You expect to receive a cash inflow of $50 million in five months. Today, you wa

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:

Explanation / Answer

PART A: Hedging our position in stocks

amount invested in stocks= $30M

Beta of the stock=0.65

step 1> Hedge value=Beta * amount invested

Hedge value=0.65*30,000,000 = 19,500,000

step 2> Now in order to hedge a long position in stocks we need to take a counter position in futures market. We need to short futures worth $19,500,000

No of stock index futures lots required= 19,500,000/1.01*200,500 = 96.29

Hence, we need to short 96 lots of stock index futures to hedge our long position in stocks.

Hedging our position in bonds

amount invested in bonds= $20M

Modified duration of the bond=10.5

step 1> Hedge value=Modified duration * amount invested

Hedge value=10.5*20,000,000 = 210,000,000

step 2> Now in order to hedge a long position in bonds we need to take a counter position in bond futures market. We need to short futures worth hedge position of $210,000,000

No of bond futures lots required= 210,000,000/8.5*102,300 = 241.50

Hence, we need to short 241 lots of bond futures to hedge our long position in bonds.

PART B: Gain from stock position: 30,000,000*0.0425= $1,275,500

Gain from bond position: 20,000,000*0.025*10.5=$5,250,000

Loss from stock index futures=96*(209,106-200,500)=$826,176

Loss from bond futures=241*(124,039-102,300)=$5,239,099

Net gain=$460,225

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