The current annual compounded risk-free rate is 0.30%. Current Data for Futures and Underlying Bond: Futures Contract: Quoted futures price 125.00 Conversion factor 0.90 Time remaining to contract expiration 3 Months Accrued interest over life of futures contract 0 Underlying Bond: Quoted bond price 112.00 Accrued interest since last coupon payment 0.08 Accrued interest at futures contract expiration 0.20
Based on Exhibit 2 and assuming annual compounding, the arbitrage profit on the bond futures contract is closest to: A 0.4158. B 0.5356. C 0.6195. Answer: The no-arbitrage futures price is equal to the following: F0(T) = FV0,T(T)[B0(T + Y) + AI0 – PVCI0,T] F0(T) = (1 + 0.003)0.25(112.00 + 0.08 – 0) F0(T) = (1 + 0.003)0.25(112.08) = 112.1640 The adjusted price of the futures contract is equal to the conversion factor multiplied by the quoted futures price: F0(T) = CF(T)QF0(T) F0(T) = (0.90)(125) = 112.50 Adding the accrued interest of 0.20 in three months (futures contract expiration) to the adjusted price of the futures contract gives a total price of 112.70. This difference means that the futures contract is overpriced by 112.70 – 112.1640 = 0.5360. The available arbitrage profit is the present value of this difference: 0.5360/(1.003)0.25 = 0.5356.
To find the no-arbitrage futures price, why is the accrued interest at futures contract expiration of 0.20 not being subtracted in the formula? Why is it being added to the adjusted price?
Schweser formula for FP = [(Full price - PVC)*(1+rf)T] - Accrued Int at maturity