Kelly's Criterion Explained: A Q&A Guide for Options Traders
Kelly's Criterion Explained: A Q&A Guide for Options Traders
By:Kai Zeng
It helps determine the right amount of cash to risk on a trade
This is part 1 of a 3-part series. Part 1, Never Go Broke: The Kelly Formula Explained, can be found here.
Many readers wrote in with questions to Part 1, which prompted this series.
The Basics
Q: What is Kelly's criterion and how is it calculated?
A: Kelly's Criterion determines the optimal percentage of your capital to allocate to a trade:
Where:
f* = optimal bankroll percentage to allocate- p = winning probability
- q = losing probability (1-p)
- b = net odds received (amount won per dollar bet)
Profitability Assessment
Q: Is there a quick way to determine if a strategy can be profitable long-term based on Kelly's calculation?
A: Kelly's formula can be simplified as:
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We can set f to 0 as a threshold and evaluate whether our received odds exceed the theoretical requirement for a given POP or success rate.
When f = 0%, the formula changes to:
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In our iron condor example, with p = 0.85 (success rate) and q = 0.15 (losing rate), the odds (b) must exceed 0.15/0.85 = 0.176 for the strategy to be potentially profitable in the long run.
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Position Management
Q: When managing positions at 50% profit, should I reference POP or P50 on the tastytrade platform? What about managing at 21 DTE?
A: The p (probability of profit) in the calculation of Kelly should match the way we manage the positions. If the position is managed at 50% winners, P50 is better than POP.
However, the realized success rate is even more accurate than the theoretical POP or P50. Traders can find the success rate of managing at 21 DTE or any other mechanics by running the lookback program on tastytrade or from our Market Measures.
Capital Allocation
Q: Does the Kelly number change based on the fluctuation of the bankroll (net liq) in the account?
A: Kelly represents the percentage of capital allocation of a certain portfolio. In our analysis, we keep this number constant, but the net liq can fluctuate after trading. Keeping the Kelly at the same level, we should expect to see more committed capital per trade if the net liq increases.
Calculating Odds
Q: How are net odds calculated?
A: Odds (b) = expected win/expected loss.
It’s better to use the realized average win/avgerage loss in this calculator. We can get these values after analyzing long-term data (lookback or from Market Measures). Using max profit/max loss is not so reliable because, in premium selling strategies, we often experience partial winners and losers.
For probability, we should use either P50 or the realized success rate when managed at 50% winners.
Kelly Fractions
Q: What's the importance of using a fraction of the calculated Kelly in real trading?
A: The Kelly number, or what we call full Kelly, is the scenario to optimize the return without considering the volatility. In practice, the half-Kelly (50% of the full Kelly) strategy can capture nearly 71% of the optimal returns with only about 38% of the volatility.
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The relationship is not linear. The half Kelly thus has a higher risk-adjusted return. Using a Kelly fraction provides a better balance between returns and risk.
Risk of Ruin
Q: Does a 0% ruin rate mean that the strategy is completely safe from losing all capital?
A: If the Kelly is positive, traders should theoretically be able to avoid depleting their capital. However, perfect sizing is difficult to achieve in real trading. Also, a streak of losing events is possible. These would cause the portfolio to achieve the expected return in a longer period of time.
Kai Zeng, director of the research team and head of Chinese content at tastylive, has 20 years of experience in markets and derivatives trading. He cohosts several live shows, including From Theory to Practice and Building Blocks. @kai_zeng1
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