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 S250) and the initial margin is 10%. You wish to enter into 10 S&P-500 futures contracts. (a) What is the notional value of your position? What is the margin? Answer: notional value $2,375,000, margin $237,500 (b) Suppose you earn a continuously compounded rate of 6% on your margin balance your 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 all a d 237,500e006/5(ST -950) x 250 x 10

Explanation / Answer

a) Notional value = Total value of the underlying asset at spot price

= 950* 250= $2,375,000 , Margin = 10% * 2,375,000 = $237,500

b)Maintaneance margin = 80%* 237,500 = 190,000

Forward Price = S * e(r *t)

S = Spot Price, r= interest rate, t= period

interest rate compounding per weekly= 6%/52

Interest rate earned = 237,500 *e(0.06/52) = 237,774.193

St = Spot Price on the Validation date, S0 = Intial Spot rate

In order to receive a margin call, it should be less than manintaneance margin 190,000

237,774.193 + (St - 950) * 2,500 < 190,000

St <( (190,000 - 237,774.193)/2500 ) + 950

St < 930.89

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