Financial Leverage

Leverage — gearing, in the British phrase — is buying with borrowed money so that the returns on the whole asset accrue to your smaller slice of equity. You already use it in more places than you may realize: a mortgage is leverage on a house, a business that borrows is leverage on its equity, a company with heavy fixed costs is leverage on its revenue, and options and futures are leverage with the borrowing built into the price. This section is the mathematics that all of those share.

Three properties make debt worth the trouble when it is worth the trouble:

Return on Equity (ROE)

Leverage raises ROE by allowing you to control a larger asset base with a smaller amount of equity — when the spread cooperates, per the arithmetic below.

Tax Deductibility –- Conditionally

For an individual, non-deductible is the default: IRC §163(h) disallows personal interest outright, and every deduction is an exception you must qualify for — qualified residence interest, investment interest against net investment income, business interest. The full inventory of the exceptions, their caps, and the IRC §265 municipal-bond trap lives in the taxation chapter (section “Tax Deductions of The Mortgage Interest”); the planning point here is only that the after-tax cost of debt $r_d$ in the formula below depends on which exception, if any, you qualify for.

Capital Efficiency

Leverage lets you hold a target asset without liquidating another. The clearest case is borrowing against a portfolio instead of selling it, which avoids realizing a gain — though that is a tax deferral bought with real interest expense and substantive margin risk, not a costless lunch.