Question

Question: Suppose that you sell short 500 shares of Intel, currently selling for \(40 per share, and give your broker \)15,000 to establish your margin account.

a. If you earn no interest on the funds in your margin account, what will be your rate of return after one year if Intel stock is selling at (i) \(44; (ii) \)40; (iii) \(36? Assume that Intel pays no dividends.

b. If the maintenance margin is 25%, how high can Intel’s price rise before you get a margin call?

c. Redo parts ( a ) and ( b ), but now assume that Intel also has paid a year-end dividend of \)1 per share. The prices in part ( a ) should be interpreted as ex-dividend, that is, prices after the dividend has been paid.

Short answer

Answer

a. (i) -13.33% (ii) 0% (iii) 23.33%

b. $ 56 or higher

c. (i) –16.67% (ii) –3.33% (iii) 10.00% and $55.20 or higher

Step-by-step solution

Definition

Short selling is the practice of selling the un-owned or the borrowed stocks through a broker.

Calculation of rate of return in given scenarios

a. The gain or loss on the short position is: (–500 xΔP)

Invested funds = $15,000

Therefore: rate of return = (–500 xΔP) /15,000

The rate of return in each of the three scenarios is:

(i) Rate of return = (–500 x $4)/$15,000 = –0.1333 = –13.33%

(ii) Rate of return = (–500 x $0)/$15,000 = 0%

(iii) Rate of return = [–500 x (–$4)]/$15,000 = +0.1333 = +13.33%

Evaluation of price rise to get margin call

b. Total assets in the margin account are $20,000 (from the sale of the stock) +

$15,000 (the initial margin) = $35,000. Liabilities are 500P.

A margin call will be issued when:

$35000 – 500P/ 500P = 0.25 when P = $ 56 or higher

Evaluation of price rise to get margin call in the given scenarios

c. With a $1 dividend, the short position must now pay on the borrowed shares:

($1/share x 500 shares) = $500.

Rate of return is now: [(–500 x ΔP) – 500]/15,000

(i) Rate of return =[(–500 x $4) – $500]/$15,000 = –0.1667 = –16.67%

(ii) Rate of return = [(–500 x $0) – $500]/$15,000 = –0.0333 = –3.33%

(iii) Rate of return = [(–500) x (–$4) – $500]/$15,000 = +0.1000 = +10.00%

Total assets are $35,000, and liabilities are (500P + 500).

A margin call will be issued when: 35,000 - 500P - 500 / 500P

= 0.25 when P = $55.20 or higher