You short-sell 400 shares of a stock for one year – i.e., you borrow and sell th

Question

You short-sell 400 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 72.25 and 74.50, respectively. At time t = 1, the ask and bid prices of the stock per share are 71.75 and 68.25, respectively. The short-seller must put up an additional 3,000 of collateral. At time t = 0.50, the stock paid a dividend of 1.50 per share. Let the effective market annual interest rate be 7%, and the interest rate at which short-sale proceeds and collateral are credited is 4%. Determine the profit or loss of the short-seller during the year.

Explanation / Answer

At time t=0, you can borrow stock and sell it at a bid price of $74.50

and at t=0, you have to buy back stock at ask price of $71.75

So capital gain from the stock = 74.50 - 71.75 = $2.75

Total capital gain = 400 * 2.75 = $1100

A dividend of $1.5 is paid at t=0.5, so you get a return on this discount for 6 months at a interest rate of 4%

= 1.5 *(1+ 4% / 2) = 1.53

Total Dividend returns = 1.53 * 400 = 612

Collateral is also credited at 4%, so total return on collateral = 3000 * (4%) = 120

So total return = 1100 + 612 + 120 = 1832

If you have invested the total money in the market, you got a return on investment at 7%

Total investment made = 72.25 * 400 + 3000 = 31900

Return = 31900 * 7% = 2233

Since the return on investment is higher investor has made a loss on his investment

A loss of 2233 - 1832 = $401

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