Question

Suppose the S&P 500 index futures price is currently 1000. One contract of S&P 500 index futures has a size of $250× S&P 500 index. You wish to purchase four contracts of futures on margin. Suppose that the initial margin is 10%. Your position is marked to market daily. The interest earnings from the margin account can be ignored.

(A) What is the notional value of your position?

(B) What is the dollar amount of initial margin?

(C) What is your actual return if the index price increases to 1010 one day from now? (Suppose you deposit the initial margin into your margin account as an initial investment.)

(D)If the maintenance margin is 80% of initial margin, what is the greatest S&P 500 index futures price one day from now at which you will receive a margin call?

Answer 1

(A) The notional value of your position = Number of contracts x Multiplier x Price of one index future = 4 x 250 x 1,000 = $ 1,000,000

(B) the dollar amount of initial margin = Initial margin xThe notional value of your position = 10% x 1,000,000 = $ 100,000

(C) Mark to market gain = Number of contracts x Multiplier x (P1 - P0) = 4 x 250 x (1,010 - 1,000) = $ 10,000

(D) If P is that price then,

Initial margin + (P - 1,000) x N x Multiplier ≤ Maintenance Margin = 80% x Initial margin

Or, 100,000 + (P - 1,000) x 4 x 250 ≤ 80% x 100,000

hence, P ≤ 1000 - 20% x 100,000 / (4 x 250) = 980

Hence, the greatest S&P 500 index futures price one day from now at which you will receive a margin call = 980