Suppose the S&P 500 index is currently 950 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? 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?

$930.89

Explanation:

The Notional value of position = Price of S&P-500 index future x Contract multiplier x no. of contracts

= 950x250x10

=$2,375,000

Margin = Total nominal value of position x Initial margin

=2375,000x10%

=$237,500

b) Maintenance margin = Initial margin x Maintenance margin

=237500 x 80%

=$190,000

Margin call will be receive when value of the Initial margin falls below maintenance margin

Thus 237500e^0.06/52 + (St -950) x250 x10 <190,000

From here St = price at which margin call will be made

=237500e^0.0011538 + (St -950) x 2500 <190,000

=237500(1.0011538) + (St -950) x 2500 <190,000

=237774.04 + (2500St - 2375000) < 190,000

=2500St - 2137226 <190,000

= 2500St <2327226

St < 930.89

Thus price below $930.89 will be called maintenance margin.

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