CFA Mock Test - Question on Margin

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sidhesh

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Hi
Was going throught the CFA Mock test and found a solution i havent come across yet in schweser.
Pardon me for my ignorance if Schweser has it.
Here is the question.
An investor opens a margin account with an initial deposit of $5,000. He then purchases 300 shares of a stock at $30 each on margin, and his account requires a maintenance margin of 30%. Ignoring commissions and interest, the price at which the investor will receive a margin call is closest to:
A. $19.05.
B. $23.08.
C. $23.81
The solution is :
equity / market value = 30%
5,000 + (p x 300) - (30 x 300) / p x 300 = 30%
P = 19.05
I cant seem to get this. Is there another way to approach this ?
Posting this as the CFA has had this in both the mocks (anyway they were consolidated from the individual test questions on their website), yet, rather be safe than sorry.
 
Investors equity in each share is $16.66 ($5,000/300 shares)
Investors initial Margin % is 55.53% (16.66/30)
Margin Call at (1-initial margin / 1- maintenance margin) = (1- 0.5553)/(1-0.3) = 63.52%
Margin Call at $30 * 0.6352 = $19.06
 
I just remember this formula:
Original price (1 - Initial margin) = Price for margin call (1 - maintenance margin)
 
I think this is the easiest way:
Your initial deposit is 5000. (This is what you have put down, your margin). The total amount spent was 30x300 = 9000.
So you’ve spent 9000, but you only put down 5000. (You borrowed 4000)
So how much did you put down as a percentage of what you spent: 5000/9000 = 0.55 (This is your initial margin %)
(1- Initial Margin / 1 - Maint Margin) x P
Well you know your initial margin now is 0.55
So it’s 1- that = (0.45/0.7) x orignal P = 30 = 19.047
 
It seems so easy after reading your explanation. Converting it in terms of percentages and applying the formula for the margin call, as basic as it could get.
Thank you so much guys.
 
I welcome any comments on these answers.

2. Stock XYZ is at 100. you are long the Jan 100 put and short the Dec 110 put. Are you:

a. Long delta, short vega
b. short delta, short vega
c. Long delta, long vega
d. Short delta, long vega.

Answer a:


8. You established the following position:

Long 100 ABCD 150 Call
Long 100 ABCD 150 Put

If the price of ABCD is $150 at expiration, what is the resulting ABCD position in your account on the business day following expiration:

a. Flat or no position in ABCD
b. Long 100,000 shares of ABCD
c. Short 100,000 shares of ABCD
d. Both B and C

answer: a


You establish the following position:

short 100 ABCD 150 Call
short 100 ABCD 150 Put

If the price of ABCD is $150 at expiration, what is the resulting ABCD position in your account on the business day follwoing expiration?

a. Flat or not position
b. Long 100,000 shares of ABCD
c. short 100,000 shares of ABCD
d. Both B and C
e. Unable to determine.

Answer: e


19. You establish the following position:

Short 1 ABCD 320 Put @6

If the delta of the put is .050 and the gamm is 0.03 what would the new delta be if ABCD decreases from 321 to 320?

a. 0.47
b. 0.50
c. 0.53
d. 0.56
e. 0.60

Answer: a


20. You have established the following positions:
long 500 abc nov 1240 call @5
long 500 abc nov 1205 puts @6
What is the traditional margin requirement?
a. $500,000
b. $550,000
c. $600,000
d. $700,000
Answer: b
 
You can follow a more lengthy and logical method as well. Initial margin is $5,000 total investment is $9,000 (300 x 30) and 30% of that is maintenance margin so it is $2,700 (30% of 9,000).
Now you can try the various prices given in solution to find how much of money will be left in the account after settlement.
a) 300 x (30 - 19.05) = 3,285; amount in account = 5,000 - 3,285 = 1,715
b) 300 x (30 - 23.08) = 2,076; amount in account = 5,000 - 2,076 = 2,924
c) 300 x (30 - 23.81) = 1,857; amount in account = 5,000 - 1,857 = 3.143
The balance goes below the maintenance margin when the price of share drops to $19.05, hence will lead to margin call.
 
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