Kelly Position Sizing and Risk Controls for a Probabilistic Edge
Summary
The document considers position sizing for a hypothetical signal that predicts an index’s direction with a 60% win probability against 40% losses. One answer applies the Kelly criterion to maximize long-run capital growth and gives a fraction of capital to wager under the stated assumptions. That result depends on the payoff structure being suitable for the binary betting formulation; a win probability alone does not determine optimal sizing when gains and losses differ in size.
A second answer suggests using implied volatility to translate a risk limit, such as a value-at-risk threshold, into trade exposure. It cautions that return distributions can have fat tails and that implied volatility skew may reflect asymmetric price risks. Kelly maximizes expected long-run growth but can entail large swings and drawdowns, so the answer recommends reducing the fraction to fit acceptable risk and using simulation to assess drawdown or ruin probabilities. These are general cautions, not a demonstrated sizing study, and the proposed volatility-based risk estimate does not remove model or tail risk.
Key ideas
- The Kelly criterion selects a position fraction to maximize long-run growth under specified probability and payoff assumptions.
- A stated win probability is insufficient for sizing if the sizes of wins and losses are not known.
- Implied volatility can inform exposure estimates tied to a chosen value-at-risk threshold.
- Fat tails and volatility skew can make simple risk estimates miss asymmetric losses.
- Full Kelly sizing can produce substantial drawdowns, so a smaller fraction and drawdown simulations may be more appropriate.
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# If I have a model that gives 10% "probability edge" over random chance, how do I calculate the position size? # If I have a model that gives 10% "probability edge" over random chance, how do I calculate the position size? Lets say that I have an imaginary model that always gives me a 10% edge over straight 50/50 odds, one day in advance, for an index (i.e. 60% chance of winning / 40% chance of losing). How would I calculate the ideal position size to maximize long term portfolio gain, given a chosen risk threshold? ## Answer by olaker (score 4, accepted) https://quant.stackexchange.com/a/1214 The optimal position size can be determined with the Kelly criterion. In your specific case, the long term growth rate of the capital X is maximized by betting $$(0.6-0.4)X=0.2X$$ at each opportunity. ## Answer by Contango (score 1) https://quant.stackexchange.com/a/1216 Use the Kelly Criterion (as suggested by @olaker). For the amount of money to put into each transaction, use Implied Volatility to calculate the amount you are risking to within a VAR (Value At Risk) of 99% (i.e. +/- 3 standard deviations of the underlying). See How to calculate future distribution of price using volatility? Caveats: - Markets price distributions have fat tails. When markets crash, they really crash. - Take into account skew on Implied Volatility (IV). For stocks, the IV skew is negative, so there is a greater chance of a rapid drop in the price. For commodities, the IV skew could be positive, there is a greater chance of a rapid increase in the price. - The Kelly Criterion means the greatest long term increase in the value in your portfolio, at the expense of huge drawdowns and large swings in the value of your portfolio. In practice, you'll have to dial down the risk until the expected drawdown is acceptable. You might have to do some Monte Carlo simulations to work out the actual risk level at any point in time. Then again, you could always use OpenGamma to handle your risk management for you. Update: See How to estimate the probability of drawdown / ruin? ## Answer by babelproofreader (score 1) https://quant.stackexchange.com/a/1229 If you want to use the Kelly Criterion you might find this link, particularly part III, useful.
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