5. Further, one can use today’s spot rates and Eq. (36.2) to back out implied spot curves for any future date and implied future paths for the spot rate of any maturity. It is important to distinguish the implied spot curve one year forward (f 1,2, f1,3, f1,4, . . .), a special case of Eq. (36.2) where μ 1, from the one-year forward rate curve (f 1,2, f2,3, f3,4, . . .). Today’s spot curve can be subtracted from the former curve to derive the yield changes implied by the forwards. (This terminology is somewhat misleading because these “implied” forward curves/paths do not reflect only the market’s expectations of future rates.)

6. Note that all one-year forward rates actually have a one-year maturity even though in the x axis of Exhibit 36–1 each forward rate’s maturity refers to the final maturity. For example, the one-year forward rate between n>>1 and n (fn−1,n) matures n years from today.

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