Kelly criterion position sizer (trader edition)
The Kelly criterion is the mathematically optimal bet size that maximises long-run log-equity growth given your edge. Full Kelly maximises growth but produces high drawdowns. Half Kelly and quarter Kelly are the institutional-standard reductions. Calculator below computes all three from your win rate and reward-to-risk ratio. AUD-native.
Calculator
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What is the Kelly criterion?
The Kelly criterion is a position-sizing formula that answers a single question: given a bet with known win probability and reward-to-risk ratio, what fraction of capital should be wagered to maximise long-run geometric (compounded) growth?
John Larry Kelly Jr. derived the formula at Bell Labs in 1956 while working on information theory. The original paper, A New Interpretation of Information Rate, applied the math to gambling on horse races but the formula generalises to any sequence of independent positive-expectancy bets, including financial trading.
The criterion is foundational to institutional money management. Major hedge funds, prop trading desks, and quantitative funds use Kelly variants as the upper bound on position sizing. Edward Thorp applied Kelly to blackjack card counting in the 1960s and later to his hedge fund Princeton Newport Partners with documented success.
The retail trading community knows the formula exists but rarely applies it correctly because:
- Estimating win rate and R:R requires a documented track record; most retail traders do not have one.
- Full Kelly produces drawdowns most retail traders cannot psychologically tolerate.
- Fractional Kelly (half, quarter) is the practical standard but rarely communicated as such in retail content.
The Kelly formula
Where p is win probability (as decimal), q = 1 - p is loss probability, and b is the reward-to-risk ratio.
The output f* is the fraction of capital to risk on each independent bet. For example, a trader with a 55 percent win rate and 1.5:1 reward-to-risk has:
f* = (1.5 × 0.55 - 0.45) / 1.5 = (0.825 - 0.45) / 1.5 = 0.375 / 1.5 = 0.25 or 25 percent of capital per trade.
This means full Kelly says to risk 25 percent of equity on every trade. The growth rate at full Kelly is:
G(f*) = p × ln(1 + f* × b) + q × ln(1 - f*) = 0.55 × ln(1.375) + 0.45 × ln(0.75) = 0.55 × 0.318 - 0.45 × 0.288 = 0.046 or roughly 4.6 percent equity growth per trade in geometric terms.
Spectacular on paper. In practice, full Kelly at 25 percent risk per trade produces equity curves with drawdowns frequently exceeding 50 percent. Most traders cannot psychologically run a strategy with that volatility, even if the long-run growth is mathematically optimal.
Why fractional Kelly is the standard
The institutional standard is half Kelly. Quarter Kelly is the conservative variant. The math behind the reduction:
- Half Kelly preserves approximately 75 percent of full Kelly's growth. Because growth is a concave function of bet size, the marginal growth lost at half Kelly is small while the drawdown reduction is large.
- Half Kelly cuts drawdowns by roughly 75 percent. Drawdown is approximately linear in bet size in the small-bet regime. Halving the bet halves the drawdown to first order, and the variance compounds favourably.
- Quarter Kelly accommodates edge-estimation error. Real win rate and R:R estimates carry standard error. Quarter Kelly leaves enough margin that even a 50 percent over-estimate of edge still produces positive growth.
The trade-off is straightforward: full Kelly is the growth-maximising bet size assuming perfect edge knowledge. Half Kelly is the growth-near-maximising bet size that survives realistic edge uncertainty. Quarter Kelly is the practical retail upper bound. Below quarter Kelly the math says you are leaving growth on the table; above half Kelly you are betting more than the institutional standard.
Worked example
Two Australian traders, same account, different documented edges. Both have AUD 10,000 accounts.
Trader A: 250 trades, 52 percent win rate, average winning trade 1.3R, average losing trade 1.0R.
Kelly: f* = (1.3 × 0.52 - 0.48) / 1.3 = (0.676 - 0.48) / 1.3 = 0.196 / 1.3 = 15 percent.
Full Kelly = 15% (AUD 1,500 per trade). Half Kelly = 7.5% (AUD 750). Quarter Kelly = 3.75% (AUD 375).
The institutional recommendation is half Kelly: risk AUD 750 per trade on a AUD 10,000 account. Note this is far higher than the typical retail "1 to 2 percent" rule. The retail rule is overly conservative for a documented positive edge but is appropriate when edge is uncertain.
Trader B: 250 trades, 58 percent win rate, average winning trade 0.9R, average losing trade 1.0R.
Kelly: f* = (0.9 × 0.58 - 0.42) / 0.9 = (0.522 - 0.42) / 0.9 = 0.102 / 0.9 = 11.3 percent.
Despite the higher win rate, Trader B's lower R:R produces a smaller Kelly fraction. Half Kelly = 5.7% (AUD 565). The reward-to-risk ratio matters more than win rate above the 50 percent threshold.
Where Kelly breaks down
Kelly assumes several conditions that real trading violates:
- Constant edge. Real trading edges drift with market regime, strategy decay, and trader fatigue. Kelly oversizes when edge degrades. Half or quarter Kelly leaves variance buffer.
- Accurate edge knowledge. Kelly assumes you know p and b precisely. In reality you estimate them from a finite sample. Sampling error means the true Kelly may be lower than the estimated Kelly.
- Independent trade outcomes. Kelly assumes trades are independent draws. In trend-following or momentum strategies, returns are serially correlated, which violates the independence assumption and inflates effective variance.
- Fixed reward-to-risk. Kelly assumes every winning trade is exactly bR and every losing trade is exactly -1R. Real trades have variable outcomes around these averages, which increases variance and reduces the safe bet size below the analytical Kelly.
These limitations are why fractional Kelly is the practical standard. Full Kelly is the theoretical maximum under idealised conditions. Half or quarter Kelly is the operational sizing that survives reality.
Related tools
- Risk of Ruin Calculator - probability of blowing up the account at a given bet size. Pairs with Kelly: Kelly sets the upper bound, risk of ruin tells you the survival probability at that bound.
- Expectancy + Profit Factor Calculator - the pre-step before Kelly: confirm your edge is positive before sizing.
- Drawdown Recovery Calculator - the non-linear math of climbing out of a Kelly-sized drawdown.
- Position Size Calculator - translates the Kelly fraction into broker lot size given stop loss in pips.
Frequently asked questions
The Kelly criterion is a mathematical formula derived by John Larry Kelly Jr. in 1956 that computes the bet size which maximises long-run log-equity growth for a sequence of independent positive-expectancy bets. For a trade with win probability p, reward-to-risk b, and loss size 1, the optimal Kelly fraction is f* = (bp - q) / b, where q = 1 - p. Below f*, growth is suboptimal. Above f*, growth turns negative and ruin probability rises sharply. The criterion is the mathematical upper bound on sustainable bet sizing.
Full Kelly maximises long-run geometric growth but produces unstable equity curves with drawdowns frequently in the 30 to 50 percent range. Half Kelly preserves approximately 75 percent of the growth rate while cutting drawdowns by roughly 75 percent. Most institutional fund managers operate at or below half Kelly because the marginal growth from full Kelly is not worth the variance. Quarter Kelly is the conservative institutional standard for traders with uncertain edge estimates.
For a fixed-fraction trader: f* = (bp - q) / b, where p = win rate (as a decimal), q = 1 - p, and b = reward-to-risk ratio (average winning trade size divided by average losing trade size). For a trader with a 55 percent win rate and 1.5 reward-to-risk: f* = (1.5 x 0.55 - 0.45) / 1.5 = (0.825 - 0.45) / 1.5 = 0.25 or 25 percent of capital per trade. Half Kelly would be 12.5 percent, quarter Kelly 6.25 percent. The calculator above computes all three plus the dollar amounts for an AUD account.
Full Kelly is rarely appropriate for retail. The formula assumes accurate knowledge of win rate and reward-to-risk; retail traders typically over-estimate both, producing oversized positions and high drawdowns. Half Kelly or quarter Kelly is safer because the reduction provides margin for estimation error. Even half Kelly at 12 percent risk per trade is aggressive by retail standards (most retail risk frameworks cap at 1-2 percent). The practical retail use of Kelly is as an upper bound: if your sizing exceeds half Kelly, you are betting too large regardless of how your equity curve has performed so far.
Kelly identifies the bet size at the threshold where geometric growth is maximised. Risk of ruin quantifies the survival probability at any given bet size. Kelly says: do not exceed this fraction. Risk of ruin says: at this fraction, here is your probability of blowing up. Sophisticated traders use both: Kelly as the upper bound, risk of ruin to size below Kelly until survival probability is acceptably high. The two metrics complement each other; using either one in isolation misses half the picture.
If the calculator returns a Kelly fraction above 20 percent, your stated edge is unusually strong. Most documented retail edges produce Kelly fractions of 2-8 percent. A Kelly above 20 percent often indicates an overstated win rate or reward-to-risk ratio. Verify your edge estimates against a track record of at least 200 trades on the same instruments and timeframes. If your edge holds across that sample, the high Kelly is real, but you should still cap practical sizing at 10-15 percent to leave variance buffer.
Yes, with the same formula structure but tighter caveats. Crypto markets have wider variance and more frequent fat-tail events than forex. The Kelly assumption of stable expectancy is more easily violated. Practical crypto Kelly application uses heavier fractional reductions (quarter Kelly or eighth Kelly) and re-estimates the edge frequently as market regimes shift. For Australian crypto traders, the AUD-denominated Kelly output from the calculator is appropriate; multiply by your spot exchange holding to get the per-trade exposure.
No. The Kelly formula returns a negative fraction for negative-expectancy strategies. Mathematically this means the optimal bet is to take the opposite side. Practically it means: do not trade this strategy. The calculator above returns a 'no Kelly bet sizes' message for negative-edge inputs to make this explicit. The Kelly criterion is undefined as a position size for strategies that should not be traded.
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