or all problems presented below assume that the initial marg

or all problems presented below, assume that the initial margin is 45% and the maintenance margin is 35%, and restoration margin is 40%. 1. You purchased 500 shares of ABC stock today @$120/share. You purchased the stock on 45% initial margin. Compute the actual margin (%), and the rate of return or ROR (96) on your investment when you close out your position on a future date if the st price is: ock a. $95 b. $110 c. $140 d. Corresponding to each of the 3 prices shown above, compute the rate of returrm to purchasing the stock on cash (i.e., employing no margin)

Solution

Current market price of ABC stock = $120 per share

Number of share’s purchased = 500 shares

The initial margin = 45%

The maintenance margin = 35%

Restoration margin = 40%

Total investment on purchase of ABC stock = Current market price of ABC stock * Number of shares

= $120 *500

= $60,000

The initial margin amount (your own investment) = Current market price of ABC stock * Number of shares * initial margin

= $120 *500 *45%

=$27,000

Therefore borrowed fund = Total investment on purchase of ABC stock - initial margin

= $60,000 - $27,000

= $33,000

a. If ABC\'s price on a future date is $95, then

Value of total investment = 500 * $95

= $47,500

And actual initial margin = Value of total investment - borrowed fund

=$47,500 - $33,000 = $14,500

Actual margin (%) = $14,500 / $47,500 = 30.53% (you will get a margin call as it is below 35%)

Rate of return or ROR on your investment = {(Value of investment - borrowed fund) - your initial investment} / your initial investment

= {$14,500 -$27,000} /$27,000

= -46.30%

b. If ABC\'s price on a future date is $110, then

Value of total investment = 500 * $110

= $55,000

And actual initial margin = Value of total investment - borrowed fund

=$55,000 - $33,000 = $22,000

Actual margin (%) = $22,000 / $55,000 = 40% (you will not get a margin call as it is above 35%)

Rate of return or ROR on your investment = {(Value of investment - borrowed fund) - your initial investment} / your initial investment

= {$22,000 -$27,000} /$27,000                          

=-18.52%

c. If ABC\'s price on a future date is $140, then

Value of total investment = 500 * $140

= $70,000

And actual initial margin = Value of total investment - borrowed fund

=$70,000 - $33,000 = $37,000

Actual margin (%) = $37,000 / $70,000 = 52.86% (you will not get a margin call as it is above 35%)

Rate of return or ROR on your investment = {(Value of investment - borrowed fund) - your initial investment} / your initial investment

= {$37,000 -$27,000} /$27,000    

= 37.04%

d. Rate of return without margin –

Initial investment = $120 *500 = $60,000

Value of total investment = 500 * $95 = $47,500

Rate of return = (Value of total investment - Initial investment)/ Initial investment

= ($47,500 -$60,000) /$60,000

= -20.83%

Value of total investment = 500 * $110 = $55,000

Rate of return = (Value of total investment - Initial investment)/ Initial investment

= ($55,000 -$60,000) /$60,000

= -8.33%

Value of total investment = 500 * $140 = $70,000

Rate of return = (Value of total investment - Initial investment)/ Initial investment

= ($70,000 -$60,000) /$60,000

= 16.67%