Question

Suppose the future price is 1200 and you wish to acquire a $10 million position in the S&P 500 index.

a) Find the notional value of one contract (amount you are agreeing to pay at expiration per futures contract)

b) Suppose you go long $10 million of the index: How many futures contracts would you enter?

c) Suppose there is 20% margin, If the S&P 500 future drops by 10, how much do you lose on your futures position?

d) Over two weeks, the future price drops 100 points, on a market-to-market basis, how much have you lost?

e)You have the choice of either paying this loss directly, or allowing it to be taken out of the margin balance. You choose to take it out from your margin. If the continuously compounded interest is 10%, Find your margin balance after two weeks.

Answer 1

1. THE NOTIONAL VALUE OF ONE CONTRACT :

ONE CONTRACT IS OF =$250 X FUTURE PRICE = $250 X1200 = $300,000

2. WE HAVE $10 MILLION

SO NO OF FUTURE CONTRACTS POSSIBLE = $10,000,000/ $300,000 = 33.33

SO WE WILL HAVE 33 FUTURE CONTRACTS

2. THE MARGIN AMOUNT = 20% X 33 X $250 X 1200 = $1,980,000

NOW IF S&P 500 FUTURE DROPS BY 10,

LOSS IS = (33 X $250 X 1200) - ( 33 X $250 X 1190) = $82,500

3. OVER THE TWO WEEKS, THE FUTURE PRICE DROPS 100 POINTS, ON A MARKET TO MARKET BASIS,

LOSS IS = (33 X $250 X 1200) - ( 33 X $250 X 1100) = $825,000

4. OVER 2 WEEKS, FUTURE DROP BY 100, SO PER DAY LOSS OF 10 POINTS

SO PER DAY LOSS OF $82500

INTEREST ON MARGIN = (1980,000 X (e^rt - 1) 1980,000 ( e^0.10(10/365)- 1)

= 1980,000 (1.0027435 - 1) =$5432.13

SO MARGIN BALANCE AFTER 2 WEEKS = 1980,000 + 5432.13 - 825000 = $1160432.13

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