The Arithmetic of Leverage

Whether debt helps or destroys you is not a matter of judgment; it is one equation. If $\text{ROA}$ is the return on the total asset, $r_d$ the after-tax cost of the debt, and $D∕E$ the debt-to-equity ratio, then the return on your own money is:

Everything follows from the sign of the term in parentheses. When the asset out-earns the debt, leverage adds to ROE in proportion to how much you borrowed. When it does not, the same multiplier runs in reverse. There is no third case, and the spread $(\text{ROA}-r_d)$ is usually much smaller and much less certain than the $D∕E$ multiplying it.

Work an example. A rental property returns 7% unlevered, financed 75% at a 6% after-tax mortgage rate, so $D∕E=3$:

A one-point spread became three points of extra return. Now let the property’s return fall to 5% — a soft year, a vacancy, a special assessment:

A two-point decline in the asset produced an eight-point decline in your return. That asymmetry is leverage working exactly as designed, and it is why the same instrument builds fortunes and ends them.

Margin calls: the mechanism that decides when you find out. Losses do not have to reach 100% to wipe you out. With a maintenance margin requirement $m$ ( Regulation T sets an initial requirement of 50%; brokers typically maintain 25–35%), a long position bought at $P_0$ with initial equity fraction $e_0$ triggers a call at:

Buy at $100 with 50% equity against a 30% maintenance requirement and the call arrives at $100\times \frac{0.5}{0.7}=\$71.43$ — a 28.6% decline, well inside a normal correction. At that point you post cash or the broker liquidates at the price the market is offering, which is the defining feature of margin: you lose the ability to wait. An unlevered investor holding the same asset through the same drawdown simply waits for the recovery. Two further pressures arrive at the same moment: the rate on the borrowing is variable and rises in exactly the tightening cycles that produce the drawdown, and meeting the call requires liquidity from somewhere — which, if every asset you hold is falling together, means selling at the bottom.

So run the formula backwards and it becomes a sizing rule. Decide the worst drawdown you must survive without being forced out — for a diversified equity portfolio, history says at least 55% — and solve for the most you may borrow: the call stays below the trough as long as the loan is under $(1-d)(1-m)$ of the position, which at $d=55\%$ and $m=30\%$ is about 31%. Then haircut it, because brokers raise house requirements in exactly the markets where you would need the old ones: borrow no more than 20–25% of a stock portfolio’s value, sized so the margin-call price sits below the worst drawdown you are planning around — not the worst one you remember. The relevant question about leverage is never “what return do I expect” but “what drawdown forces me to sell,” and now you can answer it before the market asks.