Buying Stocks on Margin


in the EOC questions of Reading 46, it says in question 21 that “stock was bought on 75% margin”. My intuitive understanding of this wording would be that 75% of the purchase money has been financed through margin, i.e. the purchaser paid own equity worth 25% of the payment.

However, looking at the question’s solution, it means that the purchaser has paid 75% of the price himself and 25% has been financed through margin (i.e. loan).

Have I mixed things up, or the book?

Thanks a lot, and good luck to you all next week!

I think I can answer my own questions. QBank also has got the following test question:

" An investor purchases stock on 25% initial margin, posting $10 of the original stock price of $40 as equity. The position has a required maintenance margin of 20%. The investor later sells the stock for $45. Ignoring transaction costs and margin loan interest, which of the following statements is most accurate?"

So if you buy a position on X % initial margin, that represents the equity amount you have to pay yourself.

Ok, now I am confused again. Another question from QBank:


An investor buys 200 shares of ABC at the market price of $100 on full margin. The initial margin requirement is 40% and the maintenance margin requirement is 25%.

At what price will the investor get a margin call?

A) $112. B) $48. C) $80.

Your answer: C was correct!

In a long stock position, the equation to use to determine a margin call is:

long = [(original price)(1 − initial margin %)] / [1 − maintenance margin %] = $100(1 − 0.4) / (1 − 0.25) = $80"

If he buys on “full margin” my understanding would be that this is equivalent to “on 100% margin” which would mean: the investor pays the entire position himself. So if he pays the entire purchase himself, why would he receive a margin call at all? He has not made use of any credit facility of the broker, so he bears the entire risk himself.

I would interpret “on full margin” to mean " to the full extent of the margin" which, in this case, is 40%.

By the way, you needn’t commit the formula above to memory; if you can calculate how much is in your margin account for a given price (which is trivial), all you have to do it test the middle number ($80 in this case): if you’re at the maintenance margin, that’s the correct answer; if not, you’re either above it (so the correct answer is the lower price) or else you’re below it (so the correct answer is the higher price).

How do you test it? Price times initial margin? 200 x 0.4 = 80?

You buy a $100 share of stock on margin; initial margin is 60%, maintenance margin is 30%. At what price will you get a margin call?

A) $57.14

B) $54.54

C) $50.00

Check $54.54 (the middle number): if the price drops to $54.54, your margin account will drop to $14.54, so your margin percentage is $14.54 / $54.54 = 26.7%, which is below the maintenance margin. Thus, the price is too low: $57.14 must be correct.

So, if forget formula the way to do it is to find the new amount of equity/capital (in the middle amount) and compare it to the maintenance margin?

That’s correct.

For clarification is it safe to interpret ‘Initial Margin’ as the equity or cash an investor has to post to take a long position? Specifically, in a question like this:

A trader buys 500 shares of a stock on margin at $36 a share using an initial leverage ratio of 1.66. The maintenance margin requirement for the position is 30 percent. The stock price at which the margin call will occur is closest to: A. $20.57. B. $25.20. C. $30.86. So here your (1-initial margin) is (1 - .6) as that is the equity required from a leverage ratio of 1.66 (1/1.66=.60)?

I think of it like this:

Leverage is simply asset/equity (remember leverage ratio from FRA?). So here 36 / 1.66 = equity of 21.7, margin must be 14.3.

Per S2000, just divide the 14.3 by the middle number, in this case 20.57. That is, 14.3/20.57 = 69.5% which means your “maintenance” equity position has to be 1 - 69.5% ~ 30%

Hi S2000,

Glad to find you again here.

I’m interested in answering those type of answers without using the formula.

How did you come up with this :

I can’t figure out how to get to the $14,54.


When you bought the stock at $100/share the margin was 60% or $60/share, so you borrowed $40/share.

Your equity is the share price less what you owe, so when the share price drops to $54.54, your equity drops to $14.54 (= $54.54 − $40.00) per share.

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Makes complete sense as usual with your answers. Thanks you S2000magician

You’re very kind.

My pleasure.