Question

Suppose that you sell short 1,000 shares of Intel, currently selling for $20 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 1 year if Intel stock is selling at: (i) $22; (ii) $20; (iii) $18? 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.

Answer 1

Short selling means selling securities which you don't own currently and then repurchasing them after some time. It is done when you anticipate the price to fall in future.

a)  rate of return after 1 year

Invested funds = $15,000

The gain or loss on the short position = –1,000 * change in price(ΔP)

rate of return = (-1000 * ΔP) / 15,000

i) $22

Rate of return = (–1,000 * $2) / $15,000 = –13.33%

ii) $20

Rate of return = (–1,000 * $0) / $15,000 = 0%

iii) $18

Rate of return = (–1,000 * (-$2)) / $15,000 = 13.33%

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

Total assets in margin account = $20,000(from sale of stock) + $15,000(initial margin)

Total assets in margin account = $35,000

Let price be P

Liabilities are 500P

Margin call will be received when = (35,000 - 1000P) / 1000P = 0.25 when P = $28 or higher.

c)  Intel also has paid a year-end dividend of $1

With $1 dividend, the short position will pay on borrowed shares ($1 / 1,000) = $1,000

Rate of return = [(–1,000 * ΔP) – 1,000] / 15,000

i) $22

Rate of return = [(–1,000 * $2) - 1,000] / $15,000 = –20%

ii) $20

Rate of return = [(–1,000 * $0) - 1,000] / $15,000 = -6.67%

iii) $18

Rate of return = [(–1,000 * (-$2)) - 1,000] / $15,000 = 6.67%

Total assets are 35,000

Liabilties are (1,000P + 1,000)

A margin call will be issued when (35,000 - 1,000P - 1,000) / 1,000P = 0.25 when P = $27.2 or higher.

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