Margin Transaction: possible error

CFA Level I Equities
#1

I got this wrong recently in a test I wrote at my college but I’m not sure why? Anyway here’s the question: I got a and b right but c wrong.

Suppose an investor initially pays $6000 towards the purchase of $10 000 worth of shares( 100 shares for $100 each). The investor borrows $4000 from his broker.

a. What is the current margin requirement and what will it be if the share price declines to $70 a share?

b. Suppose the maintenance margin is 40%. How far can the share price drop before the investor gets a margin call?

c. Suppose the investor only borrows $5000 at a rate of 9% per year. What will be the rate of return if the share price increases by 30%?

For C I got 51% but I was marked wrong? How would you do C?

#2

investor borrowed 5,000, paid 5,000 out of his pocket (equity).

share price rose to 130.

Calculation of return:

receives 130 * 100 = 13,000

Pays back 5,000 borrowed

Pays back 5,000 * 9% = 450

so return = (13,000 - 5,000 - 450 )/5,000 = 151%

Remember leverage magnifies the return when positive or negative. So if share prices rose 30% - (Which means they became 130% of original value) - the final return due to leverage will be higher than 130%.

If he had earned negative returns the final return would have been magnified then too.

#3

I calculated it this way as it was similar to another example I have seen:

10000 x 1.30 = $13 000

Equity = $5 000

Borrowed = $5 000

Paying of the principal and interest of $5 450 leaves $7 550 ($13 000-$5 450).

Therefore, the rate of return is;

(7550 - 5000)/ 5000 = 51%

Im really confused. I understand the share price rose 30% which means your return will be higher due to leverage. But why is it 151% not 51%?

#4

you already took out the principal component on the numerator, have 7550 available.

Why are you removing the 5000 again now? (What is this one you are removing additionally)?

You have 7550 left over after repaying the loan - and this was on your original equity amount of 5000. so you make 7550 / 5000 = 151%

#5

CPK: you’re leading with your chin here.

The _ proceeds _ are $13,000 − $5,000 − $450 = $7,550, but that’s not the profit.

The profit is the ending value ($7,550) less the beginning value ($5,000), or $2,550.

That’s a 51% (= $2,550 / $5,000) return.

Your calculation showed that the ending value is 151% of the beginning value which is correct: 100% is the return _ of _ principal, and 51% is the return _ on _ principal.

The $5,000 that Chris deducted is not the principal; it’s the loan repayment.

#6

Sorry that might have been an error in my wording. So you therefore only deduct the interest on the loan?

#7

Your calculation’s correct.

What is the official answer for C? Do they show the calculation?

Note that we aren’t given the holding period; if it’s not one year, then the $450 in interest is incorrect.

#8

The period was 1 year.

The answer was 40.5%.

The answer stated that $10,000 was the equity now and the borrowed amount was $5,000.

Which gave calculations as:

$15,000 x 1.30 = $19,500

therefore the return was $19,500 - $450 - $15,000 = $4,050/$10,000 = 40.50%

I personally think based on the answer the question was worded badly.

#9

The question’s stupid.

There’s no doubt that you understand the calculation, and that you’d have gotten it correct if the question were written correctly.

#10

That makes me feel so much better. I thought there was something wrong. Thanks so much for your help.

#11

My pleasure.