Kelly criterion

Size uncertainty. Not conviction.

Map bear, base, and bull outcomes, then translate the distribution into a fractional Kelly reference.

Objectivemax Σ pᵢ ln(1 + f rᵢ)

Build the outcome map

Set three plausible cases. The probabilities always total 100%.

Bear case

The thesis is wrong or risk intensifies.

30%chance

Bear-case probability

Position return in this case-30%

Use a thesis-break outcome, including plausible gap and liquidity risk.

Base case

The most likely operating and valuation path.

55%chance

Base probability adjusts automatically after bear and bull choices.

Position return in this case+10%

Use the return implied by your central thesis over the review horizon.

Bull case

Fundamentals and valuation exceed the base case.

15%chance

Bull-case probability

Position return in this case+30%

Use a plausible upside outcome, not the most optimistic target.

Sizing conservatism

This discounts the model for uncertainty. It does not change your scenario probabilities.

How to estimate the scenarios

Probability comes from evidence

Define the review horizon and what counts as success. Start with comparable historical setups, then adjust for company-specific evidence. Conviction alone is not a probability.

Returns come from outcomes

Use the return implied by each complete scenario. Include valuation change, fundamentals, gap risk, and a realistic exit. Do not use only a target or stop.

Keep the terms separate

Confidence and conviction: Use evidence quality to choose a smaller Kelly fraction, not to inflate probability.
Margin of safety: A valuation discount to estimated intrinsic value. It is not the same as drawdown.
Drawdown risk: The adverse path and portfolio impact before the thesis resolves.
Upside potential: The return in positive scenarios, weighted by their probabilities.

What this model leaves out

Kelly is one sizing lens. Liquidity, correlation, portfolio concentration, taxes, catalyst gaps, and the ability to hold through volatility can require a smaller position.

Sources and further reading

Kelly, original growth-rate framework Thorp, Kelly applied to securities Damodaran, probabilistic valuation SEC, investor behavior and bias CFA Institute, equity valuation and margin of safety

Sizing output

Positive modeled edge

Reference allocation

10.7%50% of the scenario-based full Kelly result

Full Kelly21.3%

Selected fraction50%

Chance positive70.0%

Expected position return+1.0%

Average upside14.3%

Average downside30.0%

Payoff asymmetry0.48×

Bear-case portfolio loss3.20%

A scenario map, not a command.

The model makes uncertainty visible. Treat its output as one reference point among portfolio, liquidity, and risk constraints.

Underwrite complete cases

Each scenario should combine fundamentals, valuation, timing, and a realistic exit rather than one isolated price target.

Discount uncertain estimates

Fractional Kelly scales the mathematical result when the probability distribution is less reliable than the formula assumes.

Respect the binding constraint

Downside budget, liquidity, correlation, concentration, and catalyst gaps can all require a smaller position.

This calculator is an educational heuristic, not investment advice. The scenarios are illustrative and the output is not implementation-ready without portfolio, liquidity, and mandate checks.

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