Margin Call Price

Builds onHolding Period Return (HPR) — if this page feels steep, start there.

P_{call} = P_0\,\frac{1 - IM}{1 - MM}

$P_0$: the purchase price per share
$IM$: the initial margin: the fraction of the purchase YOU fund (rest is the broker's loan)
$MM$: the maintenance margin: the minimum equity fraction the broker tolerates
$1 - IM$: the borrowed fraction — the loan, which never shrinks as the price falls
$P_{call}$: the price at which equity hits the floor and the margin call is triggered

Why it must be true

Buy on margin and you own the whole position while financing only part of it — your equity is the cushion between the stock's value and the broker's loan. The loan is fixed; the cushion is what shrinks when the price falls. The broker tolerates shrinkage down to the maintenance margin; below it, the phone rings.

The call price is where the cushion exactly hits that floor. The formula is a ratio of two "equity fractions": you started with $1 - IM$ of the price borrowed, and the broker calls when equity falls to $MM$ of current value. Buying at $40 with 50% initial and 25% maintenance margin: $40 \times 0.50/0.75 = \$26.67$ — a one-third drop, and the leverage that doubled your upside has eaten two-thirds of your equity.

The derivation

At purchase, the loan per share is fixed forever after: $L = P_0(1 - IM)$ .

At any later price $P$ , equity per share is $P - L$ , and the equity fraction is $(P - L)/P$ . The broker calls when it hits the maintenance floor:

\frac{P - P_0(1 - IM)}{P} = MM

Solve for $P$ : multiply out, gather terms in $P$ :

P(1 - MM) = P_0(1 - IM) \quad\Rightarrow\quad P_{call} = P_0\,\frac{1 - IM}{1 - MM}

Sanity: with $IM > MM$ the fraction is below 1 — the call sits below the purchase price, as it must.

When to reach for it

Finding the stock price that triggers a margin call for a leveraged long position, given initial and maintenance margin requirements.

Listen for

“margin call price / at what price will the investor receive a margin call”“initial margin of … maintenance margin of …”“bought on margin”“equity falls below the maintenance requirement”

Back-of-the-envelope

Estimate it in your head first — then the calculator only confirms.

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The classic 50/25 pair gives a clean ratio: 0.50/0.75 = 2/3 of the purchase price. Memorize that anchor and scale intuitively from it.
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Direction check: the call price must be BELOW the purchase price (for a long) — a candidate answer above P₀ has the fraction inverted.
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Higher maintenance margin → call comes sooner (higher call price): the denominator 1−MM shrinks. Check your answer moved the right way.

Traps in applying it

✗Inverting the fraction — (1−MM)/(1−IM) puts the call above the purchase price, which is impossible for a long.
✗Using the margin percentages directly instead of their complements — the algebra runs on the borrowed and floor fractions.
✗Forgetting the loan is FIXED: interest and dividends aside, only the equity moves with the price.

Limits & criticisms

The textbook version ignores margin loan interest (which grows the loan and pulls the call closer), dividends (which pad equity), and brokers' rights to set house margins above the regulatory floor or change them mid-storm — as brokers did in 2021's meme-stock episode. It also prices only the trigger, not the damage: forced sales at the call price realize the leveraged loss at the worst moment.

Where it came from

Margin rules are a child of 1929: pre-crash leverage of 10% margin amplified the collapse, and the Securities Exchange Act of 1934 handed the Federal Reserve the power to set initial margins — Regulation T's 50% has stood since 1974, with FINRA's 25% maintenance floor beneath it. Margin calls still drive market drama: the forced unwinds of 2008, the GameStop margin restrictions of 2021 and the Archegos collapse were all this formula executing at scale.

One identity, 1 questions

The exam can hide any variable. Each face below is the same equation solved for a different unknown — drill them separately.

Where the phone rings

P_{call} = P_0\,\frac{1-IM}{1-MM}

The risk-management face: know the trigger before entering the trade — leverage sets both the upside and this tripwire.

Drill this face →

On the BA II Plus

Worked example: A margin purchase at $80.00 uses initial margin of 40%; the broker requires 25% maintenance. Below what price does the margin call trigger?

1.1 [−] 0.4 [=] [STO] 1borrowed fraction
2.1 [−] 0.25 [=] [STO] 21 − maintenance floor
3.80 [×] [RCL] 1 [÷] [RCL] 2 [=]P₀ × ratio = call price

→ $64.00

Drill this formula Back to the library