Leverage Explained: How It Works and How It Ends Accounts

What leverage actually is

Leverage means controlling exposure larger than your capital. It arrives in several forms: borrowing on margin in a stock account, posting a performance bond in futures, using the embedded leverage of options, or trading a derivative that requires only a fraction of notional as collateral.

Effective leverage = Total notional exposure / Account equity

Stock account: 30,000 equity, 45,000 of stock held
   Leverage = 1.5x

Futures: 30,000 equity, one ES contract at ~275,000 notional
   Leverage = 9.2x  (regardless of the 13,000 margin posted)

Forex: 10,000 equity, 0.5 standard lots (50,000 units)
   Leverage = 5.0x

Margin posted tells you what the broker requires.
Notional divided by equity tells you what you actually own.

Volatility drag: the cost nobody mentions

Compounding is not linear. A 10 percent loss followed by a 10 percent gain leaves you below where you started. Leverage magnifies this effect, and the penalty grows with the square of the leverage factor.

Geometric return  =  L x mean  -  (L^2 x variance) / 2

Strategy: 10% expected return, 20% volatility (variance 0.04)

   L = 1:   0.10 - (1 x 0.04)/2  = 0.080   (8.0%)
   L = 2:   0.20 - (4 x 0.04)/2  = 0.120   (12.0%)
   L = 3:   0.30 - (9 x 0.04)/2  = 0.120   (12.0%)
   L = 4:   0.40 - (16 x 0.04)/2 = 0.080   (8.0%)
   L = 5:   0.50 - (25 x 0.04)/2 = 0.000   (0.0%)
   L = 6:   0.60 - (36 x 0.04)/2 = -0.120  (-12.0%)

Growth peaks around 2.5x and turns negative beyond 5x,
despite every individual year having positive expected return.

This is the same mathematics that underlies the Kelly criterion and that explains why leveraged ETFs decay in choppy markets. It is not a behavioural argument against leverage; it is arithmetic.

Margin calls and liquidation

1. 1

   Maintenance margin is breached

   Your equity falls below the required percentage of the position value, either because the position lost value or because the broker raised requirements.

2. 2

   A call is issued, or not

   Equity brokers may issue a call with a deadline. Futures and crypto venues frequently liquidate automatically with no notice at all.

3. 3

   Positions are closed at market

   The venue closes whatever is necessary at prevailing prices, which during a fast move are the worst prices of the session.

4. 4

   The loss is realised at the worst moment

   Liquidation converts an unrealised loss into a realised one at the point of maximum stress, frequently just before a reversal.

5. 5

   Requirements can rise mid-crisis

   Exchanges and brokers raise margin during volatility, which can force liquidation even if your position has not moved further against you.

Choosing a leverage level

• Derive it, do not choose it. Position sizing from risk percentage and stop distance produces an effective leverage figure. Check that number; do not set it as an input.
• Target volatility instead. Decide the portfolio volatility you want, typically 8 to 15 percent annualised for most individuals, and scale exposure to achieve it. See volatility targeting.
• Account for gaps. Leverage that is fine for normal moves may be fatal across a weekend. Test whether a three-sigma overnight gap would exceed your equity.
• Assume margin requirements can rise. Keep a buffer well above maintenance so that a requirement increase does not force liquidation.
• Apply it at portfolio level. Several individually modest leveraged positions aggregate into a high overall exposure.
• Reduce leverage as volatility rises. Constant notional means rising risk in turbulent conditions, which is the opposite of what you want.