Determining the Value of Shorted Securities That Will Elicit a Margin Call

The formula for calculating the value of securities that will elicit a margin call for shorted stock can be derived from the formula for calculating margin:

1. Margin = (Account Value - Value of Shorted Securities) / Value of Shorted Securities
2. Let m = margin ratio; a = account value; and v = value of shorted securities.
3. m = (a - v) / v
4. m * v = a - v Multiply both sides by v.
5. v + m * v = a Add v to both sides.
6. v (1 + m) = a Factor out v from the left side.
7. v = a / (1 + m) Divide both sides by 1 + m.
8. Value of Shorted Securities = Account Value / (1 + Margin)

Thus, the short account value that will trigger a margin call can be calculated with the following formula:

Calculating the Margin Call Account Value of a Shorted Security

Margin Call Account Value =	Account Value ───────────  1 + MMR	MMR = Margin Maintenance Requirement (usually 30%). Price per Share = Margin Call Account Value/Number of Shares

Example — Calculating the Margin Call Price of a Shorted Security

Using the above example, what market price of the shorted security will trigger a margin call?

The total amount on deposit in the account is $15,000 and the margin maintenance requirement is 30%. 

Therefore, the margin call value = 15,000/(1 + .3) = 15,000/1.3 = $11,538.46. This is equal to a price per share of $11,538/1,000 = $11.54 (rounded) per share. So a margin call will be triggered when the price of the shorted security rises to $11.54.

To verify, we substitute $11,538.46 into the margin formula above, and find that (15,000 - 11,538.46)/11,538.46 = 0.30 = 30%, the margin maintenance requirement. Note that if any dividends were paid out, this would have to be subtracted from the amount on deposit.