Question

You decide to sell short 100 shares of Charlotte Horse Farms when it is selling at its yearly high of $53. Your broker tells you that your margin requirement is 55 percent and that the commission on the purchase is $175. While you are short the stock, Charlotte pays a $2.40 per share dividend. At the end of one year, you buy 100 shares of Charlotte at $42 to close out your position and are charged a commission of $165 and 13 percent interest on the money borrowed. What is your rate of return on the investment? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

To find the rate of return when selling short, we calculate the difference between the initial proceeds and the costs of covering the short, including commissions, dividends, and interest on the borrowed amount. In this scenario, the investor experiences a -3.09% return.

Step-by-step explanation:

To calculate the rate of return on the investment of selling short, multiple factors including the selling price, buying price, commissions, dividends, and interest on borrowed money need to be considered. Initially, the investor sells 100 shares at $53 per share and owes a commission of $175, leading to an initial proceeds of $5,300 - $175. Assuming a margin requirement of 55%, the investor must deposit $2,915 (which is 55% of $5,300) with the broker.

Eventually, the shares are bought back at $42 per share plus a commission of $165, totalling a cost to cover of $4,365. Additionally, the investor is responsible for paying the $2.40 per share dividend, so an extra $240 must be paid. Furthermore, an interest of 13% per year on the borrowed funds needs to be taken into account. As only the initial proceeds minus the margin deposit is borrowed, the interest amounts to 13% of ($5,300 - $2,915), which is $310.05.

Net profit or loss is calculated as initial proceeds minus the cost to cover, dividends paid, and interest, thus equals $5,125 ($5,300 - $175) - $4,365 - $240 - $310.05, which results in a net loss of $90.05. To find the rate of return, divide the net profit by the initial margin deposit $2,915 and multiply by 100 to get a percentage. This results in -3.09%.