Question

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.

Answer 1

number of share index futures contracts = [(Target beta - portfolio beta)/futures beta]*portfolio value/futures value

portfolio beta is zero as presently portfolio of shares doesn't exist.

number of share index futures contracts = [(1.05 - 0)/0.80]*R30,000,000/R300,000 = 1.3125*100 = 131.25 or 131 contracts

Manager would have to Long or buy 131 share index futures contracts in order to synthetically take the desired position in the shares.

number of bond futures contracts = [(Target modified duration - portfolio modified duration)/futures modified duration]*portfolio value/futures value

portfolio modified duration is zero as presently portfolio of bonds doesn't exist.

number of bond futures contracts = [(8.25 - 0)/7.50]*R20,000,000/R200,000 = 1.1*100 = 110 contracts

Manager would have to Long or buy 110 bond futures contracts in order to synthetically take the desired position in the bonds.