Question

You expect to receive a cash inflow of $50 million in five months. Today, you want to take a long synthetic stock position equal to $30 million with a beta of 0.65 and a long synthetic bond position equal to $20 million with a modified duration of 10.5. A stock index futures contract with a beta of 1.01 is priced at $200,500. A bond futures contract with a modified duration of 8.5 is priced at $102,300. The spot LIBOR for 5-month maturity is 5% today.

A) How many bond futures contracts and stock index futures contracts do you need to trade to achieve your desired synthetic positions in stocks and bonds? Keep in mind that the number of futures contracts should be a whole number, not a fractional number.

B) Five months later when the futures expires, stocks have risen by 4.25% and the bond yield has declined by 2.5%. Stock index futures are priced at $209,106, and bond futures are priced at $124,039. What would be your net gain(loss) from your futures positions?

		NOW		ON EXPIRATION
	S=	$                30,000,000		4.25%
	B=	$                20,000,000		-2.50%
	Beta(target)=	0.65
	Duration(target,modified) =	10.5
	Beta(future)=	1.01
	f(stock)=	$200,500
	Duration(future)=	8.5
	f(bond)=	$                      102,300
A)	Actual # of stock index futures contract
	Actual # of bond futures contract
B)	Net gain from futures
	Net gain from stocks and bonds
	Show your explanation and calculations below:

Answer 1

A)

B)

Value of Stock Index Future Contracts on expiry = 122 x 209106 = 25510932

Value of Bond Future Contracts on expiry = 307 x 124039 = 38079973

Net gain(loss) from Stock Index Future Contracts on expiry = Value of Stock Index Future Contract on expiry - Initial Investment = 25510932 - 30000000 = -4489068

Net gain(loss) from Bond Future Contracts on expiry = Value of Bond Future Contract on expiry - Initial Investment =38079973 - 20000000 = 18079973

PARTICULARS	$
Net Loss from Stock Index Future Contracts	-4489068
Net Gain from Bond Future Contracts	180799730
Net Profit on Futures	176310662

FVOFStocklnderFuturesContracts = S(1 + r)"-3000000(1.276) 38280000