Question

Question 2

A fund manager expects to receive a cash inflow of R50,000,000 in three months. The manager wishes to use futures contracts to take a R30,000,000 synthetic position in shares and a R20,000,000 in bonds today. The share would have a beta of 1.05 and the bond a modified duration of 8.25. A share index futures contract with a beta of 0.80 is priced at R300,000 and a bond futures contract with a modified duration of 7.50 is priced at R200,000. Calculate the number of share index futures contracts and bond futures contracts that the manager would have to trade in order to synthetically take the desired position in the shares and bonds today. Indicate whether the futures positions are long or short.

Kindly note this is the full question.

Please assist

Answer 1

The manager wishes to invest R30,000,000 in shares and R20,000,000 in bonds. Hence, he would take a long position in the futures.

Number of share futures to buy = (required investment * beta of shares) / (futures contract price * index beta)  

Number of share futures to buy = (R30,000,000 * 1.05) / (R300,000 * 0.80) = 131.25. As fractional futures cannot be bought, this is rounded off to 131.  

Number of share futures to buy = 131

Number of bond futures to buy = (required investment * duration of bonds) / (futures contract price * duration of futures)  

Number of bond futures to buy = (R20,000,000 * 8.25) / (R200,000 * 7.5) = 110.  

Number of bond futures to buy = 110