Question

A fund manager expects to receive a cash inflow of R50 000 000 in three months. She 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 1.15 and the bond a modified duration of 6.25. A share index futures contract with a beta of 0.90 is priced at R300 000 and a bond futures contract with a modified duration of 7.50 is priced at R105 000.

Calculate the number of futures contracts required for the desired synthetic position in bonds.

Number of bond futures:

Answer 1

Solution

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 * 1.15) / (R300,000 * 0.90) = 127.78. As fractional futures cannot be bought, this is rounded off to 128.  

Number of share futures to buy = 129

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 * 6.25) / (R200,000 * 7.5) = 83.333

Number of bond futures to buy = 83