Why Historical Kelly Sizing Can Overstate Safe Spread Exposure

Summary

The document applies the Kelly betting formula to historical results from selling option spreads and asks whether a calculated allocation of about 20% of capital is too high. The response explains that Kelly is aggressive and assumes a well-specified bet with fixed win probability and fixed win and loss amounts. Under those assumptions, the calculated fraction represents the bankroll share at risk across the bet.

The response cautions that spread outcomes may not match this simple two-outcome model, especially when large losses have tail risk. It also notes that a historical estimate of the trading edge may not represent future probabilities or payoffs. Thus the arithmetic can be correct for the inputs while still producing a misleading sizing recommendation. The document gives no independent performance analysis or alternative sizing method, and the estimate's reliability depends on how representative the recorded trades are and how losses are distributed.

Key ideas

• Kelly sizing assumes the probability and payoff of each outcome are correctly specified.
• A high Kelly fraction can follow from the inputs even when the inputs poorly describe spread outcomes.
• Tail losses can make a historical win-rate and average-payoff estimate especially misleading.
• Past trading results may not represent the true future edge.
• The recommended exposure is defined by total amount at risk, not merely capital deposited per trade.

Tags

# Can a Kelly Criterion Percent be very high?


# Can a Kelly Criterion Percent be very high?












This is my personal record trading options (selling spreads) over a certain time period:







The formula for the Kelly Criterion is: $$ f=\frac{p(b+1)-1}{b} $$

where $f$ is a percentage of how much capital to place on a bet, $p$ is the probability of success, and $b$ is the payout odds (eg. 3 dollars for ever 1 dollar bet).

So if I put in my numbers: $$ f=\frac{0.8394(\frac{299}{1181.4}+1)-1}{\frac{299}{1181.4}} $$

Which equals `20.48%`

That seems really high. Accordingly to this, I should put up 20% of my portfolio per trade. What am I not understanding?

## Answer by spaceisdarkgreen (score 2)

https://quant.stackexchange.com/a/36103

I think your calculation is right and the Kelly criterion is very aggressive. Note however that it is meant to apply to the situation where you win exactly your last bet times 299 84% of the time and you lose exactly your bet times 1181.4 the other percentage of the time. This is not the case here so this is at best an estimation and it's somewhat self defeating as a risk management strategy if that 1181 number comes with a lot of tail risk (not to mention that your measured historical edge may not be representative of your true edge for a variety of reasons).

Given these caveats, yes, the kelly procedure is to sell enough spreads so that your total amount at risk (1181 times quantity) would be 20 percent of your bankroll.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.