Exhibit 21.4
Use the Information Below for the Following Problem(S)
A 3-month T-bond futures contract (maturity 20 years, coupon 6%, face $100,000) currently trades at $98,781.25 (implied yield 6.11%). A 3-month T-note futures contract (maturity 10 years, coupon 6%, face $100,000) currently trades at $101,468.80 (implied yield 5.80%). Assume semiannual compounding.
-Refer to Exhibit 21.4.Suppose the yield curve changed so the that the new yield on the T-bond contract rose to 6.5% and the new yield on the T-note contract fell to 5.5%.Calculate the profit on the NOB futures spread.(Assume coupons are paid semiannually)
A) -$5850.92
B) -$6,671.42
C) $6,671.42
D) $5850.92
E) None of the above

Question

Quizplus · Accepted Answer

First calculate the new prices of the T-bond and T-notes contracts using bond valuation formulas with semi-annual compounding.T-bond price = $94,447.89.T-note price = $103,806.81.
NOB profit = (98,781.25 - 94,447.89)+ (103,806.81 - 101,468.80)= $6,671.42
 $$\text { T-Bond Price } = 3000 \left( \frac { 1 - \frac { 1 } { 1.0325 ^ { 40 } } } { .0325 } \right) + \frac { 100000 } { 1.0325 ^ { 40 } } = \$ 94,447.89$$ $$\text { T-Note Price } = 3000 \left( \frac { 1 - \frac { 1 } { 1.0275 ^ { 20 } } } { .0275 } \right) + \frac { 100000 } { 1.0275 ^ { 20 } } = \$ 103,806.81$$

Exhibit 21.4 Use the Information Below for the Following Problem(S)