Kelly criterion position sizing: full, half or fixed risk on futures?

Contents

1. Should you size futures trades with the Kelly criterion?
2. How do you calculate the Kelly fraction and half Kelly?
3. Why does full Kelly produce such deep drawdowns?
4. How do you estimate the win rate and payoff that go into Kelly?
5. How does fixed fractional sizing differ from Kelly?
6. How do you convert a Kelly fraction into futures contracts?
7. How do nine sizing methods change the same ES trades?
8. Frequently asked questions
9. References

Should you size futures trades with the Kelly criterion?

Kelly criterion position sizing gives the fraction of capital that grows an account fastest in theory. On futures, treat that fraction as a ceiling, not a target. Win rate and payoff come from a limited trade sample, so the true edge is uncertain, and margin caps the contract count. Most systematic traders size at half Kelly or less, or at a fixed 1 to 2 percent of equity per trade.

The Kelly criterion is a formula, published by John Kelly in 1956, that converts a win rate and a payoff ratio into the fraction of capital to risk on each bet so that the long-run growth of the capital is as high as it can be. It assumes the win rate and payoff are known exactly and that you can bet any fraction you like. Neither holds for a futures trader. Your win rate is an estimate from a trade list, and you can only trade whole contracts up to what your margin allows. In AlphaPrime (Valynox), that trade list comes from backtests that charge commission and slippage on every trade, so the win rate you read is already after costs. The leverage already built into a futures contract adds a second layer, which how margin changes backtest drawdown covers in detail.

So the practical use of Kelly is as a bound. The argument of this article is simple: the full Kelly number is the most you should ever risk, half Kelly is a sensible upper limit for a tested strategy, and a fixed fraction of equity that you choose yourself, checked against that limit, is what most traders should actually run.

How do you calculate the Kelly fraction and half Kelly?

The Kelly fraction is the win rate minus the loss rate divided by the payoff ratio, and half Kelly is simply that number divided by two. Before working through the arithmetic by hand, you can put your own win rate and payoff into the free Kelly criterion calculator and read both numbers off directly.

Two inputs are needed. The win rate is the share of closed trades that ended with a profit after costs. The payoff ratio is the average winning trade divided by the average losing trade, both after costs. The formula itself:

f = p − (1 − p) ÷ b

Here f is the fraction of capital to risk on one trade, p is the win rate written as a decimal, (1 − p) is the loss rate, and b is the payoff ratio. If the formula gives zero or a negative number, the rule has no edge at these inputs and the right size is zero. The same two inputs give the expectancy per trade, which the free win rate and expectancy calculator computes; a negative expectancy and a zero or negative Kelly fraction are the same message in two forms.

Note what the 25 percent means. It is the share of the account you would lose if the trade hits its full loss. It is not the margin used or the notional value of the position. That distinction matters when the fraction is turned into contracts later.

Why does full Kelly produce such deep drawdowns?

Full Kelly sits exactly on the peak of the growth curve, where any overestimate of the edge pushes you down the far side and where a normal losing run cuts the account roughly in half. Picture a hill. The height is the long-run growth rate of the account, and the distance along the ground is the fraction risked per trade. At zero risk there is no growth. Growth rises to its highest point at the Kelly fraction. Past that point it falls, and at twice the Kelly fraction the long-run growth is zero even though every single trade still has a positive edge. Beyond twice Kelly the account shrinks over time.

Two things follow from the shape of that hill:

1. Standing on the peak leaves no room for error. Suppose your trade list says full Kelly is 25 percent, but the true edge, which you cannot see, is only 15 percent. Risking 25 percent puts you at about 1.7 times the true Kelly, close to the zero-growth point. Risking half Kelly, 12.5 percent, keeps you below the true peak, still growing.
2. The peak is a rough place even when the inputs are right. At full Kelly, the account swings in proportion to the fraction risked, and losing half of it at some point is an ordinary event in the mathematics, not a rare one. At half Kelly, the swings are much smaller, and the growth rate is still about three quarters of the peak. Giving up one quarter of theoretical growth to cut the drawdowns by far more than that is the trade most traders accept.

How do you estimate the win rate and payoff that go into Kelly?

Win rate and payoff come from a backtest trade list after commission and slippage, and with a short list they are estimates with a wide band, so the Kelly fraction built from them is a range, not a point. To show what the raw material looks like, the box below is a real run. It tested a stand-in rule, not Kelly itself: a single-contract Parabolic SAR rule as the only entry and exit, long and short, on ES daily bars from 2019-01-02 to 2025-06-30. It is the candidate the search kept out of 1,024 it tried, picked for its return against its drawdown. Picking the kept candidate after the fact flatters it; none of these numbers is a result a reader can expect, and the rule did not earn this money in any live account.

A report that shows a profit factor rather than a payoff ratio still gives you what you need. The profit factor is gross profit divided by gross loss. Dividing it by the ratio of winning trades to losing trades turns it into the payoff ratio. In the box above, 51 trades is the number that decides how much to trust the rest. In AlphaPrime, the trade list inside the Performance Report is where you count completed trades and read the average win and average loss after costs before you put either number into a Kelly formula.

Two further corrections apply. First, the candidate above is the best of a large search, and Bailey, Borwein, López de Prado and Zhu (2014) show that the best backtest in a search is inflated by the selection itself, so its win rate should be read as an upper estimate. Second, you can measure the band directly by resampling the trade list many times with replacement, the bootstrap method of Efron (1979), and reading the spread of Kelly fractions that comes out. Both corrections push the usable fraction down, which is why half Kelly, or less, is the working limit.

How does fixed fractional sizing differ from Kelly?

Fixed fractional sizing risks a percent of current equity that you choose, set through the stop distance, while half Kelly is an upper limit derived from win rate and payoff. Fixed fractional sizing is a method that risks the same chosen share of the current account on every trade, commonly 1 to 2 percent, so that the contract count rises as the account grows and falls as it shrinks. Its inputs are the current equity and the distance to the stop. It needs no win rate and no payoff, which is why it is less sensitive to estimation error.

Aspect	Fixed fractional risk	Half Kelly	Full Kelly
Inputs needed	Stop distance and current equity	Win rate and payoff ratio	Win rate and payoff ratio
Who sets the fraction	The trader chooses, commonly 1 to 2 percent	Derived from the trade list, used as an upper limit	Derived from the trade list
Size after a losing run	Shrinks with equity	Shrinks with equity and with the re-estimated edge	Shrinks with equity and with the re-estimated edge
Sensitivity to estimation error	Low	Medium	High
Drawdown depth	Small at 1 to 2 percent; deep at a high percent	Medium	Deep

The last row is the one to remember. Fixed fractional sizing is not safe by nature; it is exactly as safe as the percent you pick. At 1 percent the swings are small. At 10 or 20 percent per trade it behaves like full Kelly or worse. The backtest table in the last section uses the report's default percent for its fixed fractional row, and that default sits well above the 1 to 2 percent most traders use. It is a default setting, not a recommendation.

The two methods combine naturally. Run a fixed fraction you are comfortable with, then compare it with half Kelly from your trade list. If your fixed fraction is below half Kelly, keep it. If it is above, your chosen percent exceeds what even an optimistic read of the edge supports, so cut it. The rule is "fixed fraction, capped at half Kelly".

How do you convert a Kelly fraction into futures contracts?

Contracts equal the chosen fraction of equity divided by the dollar risk per contract, rounded down and then capped by available margin. The dollar risk per contract is the stop distance in points multiplied by the point value. The point value is the dollar change in one contract when the index moves one full point. For the E-mini S&P 500 (ES) it is $50 per point; for the Micro E-mini (MES) it is $5 per point. Exchanges can change these values, so confirm them on the exchange's contract page or with the free futures contract calculator before you size anything.

1. Pick the fraction. Half Kelly from the trade list, or your fixed percent, whichever is lower.
2. Multiply by current equity. This is the dollar amount you accept losing if the stop is hit.
3. Work out the dollar risk per contract. Stop distance in points times the point value. How to set that distance, whether in fixed ticks, from volatility, by time or with a trailing rule, is the subject of fixed, ATR, time or trailing stops for futures strategies.
4. Divide and round down. A fraction of a contract cannot be traded, and rounding up overshoots the fraction you chose.
5. Cap by margin. The contract count times the margin per contract must fit inside the equity you can commit, with room left for the drawdown.

The free position size calculator runs steps two to four from your account risk and stop distance. A strategy with no stop, like the stand-in rule in the box above, has no step three; its risk per contract is whatever the exit rule allows, which is one more reason to read its Kelly fraction with care.

How do nine sizing methods change the same ES trades?

With the same 51 trades and only the contract count changed, the result spreads from $55,293 to $748,568 in net profit and from $120,885 to $702,810 in maximum drawdown, and the two rise together. The box below takes the Parabolic SAR stand-in trades from the earlier box, ES daily bars from 2019-01-02 to 2025-06-30, the one candidate kept out of 1,024 tried, and runs them under nine money-management methods with $100,000 of capital and at most 10 contracts. Every entry and exit is identical across the rows. Each method uses the report's default settings. Every difference between rows comes from sizing alone, and the after-the-fact pick of this candidate flatters every row equally; none of it is a result a reader can expect.

Read the two highlighted rows together. The Kelly row averages 1.22 contracts, which is what the report's default way of computing the Kelly size produced under this capital and this contract cap, and it shows the smallest net profit with a drawdown of $146,760. The fixed fractional risk row averages 5.92 contracts, almost five times as many, and shows $748,568 of net profit against a $702,810 drawdown. Same trades, same dates, same exits. Only the size changed, and profit and drawdown scaled up together. Several rows show a drawdown larger than the $100,000 starting capital, which is possible only because equity had grown first; in dollars, that is the fall the trader would have had to sit through.

The lesson is not that one row is the right method. It is that sizing does not change whether a rule has an edge; it only chooses how far up the growth hill you stand and how deep the valley beside it is. A sizing method cannot rescue a rule with no edge, and an aggressive one turns a modest edge into an account-threatening drawdown.

What to do next: export the trade list of a strategy you already trust, count its completed trades, compute full and half Kelly from its after-cost win rate and payoff, and then rerun the same trades at a fixed 1 percent of equity and at half Kelly. Put each of the two equity series into the free drawdown calculator and compare the two maximum drawdowns in dollars against the account you actually have. The lower of the two fractions that you could sit through without closing the account is your size.

Frequently asked questions

How do you calculate half Kelly?

First compute the full Kelly fraction: win rate minus the loss rate divided by the payoff ratio, where the payoff ratio is the average win divided by the average loss after costs. Then divide the result by two. A 55 percent win rate with a payoff ratio of 1.5 gives a full Kelly of 25 percent and a half Kelly of 12.5 percent. Half Kelly keeps about three quarters of the theoretical growth rate with much smaller swings.

Why does full Kelly produce such large drawdowns?

Full Kelly is the fraction at the very top of the growth curve, so any overestimate of the edge moves you onto the falling side, where growth drops and reaches zero at twice the Kelly fraction. Even with exact inputs, the account swings in proportion to the fraction risked, and losing half of it at some point is an ordinary outcome. Win rate and payoff from a short trade list are rarely exact, which is why traders size below the full fraction.

How do I estimate the win rate and payoff ratio for Kelly?

Take them from a backtest trade list after commission and slippage: the win rate is the share of profitable closed trades, and the payoff ratio is the average win divided by the average loss. With only a few dozen trades, the win rate has a wide uncertainty band and the Kelly fraction swings with it, so treat the result as a range. Resampling the trade list many times gives a picture of that range, and the best candidate from a large search should be read as an optimistic estimate.

How do I convert a Kelly fraction into futures contracts?

Multiply the chosen fraction by current equity to get the dollars at risk, then divide by the dollar risk per contract, which is the stop distance in points times the point value. Round down to a whole number of contracts, then check that the contracts fit inside the margin you can commit. On ES the point value is $50 and on MES it is $5, so the micro contract allows a small account to hold a low fixed fraction without rounding down to zero.

Is fixed fractional sizing safer than Kelly?

Only if the chosen percent is low. Fixed fractional sizing risks a set share of current equity per trade, commonly 1 to 2 percent, and its drawdown depends entirely on that share; at a high percent it behaves like full Kelly or worse. A practical rule is to run a fixed fraction you can live with and cap it at half Kelly computed from your trade list.

References

• Kelly, J. L. (1956). A New Interpretation of Information Rate. Bell System Technical Journal, 35(4), 917–926.
• Bailey, D. H., Borwein, J., López de Prado, M., & Zhu, Q. J. (2014). Pseudo-Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-of-Sample Performance. Notices of the American Mathematical Society, 61(5), 458–471.
• Efron, B. (1979). Bootstrap Methods: Another Look at the Jackknife. The Annals of Statistics, 7(1), 1–26.