Question

An investor enters into 5 S&P 500 long futures contracts, each of which is currently trading at 2,150. You are given:

• Each contract has a notional value equal to 250 times the futures price.
• The initial margin is 10% of the notional value.
• The maintenance margin is 80% of the initial margin.
• The margin balance earns a continuously compounded risk-free interest rate of 5%.

Suppose the futures price one day later is 2,100 and the investor receives a margin call.

Calculate the amount of funds the investor needs to provide to satisfy the margin call.

1. 8,700

2. 12,500

3. 41,000

4. 62,500

PLEASE PROVIDE THE FULL SOLUTION

1. 76,000

Answer 1

Working Note :1 - Basic information

Current value of S&P 500 = 2150

Notional value per contract of S&P 500 futures = $ 537,500 (250*2150)

No. of contracts entered = 5

Total Notional value of 5 contracts = 2,687,500 (5*537500)

Working Note 2 : Computation of initial margin and maintenance margin

Initial Margin = 10% * Total notional value of contract

= 10% * 2687500 ( W.N.1)

= $ 268,750

Maintenance margin = 80% * initial margin

= 80% * $ 268750

= $ 215,000

Working Note 3 :- Calculation of amount investor need to provide to satify the margin call, when the value of S&P future is 2100 -

Loss when the value of future is 2100 one day later

= (2150-2100)* 250 times* 5 contracts

ie. = 50*250*5

= $ 62500

Balance in Margin account after deducting the loss incurred = 268750 - 62500

= $ 206,250

Since the balance in margin account is less than maintenance margin ($ 215,000) , entire loss of $ 62500 need to deposited to the margin account ($ 268750 - $ 206250). (refer note)

Working note 4 :- Conclusion

Hence the amount of fund investor need to provide to satisfy the margin call is Rs. $ 62,500.

Note :-

1) Initial margin means the margin which is deposited at the inception of the contract

2) Maintenance margin means the margin which should be maintained at all times, and if the margin falls below the maintenance margin , then immediately it need to bring back the margin balance to the inital margin.

3) In future contracts, margin is a deposit made with the broker inorder to open a position. There are no interest charges on future margin because it represents a deposit held with the broker to open a contract. Hence, interest earned on margin balance is irrelevant with respect the question.