Crypto Position Sizing: Why the Classic Kelly Criterion Fails Against Extreme Volatility

On March 12, 2020, bitcoin lost 39.5% between two daily closes (Binance data, BTC/USDT pair). A portfolio sized with the "full" Kelly criterion, estimated the way most guides recommend, on the previous year, was at that point exposed to 2.17 times its capital: it lost 85.8% of its value in a single session. This figure is not a textbook hypothetical; it is what the formula produces on real prices. We recomputed the Kelly criterion over nine years of bitcoin history, then tested month by month what it would have delivered in real conditions, against more cautious alternatives.

What the formula recommends over nine years of bitcoin

For continuous returns, the Kelly fraction is f* = (μ − r) / σ², where μ is the mean annual return, σ the annual volatility and r the risk-free rate, set to zero here for simplicity. Over the 3,323 sessions from August 18, 2017 to September 22, 2026, bitcoin shows a mean arithmetic return of 55.6% per year with a volatility of 66.9% (3.5% per day). The formula gives f* = 0.556 / 0.669² = 1.24: you should have held 124% of your capital in bitcoin, and therefore borrowed. The catch: that number was only knowable in 2026. In real time, an investor only has the recent past to estimate μ and σ.

An estimate that swings between −2.8 and 5.3

Recomputed at the end of each month over the previous 365 days, Kelly's "optimal" leverage is anything but a stable parameter. It reached 5.33 at the end of December 2023 and fell to −2.78 at the end of June 2026. Over 98 months, it was negative, meaning "hold nothing", 28% of the time, and above 2 in 41% of months. This instability is no mystery: with 67% annual volatility, the standard error of a mean return estimated over one year is itself 67 points. Divided by σ², it translates into an uncertainty of ±2.9 on the Kelly leverage (95% interval), the same order of magnitude as the range observed.

Worse, the estimate is procyclical. It peaks after strong rallies, when the last 365 days look flattering, and collapses after crashes. Following Kelly to the letter therefore means borrowing at the top and exiting the market just before rebounds.

Tails far beyond anything the normal distribution allows

The Kelly criterion reasons in terms of mean and variance; it ignores the shape of the extremes. Yet over the period, bitcoin recorded 19 sessions more than 4 standard deviations from its mean, where a normal distribution would predict 0.2, about 90 times fewer. Beyond 5 standard deviations, there were 5 sessions against 0.002 expected. Excess kurtosis reaches 8.7. The worst days: −39.5% on March 12, 2020, −19.5% on January 16, 2018, −19.2% on September 14, 2017, −15.4% on June 13, 2022. With leverage L, each of those sessions costs L times more: at 2.17, March 12, 2020 wipes out 85.8% of the capital.

Full, half and quarter Kelly: the eight-year test

The protocol is deliberately simple and free of look-ahead. On the first day of each month, f* is estimated over the previous 365 days (floored at zero, no short selling), and that leverage is applied until the end of the month, with daily rebalancing. The test runs from August 2018 to September 2026. It compares plain buy-and-hold (leverage 1), full Kelly, half Kelly, quarter Kelly and a volatility-targeting rule. Fees, the financing cost of leverage and slippage are not modeled, which flatters the leveraged strategies.

The results leave no room for doubt. Buy-and-hold multiplies capital by 13.1 (+37.4% per year), at the cost of a maximum drawdown of 76.6%. Full Kelly ends at 0.15 times the initial stake (−20.9% per year), after a maximum drawdown of 99.3% and 39 sessions losing more than 20%. Half Kelly multiplies capital by 4.9 (+21.6% per year) but suffers a maximum drawdown of 84.3%, worse than bitcoin held without leverage. Quarter Kelly limits the damage to 54.9%, for a return of 17.9% per year.

The lesson goes beyond leverage. Shrinking the Kelly fraction reduces the damage but does not fix the estimation error: even halved, the rule buys after rallies and stays out of the market 26 months out of 98, often right when recoveries begin.

Diversifying across cryptos does not protect on the worst days

Spreading risk across several tokens looks like a natural defense. The data say otherwise. Over the period, the correlation between bitcoin's and ether's daily returns reaches 0.78. On bitcoin's 20 worst sessions, ether fell 20 times out of 20, by 16.8% on average, versus 15.1% for bitcoin. Intra-crypto diversification vanishes precisely on the days you would need it.

Stop-losses offer more fragile protection than they seem

A stop placed 10% below the previous close would have been hit intraday 93 times since 2017. In 63 of those cases (68%), bitcoin nonetheless closed the day above the stop level, and 8 times higher on the day: the stop sold at the low of the session. In a flash crash, execution also often happens well below the intended price. A stop limits how long a mistake lasts; it does not replace prudent sizing.

Size on volatility rather than on expected return

A more robust alternative is not to estimate returns at all. Volatility targeting sets exposure to 40% divided by the volatility of the last 30 days, never exceeding 1. On the same test, this rule multiplies capital by 8.3 (+29.8% per year), with a maximum drawdown cut to 64.2% and a worst session of −26.3% instead of −39.5%. It gives up some return compared with buy-and-hold, but it relies on recent volatility, which is far more persistent, and therefore more predictable, than average returns.

In practice: never size a crypto position on a full Kelly estimated over one year; if you use Kelly, stay at a quarter and cap exposure at 1; prefer a rule based on volatility; and do not count on other tokens to cushion a crash. The simulation tools available on /outils let you test these rules on your own assumptions, for educational purposes. Method: daily UTC closes of the BTC/USDT and ETH/USDT pairs published by Binance, from August 18, 2017 to September 22, 2026, TrueVerdikt calculations. Past results do not predict future results and do not constitute investment advice.