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.

Indicate whether the fund manager should sell (short) or buy (long) these bond futures.

the above number of bond futures.

Answer 1

Number of share index futures = R30,000,000*Beta of share/(Price per future contract*Index beta) = R30,000,000*1.15/(R300,000*0.9) = R34,500,000/R270,000 = 127.78 = 128 contracts

Number of bond futures contract = R20,000,000*Modified durattion of bond/(price per bond future*modified duration of bond future) = R20,000,000*6.25/(R105,000*7.5) = 125,000,000/787,500 = 158.73 = 159 contracts

The fund manager is going to receive R50million after 3months, hence pay that 50million that time through future contruct, so take buy (Long) position today in both the share & bond futures.