Which position sizing method should I actually use?

For most people: fixed-fractional at 1-2% risk per trade. For systematic strategies with well-estimated edge: half-Kelly. Full Kelly and Optimal-f are theoretically optimal but punishing in practice because they assume your inputs are exactly right. They aren't.

What is the Kelly criterion?

Kelly (1956) is the bet sizing rule that maximizes the long-run growth rate of capital. For a discrete bet: f* = (p·b − q) / b, where p is win probability, q is loss probability, b is the odds (win/loss ratio). For continuous returns: f* = μ/σ². The intuition: bet more when edge is bigger, less when variance is bigger.

What is Optimal-f and how is it different from Kelly?

Optimal-f (Vince, 1990) is the bet size that maximizes terminal wealth assuming the WORST historical loss is the bound on a single trade. Where Kelly uses probability distributions, Optimal-f uses one extreme observation. This makes it more aggressive than Kelly — and more dangerous if the worst loss in your sample isn't actually the worst possible loss.

What is fixed-fractional position sizing?

Fixed-fractional risks a constant percentage of account equity on every trade — typically 1% to 2%. Position size = (account × risk%) / |entry − stop|. Simple, robust, and the worst-case loss is bounded at the percentage you chose. The standard recommendation for non-quantitative traders.

Why is full Kelly considered too aggressive?

Full Kelly is optimal IF your edge estimate is exactly right. If you overestimate edge by 20% (very common with real strategies), full Kelly bets ~40% more than it should. The result: drawdowns of 30-50% are routine, drawdowns of 70%+ happen occasionally, and recovery from those is psychologically devastating even when mathematically possible.

What is the practical decision rule for choosing between them?

Discretionary trading or untested system → fixed-fractional 1-2%. Systematic strategy with 200+ live trades and Sharpe > 1.0 → half-Kelly. Allocator-level portfolio with multiple uncorrelated strategies → Kelly-per-strategy capped at fractional Kelly aggregate. Optimal-f → almost never; use only with explicit overrides on the worst-loss assumption.

Can Kelly recommend a NEGATIVE bet?

Yes. If your edge is negative (expected loss per trade), Kelly returns a negative fraction. The correct action is f* = 0 — do not bet. Some practitioners interpret negative Kelly as "bet against this strategy" (short it), which is correct in symmetric markets but dangerous because the strategy you discovered is losing might be losing for non-stationary reasons that flip.

How does correlation affect Kelly when sizing multiple strategies?

Kelly was derived for a single bet. For a portfolio of correlated strategies, naive Kelly per strategy aggregates to over-betting. The correct multivariate form solves f* = Σ⁻¹·μ (covariance matrix inverse times expected returns). Practically: compute Kelly per strategy independently, then scale ALL strategies by a single fractional-Kelly factor so the aggregate position never exceeds your risk budget.

What about flat percent position sizing — like "always 10% of account per trade"?

That is fixed-PERCENT position sizing (a.k.a. fixed-dollar-percent), NOT fixed-fractional. The difference: fixed-percent doesn't account for the stop distance, so a 10% position with a 50% stop is risking 5% of account while a 10% position with a 5% stop is risking 0.5%. Always use fixed-FRACTIONAL (risk-based) not fixed-percent (notional-based) unless you have specific reasons.

Is there a calculator for these?

Yes. The QuantOracle Kelly Criterion Calculator gives full Kelly, half-Kelly, and quarter-Kelly fractions for any win rate and payoff ratio. The Position Size Calculator does fixed-fractional sizing given account size, risk %, entry, and stop. Optimal-f isn't separately calculated because most practitioners avoid it; if you want it, run Kelly and Optimal-f is approximately 1.0 - (1 - Kelly)^k for some scaling factor depending on your loss distribution.

Kelly vs Fixed Fractional vs Optimal-f: Which Position Sizing Method?

Use…	When…	Watch out for…
Fixed-fractional	Discretionary trading / untested system / unknown edge	Doesn't optimize growth; capped upside
Half-Kelly	Systematic strategy with 200+ trades and stable edge	Still drawdown-heavy if edge is overestimated
Full Kelly	Theoretical analysis / closed-form derivations only	30-50% drawdowns are normal even with correct inputs
Optimal-f	Almost never — best used to sanity-check Kelly	Anchors on one extreme observation; usually over-bets

What each method optimizes

Position sizing has one job: decide how much of your account to put at risk on each trade. The three methods below answer the same question but with different objectives. The objective you pick determines how aggressive the answer is.

Fixed-fractional: bound the worst case

position size = (account × risk_pct) / |entry − stop|

Fixed-fractional risks a constant percentage of equity per trade — usually 1% to 2%, the "1% rule" popularized by Van Tharp. It does not optimize anything in particular; it just guarantees that no single loss exceeds the fraction you chose. Over time the account compounds because the dollar risk scales with equity. Simple, robust, predictable drawdown behavior.

Kelly: maximize the long-run growth rate

f* = (p · b − q) / b (discrete) or f* = μ / σ² (continuous)

Kelly (J. L. Kelly Jr., Bell System Technical Journal, 1956) is the fraction that maximizes the expected logarithm of wealth — equivalent to maximizing the long-run geometric growth rate of the account. It is provably optimal in the limit of infinite trials. The path to that infinity includes drawdowns that most investors cannot stomach.

Optimal-f: maximize terminal wealth assuming worst-case bound

find f that maximizes Σ ln(1 + f · return_i / |worst_loss|)

Optimal-f (Ralph Vince, "Portfolio Management Formulas", 1990) finds the bet size that maximizes terminal wealth, anchoring on the worst single loss in your sample. It is essentially Kelly recast to use one extreme observation rather than a distribution. Usually more aggressive than Kelly. Dangerous because you're betting that the worst loss in your sample is actually the worst possible loss. It almost never is.

A concrete example: 55% win rate, 1.5:1 payoff

A strategy wins 55% of the time. Average win is $150, average loss is $100 (1.5:1 payoff ratio). Worst single loss in 500 historical trades was $400. What does each method recommend for a $100,000 account?

Method	Risk per trade	Position size (% of $100K)	Expected drawdown
Fixed-fractional (1%)	$1,000	10× position with $100 stop	~10-15%
Fixed-fractional (2%)	$2,000	20× position with $100 stop	~20-30%
Half-Kelly	~$12,500	12.5% of account	~25-35%
Full Kelly	~$25,000	25% of account	~45-60%
Optimal-f (worst=$400)	~$32,000	32% of account	~55-70%

Same strategy, dramatically different bet sizes. Kelly says bet 25% of the account on a trade with 55% win probability. That feels insane to most traders — and it should, because it is, unless your edge estimate is perfect. Which it is not.

When each one over-bets (and how badly)

Full Kelly: doubles risk when edge is overestimated 20%

Kelly is optimal when your edge estimate is exactly right. The relationship between estimation error and over-bet is convex:

Edge overestimated by 10% → Kelly over-bets by ~20%, growth rate halved
Edge overestimated by 20% → Kelly over-bets by ~44%, growth rate goes to zero
Edge overestimated by 30% → growth rate becomes negative

Most retail strategies overestimate edge by 30-50% due to overfitting, survivorship bias, and look-ahead bias in backtests. Plugging an overestimated edge into Kelly is a fast way to lose money fast.

Half-Kelly: the practical compromise

Half-Kelly (50% of full Kelly fraction) captures about 75% of the long-run growth advantage with about a quarter of the drawdown. The math: long-run growth rate is quadratic around the optimum, so deviating by 50% from optimal sacrifices much less than 50% of the growth.

Most quant funds with stable edge use half-Kelly or quarter-Kelly at the strategy level. Renaissance Technologies famously sizes at fractional Kelly, never full. If they don't trust their own edge estimates that much, you shouldn't either.

Optimal-f: anchored on one observation

Optimal-f's denominator is the single worst historical loss. If the actual worst possible loss is 2x what your sample contains — and tail observations are routinely larger than sample maxes — Optimal-f recommends a bet that is too big by exactly that factor. When the new worst loss arrives, the over-bet eats the entire account.

A common Optimal-f failure mode: the strategy ran in a calm regime for 18 months, the worst loss in sample was 1%, Optimal-f sized at 30% of account per trade. The first regime change brought a 3% loss. Account down 90%. This pattern shows up in retail trading forums every few years.

The half-Kelly trick (why almost everyone uses it)

Half-Kelly (f = 0.5 · f*) is the de facto industry standard for systematic strategies. The reasons:

Robust to estimation error. If your edge estimate is 20% too high, half-Kelly is still safely sub-optimal rather than catastrophically over-betting.
Captures most of the growth. Geometric growth is concave around the Kelly optimum — losing 50% of position size sacrifices only ~25% of long-run growth.
Much smaller drawdowns. Full Kelly typically has 50%+ drawdowns; half-Kelly typically has 25-30%. The psychological difference is enormous.
Survivorship. The trader who size with half-Kelly is still trading after a year. The trader who used full Kelly may not be.

Some shops go further to quarter-Kelly (0.25 · f*) for strategies with shorter live history, less confidence in the input distribution, or higher fat-tail risk. The QuantOracle Kelly Criterion Calculator shows full, half, and quarter-Kelly side by side for exactly this reason.

The decision rule

Discretionary trader or untested system → fixed-fractional 1-2% per trade. Use the position size calculator. Don't complicate it.
Systematic strategy with 200+ live trades and Sharpe > 1.0 → half-Kelly at the strategy level. Use the Kelly criterion calculator to find f*, then bet 0.5·f*.
Portfolio of multiple uncorrelated strategies → compute Kelly per strategy, then scale all strategies by a single fractional-Kelly multiplier so the aggregate gross exposure stays bounded.
You're not sure about your edge → fixed-fractional. Default to robust. Move to Kelly only after live evidence justifies the upgrade.

Related calculators

Kelly Criterion Calculator — full / half / quarter-Kelly fractions for any win rate and payoff
Position Size Calculator — fixed-fractional sizing given account, risk %, entry, and stop
Drawdown Calculator — verify your sizing choice against historical drawdown
Monte Carlo Simulation Calculator — simulate the path distribution at different position sizes before committing

References

Kelly Jr., J. L. (1956). "A new interpretation of information rate." Bell System Technical Journal, 35(4), 917-926.
Thorp, E. O. (1962). "Beat the Dealer." Random House. — first practical application of Kelly.
Vince, R. (1990). "Portfolio Management Formulas." John Wiley & Sons. — Optimal-f introduction.
Van Tharp, V. K. (1998). "Trade Your Way to Financial Freedom." McGraw-Hill. — popularized the 1% rule for fixed-fractional sizing.
MacLean, L. C., Thorp, E. O., & Ziemba, W. T. (2010). "The Kelly Capital Growth Investment Criterion." World Scientific. — survey of fractional-Kelly practice.

Kelly vs Fixed Fractional vs Optimal-f: Which Position Sizing Method Should You Use?

The 30-second answer