Questions 1:

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+r _{f})^{T}] - Accrued Int at maturity**