Question

Suppose that you sell short 500 shares of XYZ, currently selling for $40 per share, and give your broker $15,000 to establish your margin account.

If you earn no interest on the funds in your margin account, and assume that XYC pays no dividends.

a.) So what will be your rate of return after one year if XYZ stock is selling at:

i.) $44.00

ii.) $40.00

iii.) $36.00

b.)

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

c.)

Try parts (a) and (b) again, but now assume that XYZ 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.

i.) $44.00

ii.) $40.00

iii.) $36.00

Answer 1

(a) Given,

I sell short 500 shares of XYZ

Currently selling @ 40 per share and paid an amount of $15,000 for Margin Balance.

(i) After 1 year, if XYZ stock is selling at $44

Required: Rate of Return after 1 year

If stock sells at $44,

Loss on contract = (40 - 44)×500 = (2,000)

Rate of return

= Return on investment÷initial investment

=(2,000)÷15,000 = -13.33%

(ii) After 1 year, if XYZ stock is selling at $40

Required: Rate of Return after 1 year

If stock sells at $40,

No loss or no profit on contract

Therefore rate of return is nil.

(iii) After 1 year, if XYZ stock is selling at $36

Profit on contract = (40 - 36)×500 = $2,000

Rate of Return = 2,000÷15,000 = 13.33%

(b) If maintenance Margin is 25%, how high can XYZ price rise, before we get a margin call

Maintenance Margin = 25% of initial Margin

= 15,000×25% = 3750

Let us assume the price be X

Now in order to get a margin call, we need to suffer a loss of $11,250 i.e., 15,000 - 3,750

In order to suffer a loss of $11,250 the price shall be as follows

(X - 40)×500 = 11,250

X = $62.5

Therefore the price raise shall be at $62.5 in order to get a margin call

(c) In case if XYZ pays a dividend of $1 per share,

(i) Calculation of rate of return if after 1 year stock price trades at $44

Rate of return =[ (40 - 44)×500 + 1×500]÷15,000

= (1500)÷15,000 = -10%

(ii) Calculation of rate of return if after 1 year stock price trades at $40

Rate of return = [(40 - 40)×500 + 1×500]÷15,000

= 3.33%

(iii) Calculation of rate of return if after 1 year stock price trades at $36

Rate of return =[( 40 - 36)×500 + 1×500]÷15,000

= 23.33%

Calculation of price rise of XYZ stock to get a margin call, if maintenance Margin is 25% of initial Margin

Maintenance Margin = 15,000×25% = $3,750

Let us assume price be X

Now in order to get a margin call, we need to suffer a loss of $11,750 i.e., 15,000+500-3,750

(X - 40)×500 = 11,750

X = $67.5

Therefore the price rise shall be at $67.5 in order to get a margin call.