Question

Let's assume that you desire to short-sell 1,000 shares of ABC stock, which has a bid price of $14.74 and an ask price of $14.96. You cover the short position 6 months later when the bid price is $13.02 and the ask price is $13.20.  

(a) Taking into account only the bid and ask prices (ignoring commissions and interest), what profit did you earn?

(b) Suppose that there is a 0.4% commission to engage in the short-sale (this is the commission to sell the stock) and a 0.4% commission to close the short-sale (this is the commission to buy the stock back). How do these commissions change the profit in the previous answer?

(c) Suppose the effective 6-month interest rate is 2% and that you are paid nothing on the short-sale proceeds. How much interest do you lose during the 6 months in which you have the short position? Consider both cases, without commissions or with commissions.

Answer 1

a. Taking into account only the bid and ask prices (ignoring commissions and interest), what profit did you earn?

(1000 × 14.74) - (1000 × 13.2) = 1540

b. Suppose that there is a 0.4% commission to engage in the short-sale (this is the commission to sell the stock) and a 0.4% commission to close the short-sale (this is the commission to buy the stock back). How do these commissions change the profit in the previous answer?

[1000 × 14.74 × (1-.004)] – [1000× 13.2 × (1+.004)]) = 1428.24

c.Suppose the effective 6-month interest rate is 2% and that you are paid nothing on the short-sale proceeds. How much interest do you lose during the 6 months in which you have the short position? Consider both cases, without commissions or with commissions.

=(1000×14.74 × (1-.002)) × (.002) = 29.42104