Can a Kelly Criterion Percent be very high?

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

• Win Rate: 83.94%
• Average Win: $299 • Average Loss:$1,181.40

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?

• Your reaction is very common. Many people bet less than the full Kelly for 2 reasons: (1) The strategy is optimal in the long run (or for a log utility investor) but quite volatile in the short run, (2) You cannot be sure that 299/1181.40 are the true odds, they may be overstated due to recent good luck or other reasons. Sep 20, 2017 at 15:35

1 Answer

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.

• Well - the 299 and 1181 are actually the averages of my trades over a few months. So it's not the LAST trade, but an average. Even if I calculate on a SPECIFIC spread, the Kelly percent is like 15%, which seems high. Normally, I trade with 2-5% of my account size, so it's a bit shocking to see Kelly suggest something so high. Sep 21, 2017 at 1:31
• @Shamoon I understood it to be an average (and you're right that a more correct way would be to do it for a specific strategy). The point I was making was that when you have a range of outcomes (not binary) the kelly criterion would generalize to maximizing the expected log of your wealth under this distribution. If there is a sizable negative tail to the distribution you might find this is much less than what your method gives, even if there's sizable upside tail as well. Nonetheless, even under ideal circumstances, many people find it a bit aggressive, as noob2 said in the comments. Sep 21, 2017 at 1:44