Question

You short sell 1000 shares of Internet Dreams. The initial margin requirement is 50%. A year later, the price has risen up from $40 to $50 and the stock has paid a dividend of $3.  

a) What is the remaining margin on the account?

b) If the maintenance margin requirement is 30%, will you receive a margin call?

c) What is the rate of return on this investment?

Answer 1

What is the remaining margin in the account?

P₀ = $ 40; P₁ = 500; N = 1,000; Dividend per share , D = 3

Initial margin required = 50% x N x P₀ = 50% x 1,000 x 40= $ 20,000

Remaining margin = Initial margin + Payoff from the short position

Payoff from the short position = (P₀ - P₁ - D) x N = (40 - 50- 3)x 1,000 = - $ 13,000

Hence, Remaining margin = $ 20000 - $ 13,000 = $ 7000

b.

Short margin = Remaining margin / Value of short shares today = $ 7000 / (N x P₁) = 7000 / (1,000 x 50) = 14%

Short margin = 14.00% < margin requirement of 30%, so there will be a margin call.

c.   What is the rate of return on the investment?

Rate of return = Payoff from short position / Initial margin = -13000 / 20000 = - 65.00%