Risk & volatility

Kelly criterion

Kelly criterion is a position-sizing formula that estimates the fraction of capital maximizing long-run expected logarithmic wealth, given reliable probabilities of gains and losses and their payoff sizes.

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What it means

The Kelly criterion addresses a sizing question: if a risky opportunity can be taken repeatedly, what fraction of available capital maximizes the expected growth rate of wealth? Its answer depends on both the probability of a gain and the size of gains relative to losses. A high chance of success alone is not enough.

Kelly is a mathematical benchmark, not a requirement to use the calculated fraction. The standard formula assumes a repeatable, two-outcome opportunity with known probabilities and payoffs. Stocks have many possible outcomes, and those inputs must be estimated, so a calculated fraction can be highly sensitive to errors.

How it is calculated

For a simplified trade that either gains a specified amount or loses a specified amount, the full-Kelly fraction is f* = (b × p − q) / b = p − q / b.

  • f* is the fraction of capital allocated to the opportunity, expressed as a decimal.
  • p is the probability of the gain, expressed as a decimal.
  • q = 1 − p is the probability of the loss.
  • b is the net gain per US$1 lost if the favorable outcome occurs. For example, gaining US$2 when the unfavorable outcome loses US$1 gives b = 2.

This version assumes that the allocated capital is lost in the unfavorable outcome and earns b times that capital in the favorable outcome. If only part of a stock position would be lost, the formula’s fraction instead refers to capital at risk; converting it into a stock position requires an explicit loss assumption. Transaction costs should be included in the estimated net payoffs. If the calculation is zero or negative, the simplified model finds no positive allocation that improves expected logarithmic wealth.

Worked example

Suppose, hypothetically, a repeatable opportunity has a 60% chance of gaining US$2 for each US$1 at risk and a 40% chance of losing that US$1. Assume capital of US$10,000, and that the full amount allocated is at risk.

  1. Set p = 0.60, q = 0.40 and b = 2.
  2. Calculate f* = 0.60 − 0.40 / 2 = 0.40.
  3. Multiply by capital: 0.40 × US$10,000 = US$4,000.

The full-Kelly result is 40% of capital, or US$4,000 under these particular assumptions. It is not an estimate of what a real stock trade will earn. Changing the probability to 50%, while keeping the same payoffs, changes the result to 0.50 − 0.50 / 2 = 0.25, or 25%.

Why it matters before you trade

Kelly separates the chance of a favorable outcome from the size of its payoff. Before placing an order, that distinction helps reveal whether a sizing calculation relies on an unsupported probability, an unrealistic loss limit or costs that have been left out. Spread, market impact and other execution costs can change net payoff assumptions.

Full-Kelly sizing can also produce large positions and substantial short-term losses. Investors may examine fractional Kelly—such as half of a calculated fraction—as a more conservative mathematical scenario, but no fraction removes estimation risk. Correlated positions and portfolio concentration matter too: treating several stocks as independent opportunities can understate their combined risk.

How PreTrAIde uses it

The product facts do not state that PreTrAIde calculates a Kelly fraction or uses Kelly sizing. Its pre-trade analysis checks a user-built stock basket before an order is placed and provides per-line and basket verdicts, risk assessments, success probabilities and suggested execution strategies as decision support, not recommendations.

PreTrAIde also estimates spread, market impact and one-day 95% value at risk, and measures basket concentration. Those checks can inform questions about costs and exposure that a separate Kelly calculation would need to consider. A PreTrAIde success probability is a model estimate between 5% and 95%; it is not automatically the probability of a Kelly-defined gain, and it does not specify that gain’s payoff.

Common mistakes

  • Using win rate alone. The formula also needs the relative sizes of gains and losses.
  • Treating an estimate as known. Small probability or payoff errors can materially change the fraction.
  • Confusing capital at risk with position value. They coincide only under the worked example’s full-loss assumption.
  • Ignoring other holdings. Correlation and concentration can make individually calculated fractions unsuitable for a combined basket.

Frequently asked questions

What is the Kelly criterion formula?

For a simplified two-outcome opportunity, the full-Kelly fraction is `f* = p − (1 − p) / b`, where `p` is the gain probability and `b` is the net gain per unit lost. The result depends on how gains, losses and capital at risk are defined.

Is half-Kelly safer than full Kelly?

Half-Kelly uses half the calculated full-Kelly fraction, reducing the amount exposed under the same assumptions. It does not eliminate losses or make uncertain probability and payoff estimates reliable.

Can I use PreTrAIde's success probability in the Kelly formula?

Not directly. PreTrAIde's success probability is a model estimate, not necessarily the probability of a specifically defined gain versus loss; a Kelly calculation also requires corresponding net payoff sizes.

Related terms

Position sizing Position sizing is the process of deciding how many shares to hold or trade based on available capital, intended portfolio weight and the amount of risk an investor is prepared to take. Risk per trade Risk per trade is the estimated amount or percentage of account equity that could be lost on one trade if an assumed exit price is reached, excluding losses beyond that price. Success probability Success probability is a model-estimated percentage attached to a pre-trade verdict, expressing the model’s assessed chance of meeting its defined success criteria, not the chance of earning a return. Transaction costs Transaction costs are the explicit fees and implicit trading costs incurred when executing a trade, including commissions, the bid-ask spread and market impact. Portfolio concentration Portfolio concentration is the extent to which a portfolio’s value depends on a small number of holdings or on shared exposures such as a sector or country. Pre-trade analysis Pre-trade analysis is the assessment of a proposed stock order or basket before placement, estimating execution costs, liquidity and risk to inform the investor’s decision and execution approach.

Risk & volatility

Volatility Historical volatility Implied volatility Annualized volatility Daily volatility Parkinson volatility estimator Yang-Zhang volatility estimator GARCH model All glossary terms →

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Educational content, not investment advice. PreTrAIde is analysis software, not a broker: it never executes orders, and its verdicts are decision support, not recommendations to buy or sell.