Suppose the S&P 500 index is currently 950 and the initial margin is 10%. And th

Question

Suppose the S&P 500 index is currently 950 and the initial margin is 10%. And the maintenance margin is 75% of the initial margin. You wish to enter into 10 S&P 500 futures contracts. Each contract permits delivery of 250 units of the index exactly 3 months from now. 8. Suppose you earn a continuously compounded rate of 6% on your margin balance, your position is marked to market weekly. What is your margin balance in 1 week, if the future price drop to $945? Calculate the amount of this margin call. If the future price decreases, what's the effect to your total profit compared to forward contract with forward price drop? a. b. c. d. If the future price at week 2 rise to 947, what's your margin balance? (You need week 1's balance to do this question)

Explanation / Answer

a. The notional value of position after price drop is $945 x 10 x 250 = $2,362,500. The initial margin is $2,362,500 x 10% = $236,250. Therefore, balance after 1 week is calculated as $236,250 x e6% x 1/52 = $236,522.75

b. Let the amount of margin call be M. The required maintenance margin is $950 x 7.5% x 250 x10, must be greater than or equal to 236,522.75 - ($950-M) x 250 x10, which is the amount in the margin account after marking the loss to the market. We calculate the margin call price:

$950 x 7.5% x 250 x10 = 236,522.75 - ($950 - M) x 250 x 10

Or, 2,500(950-M) = 236,522.75 - 178,125

Or, 950 - M = 58,397.75/2,500

Or, M = $926.64

Therefore, amount of margin call = ($950 - 926.64) x 250 x 10

= $58,400

d. The margin balance in week 2 is calculated as:

The notional value of position after price rise in week 2 is $945 x 10 x 250 + ($947-$945) x 10 x 250 = $2,367,500. The initial margin is $2,367,500 x 10% = $236,750. Therefore, balance in week 2 is calculated as $236,750 x e6% x 1/51

= $237,028.69

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