Question

Given the following information,

The margin requirement=50%.

The margin call ratio = 30%.

Stock price: $ 60

Interest rate on margin borrowing (call rate): 5%

Expected dividend: $2

Holding period: 1 year

Please estimate a) the margin trading return if the stock price increases to $80

b) the margin trading return if the stock price decreases to $45

c) the price which triggers the margin call.

d) If the margin-call triggering price is $25, please estimate the margin requirement, given everything else equal.

Answer 1

a) the margin trading return if the stock price increases to $80

Margin requirement=50% of Stock price: $ 60 i.e, $30

Interest rate on margin borrowing (call rate): 5%

Expected dividend: $2

Margin trading return = (80-60-1.5+2)/30 = $20/$30 = 68.33%

b) the margin trading return if the stock price decreases to $45

Similar to above, 45-60=-$15

Interest rate on margin borrowing (call rate): 5%

Expected dividend: $2

Margin trading return = (45-60-1.5+2)/30 = -$15/$30= -48.33%

c) the price which triggers the margin call is 60-21 = $39.

A margin call occurs when the account value falls below the broker's required minimum value.

Margin call ratio = 30%, Margin requirement=50% of Stock price: $ 60 i.e, $30

Therefore, broker's required minimum value $30*30% = $9, So, client has time till stock price goes down to $21.

d) If the margin-call triggering price is $25, please estimate the margin requirement, given everything else equal.

Given the Margin call ratio is 30%, If the margin-call triggering price is $25, the margin requirement would be $50.

At price $25, Stock is down $35 which is 70% of Initial margin requirement. So, margin requirement would be

$35 = 70%

X = 100%

Cross Multiply to find X = $35/70% = $50.