Question

A stock has a bid price of £80.45 and an ask price of £80.55. Suppose you short
sell 400 shares of this stock, and then cover the position 6 months later, when the bid and ask
prices are £78.15 and £78.25. Assume you pay 0.3% brokerage fee on each transaction. Also,
assume that you invest the short sale proceeds for the 6 months at 3% per annum interest rate
with semi-annual compounding. What is your profit?

Answer 1

When you feel the price of a stock is likely to decline, you can make money by shorting the stock. To short, you will have to sell first and buy later.

We can sell the shares at the bid price so sell at £ 80.45

Net reciepts will be

= Sale Value - brokerage paid

= £ 80.45 * 400 shares - (£ 80.45 * 400)*0.3%

= £ 32180 - (£ 32180 * 0.3%)

= £ 32180 - £ 96.54

= £ 32083.46

Deposit  net sale proceeds £ 32083.46 for 6 months at 3% per annum compounding semi annually.

Interest earned on deposit = £ 32083.46 * 3%/2

= £ 481.25

Total amount realized = deposit amount + Interest earned

= £ 32083.46 + £ 481.25

= £ 32564.71

After six month we have square off our position by buy the shares at the previailing prices

We can buy the shares at the ask price so buy at £ 78.25

Total amount to be paid for the transacton

= purchase price + brokerage

= £ 78.25 * 400 shares + ( £ 78.25 * 400) * 0.3%

= £ 31300 + (£ 31300 * 0.3%)

= £ 31300 + £ 93.9

= £ 31393.9

Profit = Total amount realized - Purchase price for the shares

= £ 32564.71 -  £ 31393.9

= £ 1170.81