Lecture207 - Lecture 7 The Term Structure of Interest Rates...

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Lecture 7 The Term Structure of Interest Rates Continued. I. Overview A) Estimating implied forward rates from current rates B) Using implied forward rates to hedge future debt assets and obligations C) Trading strategies II. Estimating implied forward rates from current rates A) Given spot rates z 1 , z 2 , … z T , we can estimate implied forward rates. Let j f t denote the t year spot rate j years from now. Given z j and z t+j we can estimate the implied t year spot rate j years from now, j f t . Recall the implied forward rate j f t is the future spot rate that will make an investor indifferent between investing in a t+j year zero coupon bond or investing in a j year zero coupon bond and then re-investing the money in a t-year zero coupon bond j years from now. (1+z t+j ) t+j = (1+z j ) j * (1+ j f t ) t or j f t = [(1+z j ) -j *(1+z t+j ) t+j ] 1/t - 1. Example: The zero-coupon yield curve and implied forward yield curves can be found in the following table
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Years to maturity Spot rates 10/13/00 Implied forward rates 10/13/01 Implied forward rates 10/13/02 Implied forward rates 10/13/05 Implied forward rates 10/13/15 1-year 5.949% 5.6252% 6.6805% 2-year 5.787% 6.1516% 6.436% 3-year 6.084% 6.1651% 6.5464% 4-year 6.111% 6.3154% 5-year 6.242% 6.4701% 4.542% 10-year 6.356% 6.5587% 4.9147% 15-year 6.453% 5.8822% 4.8769% 20-year 5.972% 5.7335% 25-year 5.835% 5.5464% 30-year 5.662% These implied forward rates are poor predictors of actual future rates. The implied forward rates can be used to hedge future interest rate assets and liabilities. II. Using Forward Rates to Hedge Against Future Interest Rate Changes A) Forward rates can be thought of as “break even” rates on interest rate hedges. Example: Suppose you run a bank that makes long-term ARM loans based on the yield on 15-year bonds and borrows money in the medium-term portion of the yield curve by issuing 5-year CDs to your customers. The yield on your ARM loans is equal to the yield on 15-year gov’t bonds plus a fixed premium. Your CD’s pay a yield slightly above the yield on a 5- year gov’t bond. Thus your bank makes profits when the yield curve is upward sloping in the 5- 15 year range. If the yield curve inverts your profits will be hurt. Thus, you have an incentive to hedge in such a way that you will make money if the yield curve inverts. The implied forward rates are the rates at which dynamic hedging strategies break even. To hedge against an inversion 5 years from now in the 5-15 year range of the
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Lecture207 - Lecture 7 The Term Structure of Interest Rates...

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