Leverage and Margin

Leverage is investing with borrowed money so that a small amount of your own capital controls a larger position. If you put up $10,000 of your own and borrow another $10,000 to buy $20,000 of stock, you are "2x levered." The appeal is obvious: your gains are calculated on the full $20,000, not just your $10,000, so a good move pays double. The catch is exactly as obvious once you see it, your losses are also calculated on the full $20,000. Leverage does not change whether a bet is good; it just turns up the volume on the outcome, in both directions.

Returns get multiplied

Define leverage $L$ as the ratio of your total position to your own equity. With no borrowing $L = 1$; borrow an equal amount and $L = 2$. Ignoring borrowing costs for a moment, your equity return is simply the asset's return scaled by $L$:

$$r_{\text{equity}} = L \times r_{\text{asset}}.$$

So at $L = 2$, a $+10\%$ move in the asset becomes a $+20\%$ return on your money, and a $-10\%$ move becomes $-20\%$. The line relating the two just gets steeper as $L$ rises, the same slope on the way up and on the way down.

Margin: the collateral leash

To lend you money, a broker demands collateral, your own equity in the position, and sets rules on how thin it can get. Two thresholds matter. The initial margin is the minimum equity fraction to open the trade (often 50% for stocks, i.e. up to $L = 2$). The maintenance margin is the lower fraction (say 25%) you must keep as the position moves. Your equity in the position at any time is

$$\text{equity} = \text{position value} - \text{loan}.$$

When a losing move drives equity below the maintenance requirement, you get a margin call: post more cash immediately, or the broker liquidates your position, often at the worst possible price. This forced selling is what turns leverage from merely risky into genuinely dangerous, it can wipe you out on a move that would have been survivable unlevered.

Worked example

You put up $10,000, borrow $10,000, and buy $20,000 of stock ($L = 2$). Maintenance margin is 25%.

• Stock rises 10% to $22,000. Repay the $10,000 loan and your equity is $12,000, a $+20\%$ return on your $10,000. Double the asset's move, as promised.
• Stock falls 10% to $18,000. Equity is $8,000, a $-20\%$ return. Also doubled.
• How far can it fall before a margin call? You need $\text{equity} / \text{position} \ge 25\%$. With position value $20{,}000(1 + r)$ and loan $10,000,

$$\frac{20{,}000(1+r) - 10{,}000}{20{,}000(1+r)} \ge 0.25 \;\Longrightarrow\; 20{,}000(1+r) \ge \frac{10{,}000}{0.75} = 13{,}333.$$

That gives $1 + r \ge 0.667$, i.e. a drop of about 33% triggers the call. An unlevered holder shrugs off a 33% dip and waits for recovery; the levered holder is forced to sell at the bottom and locks in the loss.

Common pitfalls

• Leverage does not improve a bad bet. It scales expected return and risk by the same $L$, so it leaves the risk-adjusted return (the Sharpe ratio) unchanged, minus borrowing costs, which make it slightly worse.
• Volatility compounds against you. Because losses hurt more than equal gains help (a $-50\%$ then $+50\%$ leaves you down 25%), high leverage on a bouncy asset can bleed capital even when the asset ends flat. Higher Volatility plus leverage is a slow leak.
• The margin call is path-dependent. You can be right about where the price ends up and still be liquidated by a temporary dip along the way. Sizing to survive the path, not just the destination, is the heart of position sizing and the Kelly criterion.
• Borrowing costs are real. The interest on the loan is subtracted from every outcome, so leverage only pays if your expected return comfortably exceeds the borrow rate.