You short-sell 500 shares of a stock for one year – i.e., you borrow and sell th

Question

You short-sell 500 shares of a stock for one year – i.e., you borrow and sell the shares at time t = 0, and you purchase and return the shares at time t = 1. At time t = 0, the ask and bid prices of the stock per share are 75.25 and 73.50, respectively. At time t = 1, the ask and bid prices of the stock per share are 70.75 and 69.25, respectively. The short-seller must put up an additional 5,000 of collateral. At time t = 0.25, the stock paid a dividend of 1.20 per share. Let the effective market annual interest rate be 6%, and the interest rate at which short-sale proceeds and collateral are credited is 2%. Determine the profit or loss of the short-seller during the year.

Explanation / Answer

Amount received from short of stock= 73.5*500=36,750

The above amount after one year=36,750*e^(2%*1)=37,492.40

Collateral amount raised= 5000

Amount of collateral after one year=5000*e^(rt)=5000*e^(2%)*1)

=5000*e^(0.02)=5101

Cost of collateral=5101-5000=101

dividend paid= 1.2*500=600

Value of dividend after 1 year assuming it is deposited and interest received is 6% per annum

=600*e^(0.75*6%)=627.24

Amount has to be paid after one year for shortsell=70.75*500= 35,375

=37,492.4-101+627.24-35,375

=2643.64(gain)

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