The annual coupon rate on a 1-year treasury bond is 5.5%.The coupon on a 2-year treasury bond is 5.8%.What is the implied YTM on a hypothetical 2-year zero coupon treasury bond?

Question

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The implied yield to maturity (YTM) on a 2-year zero coupon bond can be calculated using the bootstrapping method, which involves using the yields of shorter-term bonds to derive the yield of a longer-term bond. Given the annual coupon rates and assuming a face value of $100 for simplicity, the calculation would involve solving for the YTM that equates the present value of the bond's cash flows to its price. Since the bond is a zero-coupon bond, its cash flows consist only of the face value at maturity. The calculation involves finding the rate that equalizes the present value of the $100 to be received in two years with the current prices of the 1-year and 2-year coupon bonds, taking into account the given coupon rates. The correct answer, 5.81%, reflects the compounded effect of the given yields over the two years, indicating a slightly higher yield expectation for the zero-coupon bond compared to the coupon bonds, which is typical due to the zero-coupon bond's higher interest rate risk and delayed cash flow.

The Annual Coupon Rate on a 1-Year Treasury Bond Is