CFA Practice Question

Today is January 1, 20X1. A Treasury bond with 6 years to maturity and six-monthly coupons of \$20 (payable on January 1 and July 1) has a yield of 3.8%. The six-month spot rate is 3.1%, the 12 month spot rate is 3.4%, and the 18 month spot rate is 3.57%. Suppose you have entered into the long side of the F(0,18 mo) forward contract for this bond (18 mo means settlement on July 1, 20X2). On July 1, 20X1 the yield on the bond rises to 3.9%, the six-month spot rate is 3.4%, and the 12 month spot rate is 3.6%. Calculate the value of the forward contract on July 1, 20X1 that you had entered into six months earlier.
A. -3.67
B. -3.54
C. -3.42
Explanation: First find the forward price. Find the PV of the next three dividends = \$57.9978. Then subtract this PV from the bond price today = \$1,010.64 - \$58.00 = \$952.64. Finally multiply last number by (1+r)^3 to get the forward price = \$952.64 * (1+0.01785)^3 = \$1,004.57

Similarly calculate the forward price on July 1, 20X1 to be \$1,001.03. Now change in forward price = \$1,001.03 - \$1,004.57 = -\$3.54. This needs to be discounted by 2 six month periods as settlement is on July 1, 20X2, whereas we need value on July 1, 20X2. Discounting gives = -\$3.54 / (1+0.018)^2 = -\$3.41