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**

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