The math of leverage: why trading accounts melt so fast

Leveraged accounts melt quickly because leverage does not only magnify price moves; it also magnifies costs, liquidation risk and the compounding effect of consecutive losses by the same factor. Even if the price eventually goes your way, a brief move against you along the way can close the position.

Leverage lets you open a position larger than the collateral (margin) you deposit. With $1,000 of margin and 10x leverage, you carry a $10,000 position. All figures in this article are hypothetical and rounded to keep the math simple.

The core equation: move × leverage

The return on your margin is roughly the price change multiplied by the leverage. The same multiplication also tells you how large an adverse move it takes to wipe out the margin.

The last column is a rough upper bound. The exchange does not wait for the margin to hit zero; it liquidates the position when it falls to the minimum level called maintenance margin. Liquidation is the forced closing of a position whose collateral is no longer sufficient. That is why a 10x position closes in practice on an adverse move somewhat smaller than 10%.

Path dependence: right call, zero result

For an unleveraged buyer, what usually matters is the starting and ending price. For a leveraged position, the path in between matters too.

A hypothetical example: an asset trades at $100, and two people open long positions at the same moment.

• Anna buys without leverage.
• Ben uses 20x leverage; his liquidation level is about $95.50.

The price first drops to $95, then climbs to $110. Anna is up 10%. Ben was liquidated the moment the price touched $95.50; none of the rally that followed belongs to him. They made the same call and got completely different results.

As leverage grows, the liquidation level moves inside the asset's ordinary range of fluctuation. For a hypothetical asset that swings about 3% a day on average, a 5% adverse move is nothing unusual; for a 20x position, it means the entire margin.

Costs are charged on the position

Trading fees and funding payments are charged not on your margin but on the full size of the position. The higher the leverage, the bigger the share of your margin the same rates consume.

Let's calculate with hypothetical rates: a 0.05% fee per trade and 0.01% funding every 8 hours.

• Fees: opening and closing a position costs 0.1% in total. At 10x leverage that is 1% of your margin. Someone who trades 20 times a month hands over roughly 20% of their margin in fees even if the price never moves.
• Funding: three payments a day add up to 0.03% of the position. At 10x leverage that is 0.3% of margin per day, or about 9% over 30 days. Funding is the periodic payment between longs and shorts in perpetual contracts; its direction and size depend on the market, so sometimes you pay and sometimes you receive.

The gap between buy and sell prices (the spread) and fills at a worse price than expected (slippage) are magnified by leverage in exactly the same way.

Losses raise leverage on their own

In a position of fixed size, every loss shrinks your margin while the position stays almost the same. As a result, your effective leverage, the ratio of position size to remaining margin, climbs by itself.

A hypothetical example: $1,000 of margin and a $5,000 position, so 5x. If the price falls 10%, the loss is $500. Remaining margin is $500 and the position is worth $4,500. Effective leverage is now 9x. The next 1% move hits almost twice as hard as it did at the start. The smaller the account gets, the more fragile it becomes.

Consecutive losses also compound multiplicatively. Assume you enter each trade with all remaining margin at the same leverage and cut the loss when the price moves 2% against you:

Five losses in a row are not rare. In a series of 100 trades with a coin-flip 50% chance of winning each one, the probability of seeing at least one streak of five or more losses is about 81%. And for an account that has lost 67% to get back to where it started, it needs a gain of about 205%.

Constant leverage and volatility drag

Some traders resize their positions to their remaining margin every day to keep leverage constant; leveraged products that rebalance daily work in a similar way. In that case even a choppy but sideways market wears the account down.

A hypothetical example: the price rises 10% one day and falls 10% the next.

• No leverage: 1.10 × 0.90 = 0.99, a 1% loss
• Constant 3x: 1.30 × 0.70 = 0.91, a 9% loss
• Constant 5x: 1.50 × 0.50 = 0.75, a 25% loss

Although the price barely moved, constant 5x leverage took a quarter of the account. This is called volatility drag. In this example the loss grows exactly with the square of the leverage: 1% without leverage, 9 times that at 3x, 25 times that at 5x.

Key takeaways

• Leverage magnifies price moves, costs and the compounding of losses by the same factor.
• The adverse move that wipes out margin is roughly 1 ÷ leverage; maintenance margin shortens that distance a little more.
• Being right about direction does not prevent a liquidation caused by a brief move against you along the way.
• Fees and funding are charged on position size; at 10x, small rates can eat a large share of your margin.
• Losses push effective leverage higher, and with constant leverage, volatility drag grows with the square of the leverage.