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Bonds A and B have 3-year maturity. Bond A has coupon rate 2% and trades at $985,76. Bond B has coupon rate 4% and trades at $1,042.92. A zero-coupon bond with 1-year maturity trades at 977.52. All bonds have a face value of $1,000.
(a) Compute the one-year spot rate. Compute the two- and three-year rates under the assumption that they are equal.
(b) Suppose that one year from today (just after bonds A and B pay the first coupon payments) the term structure becomes flat at 2.45%. Compute the one-year return of an investment in each of Bonds A and B. That is, the investor buys a bond today, and sells it one year from today just after bonds A and B pay the first coupon payments. Compare the two returns (return of investing in bond A to the return of investing in bond B) and explain the intuition behind the comparison.
(c) Suppose that the investor holds Bonds A and B until maturity, investing the coupons at the relevant spot rates. Suppose that one year from today (just after bonds A and B pay the first coupon payments) the term structure becomes flat at 2.45%. Suppose also that the term structure remains flat at 2.45% until the bonds mature. Compute the annualized three-year return of the investment in each of the two bonds. Compare the two returns and explain the intuition behind the comparison.
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