Stuck: Arbitrage profit made on futures/forward on bond (derivatives)
I am stuck at this question… for so long.. desperately need help!
Quoted futures price = 125
Conversion factor = 0.90
Time remaining to contract expiration = 3 months
AI over the life of futures contract = 0
Quoted bond price = 112
AI since last coupon payment = 0.08
AI at futures contract expiration = 0.2
Current annual risk-free rate = 0.30%
What is arbitrage profit on the bond futures contract?
In the solution, they recalculate the adjusted price of the futures (125 x 0.9) and then add 0.20. Shouldn’t the 125 already include AI at time T? Anyway the final answer is 0.5356.
I was attempting to convert the quoted bond price to quoted futures price and compared with the given quoted futures price of 125 to find the arbitrage value.
Formula used, F0(T) = [ (Price of Bond + Accrued Interest at time 0) – PVCI] – (Accrued Interest at time T) = 111.88
Therefore, quoted F0(T) = 111.88/0.9 = 124.31
Value of the arbitrage = (125 – 124.31)/ [ 1 + (0.0003) (3/12) ] = 0.68948
I would have thought whether you compare between futures price or quoted futures price, the arbitrage value should be the same. but clearly i am wrong! Masters, teach me!