Kelly Sizing with Win and Loss Averages

Summary

The document considers whether a proposed Kelly fraction is appropriate for a trading record described by a win rate and average win and loss sizes. One response gives the standard expression for the special case where every win has the same size and every loss has the same size, and relates it to the probabilities of winning and losing. In that setup, the fraction depends on both the win probability and the magnitudes of wins and losses.

The key caveat is that substituting average win and loss sizes when trade outcomes vary may not preserve the assumptions behind the formula. The response calls that substitution a possible approximation rather than establishing it as exact. A second response points to alternative explanations of Kelly sizing, including a version that incorporates dispersion in outcomes. The exchange raises the issue but does not derive that extension or assess the trader’s data, so it does not establish an optimal allocation for the stated record.

Key ideas

• The basic Kelly expression shown assumes wins and losses have fixed sizes within their respective outcome classes.
• A win probability and corresponding loss probability enter the fraction alongside win and loss magnitudes.
• Using average win and loss sizes for variable outcomes may only approximate the fixed-outcome formula.
• The discussion points to outcome variability as a relevant consideration but does not derive a complete adjustment.

Tags

# Am I calculating my Kelly Criterion correctly?


# Am I calculating my Kelly Criterion correctly?












I'm taking a look at my trading history over a particular time period and have 500 trades on with an win rate of 82%. My average win is $W$. My average loss is $L$. So am I correct in assuming the Kelly Criterion is:

$$ \frac{0.82 \times (W / L + 1) - 1}{W / L} $$

## Answer by nbbo2 (score 2)

https://quant.stackexchange.com/a/36493

According to Skiena (link page 21) the Kelly fraction in the case of wins all equal to W and losses all equal to L is:

$$f=\frac{pW-qL}{WL}=p/L-q/W$$

where $q=1-p$ and $p$ is the probability of a win.

When the wins and losses are random, with average $W$ and $L$ respectively, I am not sure this formula is completely justified. But it might be a good approximation

## Answer by babelproofreader (score 2)

https://quant.stackexchange.com/a/36503

When it comes to Kelly, I've always liked the explanation at http://www.financialwisdomforum.org/gummy-stuff/kelly-ratio.htm. At this link there are three versions of Kelly explained, if you don't mind the "chatty" style. The third version brings in the standard deviation of wins and losses, which I think is very useful.

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