie during the Three '10 term at University of New South Wales.

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1 term structure - What Practitioners Need to Know . . . ....

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