Suppose the S&P-500 index futures price is currently 950 (with a contract multip

Question

Suppose the S&P-500 index futures price is currently 950 (with a contract multiplier of $250) (a) What is the notional value of your position? What is the margin? Answer: notional (b) Suppose you earn a continuously compounded rate of 6% on your margin balance, your and the initial margin is 10%. You wish to enter into 10 S&P-500 futures contracts. value $2,375,000, margin $237,500 position is marked to market weekly, and the maintenance margin is 80% of the initial margin. What is the greatest S&P-500 index futures price 1 week from today at which you will receive a margin call? Answer: S930.89 Hint: The maintenance margin is 190,000. In order to receive a margin call, we need 237,500e 0·06/52 + (ST-950) × 250 × 10

Explanation / Answer

a)) Notional value of my position = Future price * contract size*number of contracts

= 950 * 250*10

= 237500

Since initial margin i need to deposite the 10% of my portfolio value, hence it would be 10% of 237500

= 23750

b)) Maintenance margin = 80% of my position

= 80% of 237500

= 190000

Since i will be earning 6% annually on my margin balance hence after a week my position will be of

= 23750 * e^(0.06/52)

Suppose the spot price after a week is St, hence my position at that time will be of

= St*250*10

for me to get a margin call my overall position should be lesser than maintenance margin.

hence, 23750 * e^(0.06/52)+(St*250*10)-(950 * 250*10)<190000

=> St <930.89

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