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A '''[[Margin call]]''' is a demand from a [[Broker|broker]] or other financial intermediary requiring an investor to provide additional funds or eligible collateral when the value of a [[Margin account|margin account]] falls below the required maintenance margin.

Margin calls can arise when the market value of securities purchased with borrowed funds declines, when the value of collateral falls, or when applicable margin requirements increase.

==Margin account==

When an investor purchases securities on margin, the investor contributes part of the purchase price while borrowing the remainder from the broker.

A simplified relationship is:

<math>
\text{Asset Value}
=
\text{Investor Equity}
+
\text{Margin Loan}
</math>

Therefore:

<math>
\text{Investor Equity}
=
\text{Asset Value}
-
\text{Margin Loan}
</math>

where:

* <math>\text{Asset Value}</math> = current market value of the securities;
* <math>\text{Investor Equity}</math> = investor's equity in the margin account;
* <math>\text{Margin Loan}</math> = amount borrowed from the broker.

==Maintenance margin==

The '''maintenance margin''' is the minimum proportion of the market value of the securities that must be maintained as the investor's equity.

The maintenance margin requirement can be represented as:

<math>
\frac{\text{Equity}}
{\text{Market Value}}
\geq
m
</math>

where <math>m</math> is the applicable maintenance margin requirement.

Equivalently:

<math>
\text{Equity}
\geq
m\times\text{Market Value}
</math>

A margin call can occur when:

<math>
\frac{\text{Equity}}
{\text{Market Value}}
<
m
</math>

==Example==

Suppose an investor purchases securities worth $10,000 using $6,000 of personal funds and a $4,000 margin loan.

Initially:

<math>
\text{Equity}
=
\$10{,}000-\$4{,}000
=
\$6{,}000
</math>

The initial equity percentage is:

<math>
\frac{\$6{,}000}{\$10{,}000}
=
60\%
</math>

Suppose the maintenance margin requirement is 30%.

If the market value of the securities falls to $7,000, assuming the loan remains $4,000:

<math>
\text{Equity}
=
\$7{,}000-\$4{,}000
=
\$3{,}000
</math>

The resulting equity percentage is:

<math>
\frac{\$3{,}000}{\$7{,}000}
\approx
42.9\%
</math>

No margin call would arise solely from the 30% maintenance requirement because the equity percentage remains above 30%.

If the market value instead falls to $5,000:

<math>
\text{Equity}
=
\$5{,}000-\$4{,}000
=
\$1{,}000
</math>

and:

<math>
\frac{\$1{,}000}{\$5{,}000}
=
20\%
</math>

Because 20% is below the 30% maintenance requirement, the account would be subject to a margin call under this simplified example.

==Margin call amount==

The minimum equity required to satisfy a maintenance margin requirement is:

<math>
\text{Required Equity}
=
mV
</math>

where:

* <math>m</math> = maintenance margin requirement;
* <math>V</math> = current market value of the securities.

The amount of additional equity required can therefore be expressed as:

<math>
\text{Margin Call Amount}
=
\max
\left(
0,\,
mV-E
\right)
</math>

where <math>E</math> is the investor's current equity.

For the example above, with a market value of $5,000 and a 30% maintenance requirement:

<math>
\text{Required Equity}
=
0.30\times\$5{,}000
=
\$1{,}500
</math>

Current equity is $1,000, so the additional equity required is:

<math>
\$1{,}500-\$1{,}000
=
\$500
</math>

==Effect of a declining market==

A decline in the market value of securities purchased on margin reduces the investor's equity, assuming the margin loan remains unchanged.

The relationship is:

<math>
\Delta\text{Equity}
=
\Delta\text{Market Value}
-
\Delta\text{Margin Loan}
</math>

If the loan does not change:

<math>
\Delta\text{Equity}
=
\Delta\text{Market Value}
</math>

Thus, losses in the underlying securities can reduce the investor's equity and eventually cause the account to fall below the maintenance requirement.

==Meeting a margin call==

An investor may generally satisfy a margin call through one or more methods permitted by the broker, such as:

* depositing additional cash;
* depositing eligible securities or other collateral;
* selling securities to reduce the margin loan.

If securities are sold, the proceeds can be used to repay part of the outstanding margin loan.

A simplified relationship after a sale is:

<math>
\text{New Loan}
=
\text{Old Loan}
-
\text{Sale Proceeds}
</math>

subject to applicable interest, transaction costs, and brokerage rules.

==Broker liquidation==

If an investor does not satisfy a margin call within the required period, the broker may have the contractual or regulatory authority to liquidate securities in the account.

A simplified liquidation sequence is:

<math>
\text{Market Decline}
\rightarrow
\text{Lower Equity}
\rightarrow
\text{Maintenance Margin Breach}
\rightarrow
\text{Margin Call}
\rightarrow
\text{Possible Liquidation}
</math>

The broker's ability to liquidate securities, the timing of liquidation, and the amount of notice required depend on the applicable account agreement, market rules, and jurisdiction.

Forced liquidation can occur at unfavorable market prices, particularly during periods of high market volatility.

==Leverage and margin calls==

Margin trading creates [[Leverage (finance)|financial leverage]] because the investor controls assets using both personal capital and borrowed funds.

A simplified leverage ratio is:

<math>
\text{Leverage}
=
\frac{\text{Asset Value}}
{\text{Investor Equity}}
</math>

Higher leverage means that a given percentage decline in the value of the underlying securities can produce a larger percentage decline in the investor's equity.

For this reason, margin calls represent an important risk associated with leveraged investing.

==Margin call versus initial margin==

The '''initial margin''' is the amount of equity or collateral required when a leveraged position is established.

The '''maintenance margin''' is the minimum equity level that must generally be maintained after the position has been established.

A simplified distinction is:

<math>
\text{Initial Margin}
\rightarrow
\text{Requirement to Establish Position}
</math>

<math>
\text{Maintenance Margin}
\rightarrow
\text{Requirement to Maintain Position}
</math>

A margin call generally occurs when the account falls below the applicable maintenance requirement.

==Risks==

Margin trading can magnify both gains and losses.

If the value of securities rises, leverage can increase the return on the investor's own capital.

If the value of securities falls, leverage can accelerate losses and can result in:

* a margin call;
* forced liquidation;
* additional losses during rapid market declines;
* interest expenses on borrowed funds;
* losses exceeding the investor's initial cash contribution in some circumstances.

The exact consequences depend on the securities held, borrowing arrangements, margin requirements, and applicable regulations.

==See also==

* [[Margin (finance)]]
* [[Margin account]]
* [[Initial margin]]
* [[Maintenance margin]]
* [[Leverage (finance)]]
* [[Short selling]]
* [[Collateral (finance)]]
* [[Broker]]
* [[Liquidation]]
* [[Risk management]]
* [[Financial risk]]

[[Category:Financial markets]]
[[Category:Investment]]
[[Category:Risk management]]
[[Category:Financial mathematics]]