Calculating a Margin Call Price from the Initial Margin Requirement
Summary
This note explains how to interpret an initial margin requirement when calculating the stock price that triggers a maintenance margin call. The requirement is the investor’s equity contribution to the purchase, so the financed portion is the complement of that percentage. In the example, the investor buys Microsoft shares using a broker loan, and the loan amount is calculated from the portion not covered by the initial margin.
To find the call price, the note sets account equity—share value minus the original loan—equal to the maintenance margin fraction of current share value, then solves for the stock price. It reports a trigger price of 89.36 for the stated example. The calculation assumes a fixed loan balance and does not incorporate accrued interest, despite the problem stating a loan rate; it also does not discuss fees, margin-rule changes, or broker-specific practices.
Key ideas
- The initial margin percentage represents the investor’s contribution to the purchase price.
- The borrowed fraction is the complement of the initial margin requirement.
- A margin call occurs when account equity reaches the maintenance margin fraction of current market value.
- The example solves for the stock price by equating equity after the loan to the maintenance requirement.
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Full text
# Initial margin requirement as percentage, not dollar value
# Initial margin requirement as percentage, not dollar value
Problem from Finan, FM/2
> On 12-30-1998, you decided to bet on the January effect. On that day, you bought 400 shares of Microsoft on margin at the price of 139 per share. The initial margin requirement is 55% and the maintenance margin is 30%. The annual cost of the margin loan is 6.5% To what price must Microsoft fall for you to receive a margin call?
So if we use the Initial margin requirement formula $$IM=P\cdot{Q}\cdot{IM\text{%}}$$
But the correct answer of 89.36 as Microsoft price is given only if $\text{IM%}$ is 45%. Does this mean that we use $1-IM\text{%}%$ as the initial margin percentage? I'm confused about the wording because the problem gives you initial margin requirement as a percentage and not as a dollar value. If you put 55% in the above equation you do not get the right answer. No where in the texts that I'm using does it state initial margin requirement as a percentage is $1-IM\text{%}$?
## Answer by Eleven-Eleven (score 2, accepted)
https://quant.stackexchange.com/a/8193
Nevermind, I just found the quote i needed:
When buying on margin, the investor borrows part of the purchase price of the stock from a broker or brokerage firm and contributes the remaining portion (<----IM requirement)... so thus when calculating, if IM requirement is 55%, the amount of the loan is 45%....
so then calculating the price, we do $$\frac{400\cdot{X}-400\cdot{139}\cdot{.45}}{400\cdot{X}}=.3$$ Solving for X gives us $89.36.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.