Leverage: the arithmetic of being wrong

Leverage is any arrangement in which a dollar of your money controls more than a dollar of exposure. A margin loan is leverage; a futures contract is leverage; a fund that promises twice the index's daily move is leverage; a perpetual future at 20× is leverage with a liquidation engine attached. The instrument does not matter much. What matters is one piece of arithmetic that holds for all of them, and this page is mostly that arithmetic.

The recovery table

A loss and the gain that undoes it are not the same size. Lose 10% and you need 11.1% to get back to even; lose 50% and you need 100%; lose 90% and you need 900%. The relationship is gain needed = loss ÷ (1 − loss), and it is the reason the drawdown page says the drawdown is the number that decides whether you survive.

Leverage moves you down that table faster than it moves you up it. A 2× position turns a 25% drawdown in the underlying into 50% in the account, which needs 100% to recover; the same 2× on the way back up only doubles a gain that has to be twice as large to begin with. Every row of that table is a sentence about asymmetry, and leverage multiplies the asymmetry.

A futures contract is leverage, named or not

The desk trades the Micro E-mini S&P 500, which the CME rulebook prices at $5 per index point. With the index near 7,800 (the August 2026 level in the desk's own data) one contract controls about $39,000 of exposure. Tradovate's day-trading margin for it, as the desk read it on Aug 27, 2026, was $50 — which means a trader is allowed to hold $39,000 of S&P 500 exposure on a deposit of roughly one eight-hundredth of it. Nobody has to borrow anything for that to be leverage; the leverage is the ratio of exposure to the money at risk, and here it is enormous. The overnight margin, $2,858 on the same date, is the exchange's own estimate of what a day's move can cost, which is why the margin page exists and why the desk's hands size from the stop, not from the margin. A 20-point adverse move is $100 per contract; on a $5,000 account holding ten contracts because the day margin allowed it, that routine move is 20% of the account, and the table above says what 20% costs to earn back.

The honest framing is not "futures are leveraged, be careful." It is that a futures account's leverage is whatever the trader sets it to by choosing the contract count, and the only sane way to choose it is backwards from the stop — the sizing page is the arithmetic. The margin tells you what the broker will let you do; it tells you nothing about what you can afford.

The product that loses on a flat market

A leveraged fund promises a multiple of the index's daily move, and resets every day. The SEC's investor bulletin on these products works a two-day example: an index at $1,000 falls 10% to $900, then rises 10% to $990 — down 1% over the two days. A 2× fund falls 20% to $800 and then rises 20% to $960 — down 4%. The index lost 1%; the fund lost 4%. Over longer stretches the bulletin gives real cases without naming them: over four months in which "a particular index gained 2 percent," a 2× fund on it "fell by 6 percent" and a −2× fund "fell by 25 percent"; over the same period a 3× fund on another index "fell 53 percent" while that index "actually gained around 8 percent," and the −3× fund "declined by 90 percent." The mechanism is the daily reset compounding against volatility, and it is not a defect; it is what the product is. A daily-reset fund is a one-day instrument, and anyone holding it for a month is holding a different bet than the one on the label.

What a margin agreement actually says

In a stock account, Regulation T lets a customer borrow up to half the purchase price — the initial requirement "is 50 percent of the current market value" — and FINRA's maintenance requirement for long equity "is generally 25 percent of the current market value," checked daily; brokers set their own house requirements above that. The part that matters is in the disclosure every margin customer signs, FINRA Rule 2264, and it is worth reading in the broker's words rather than the trader's: "The firm can force the sale of securities or other assets in your account(s)"; "The firm can sell your securities or other assets without contacting you"; "You are not entitled to choose which securities or other assets in your account(s) are liquidated"; "The firm can increase its 'house' maintenance margin requirements at any time" without advance written notice; "You are not entitled to an extension of time on a margin call."

A futures account is sharper still. There is no loan, so there is no call in the stock sense: when the account's equity falls below the maintenance level the broker liquidates, and the margin page describes the March 2020 case in which the exchange nearly doubled the requirement in three weeks. Leverage is not only a multiplier on your losses; it is a transfer of the decision about when you lose from you to the broker, at the moment you can least afford the broker to decide.

Why the optimal bettors stop short

If leverage were simply bad, the answer would be zero and the page would be shorter. It is not; it is a dial, and there is a theory of where to set it. Kelly's 1956 result gives the fraction of a bankroll to risk that maximises the long-run growth rate of the bankroll, and Thorp — who used it at the blackjack table and then in the stock market — spent much of his 2006 paper on why practitioners bet less than that fraction. The full Kelly bet maximises growth, but with swings most people cannot live through. Thorp's figures: at full Kelly the probability of doubling before halving is only 2/3, and "the chance of ever losing half the starting capital is 1/2 for f = f but only 1/8 for f = f/2." Half Kelly gives up a quarter of the growth rate ("g(f/2) = .75 g(f)") for that safety, and Thorp reports that most people "strongly prefer the increased safety and psychological comfort of 'half Kelly.'" The second reason is the one that applies to every backtest on this site: the edge the formula takes as given is an estimate, estimates of an edge are "more likely to be too high than too low," and "using too large an f and overbetting is much more severely penalized than using too small an f and underbetting." The true optimum is smaller than the computed one, and nobody knows by how much; that is where the people who solved the problem actually sit. The desk's sizing page lands in the same place from the other direction: 0.5% to 2% of the account per trade, sized from the stop, is a fraction of what any backtest's edge would permit, on purpose.

Where the desk stands

Every figure the desk publishes is hypothetical and before costs of leverage the reader might choose to add; the desk's hands trade one contract per slot by default and the configurator shows what more would have done, on the ledger, with the drawdown beside the return. A member who wants to know how much leverage a strategy can carry has the wrong question; the right one is how much drawdown they can carry, and the table at the top of this page converts one into the other.

• Position sizing from the stop, not the account
• Drawdown is the number that decides whether you survive
• How to read a track record (and the ten ways it lies)

← Risk, the common thread · All of Learn