By Ilya Kipnis
This post will be about implementing and investigating the running Kelly Criterion — that is, a constantly adjusted Kelly Criterion that changes as a strategy realizes returns.
For those not familiar with the Kelly Criterion, it’s the idea of adjusting a bet size to maximize a strategy’s long term growth rate. Both https://en.wikipedia.org/wiki/Kelly_criterionWikipedia and Investopedia have entries on the Kelly Criterion. Essentially, it’s about maximizing your long-run expectation of a betting system, by sizing bets higher when the edge is higher, and vice versa.
There are two formulations for the Kelly criterion: the Wikipedia result presents it as mean over sigma squared. The Investopedia definition is P-[(1-P)/winLossRatio], where P is the probability of a winning bet, and the winLossRatio is the average win over the average loss.
In any case, here are the two implementations.
investoPediaKelly 0] 0]
Let's try this with some data. At this point in time, I'm going to show a non-replicable volatility strategy that I currently trade.
For the record, here are its statistics:
Close Annualized Return 0.8021000 Annualized Std Dev 0.3553000 Annualized Sharpe (Rf=0%) 2.2574000 Worst Drawdown 0.2480087 Calmar Ratio 3.2341613
Now, let’s see what the Wikipedia version does:
The results are simply ridiculous. And here would be why: say you have a mean return of .0005 per day (5 bps/day), and a standard deviation equal to that (that is, a Sharpe ratio of 1). You would have 1/.0005 = 2000. In other words, a leverage of 2000 times. This clearly makes no sense.
The other variant is the more particular Investopedia definition.
Looks a bit more reasonable. However, how does it stack up against not using it at all?
Turns out, the fabled Kelly Criterion doesn't really change things all that much.
For the record, here are the statistical comparisons:
Base Kelly Annualized Return 0.8021000 0.7859000 Annualized Std Dev 0.3553000 0.3588000 Annualized Sharpe (Rf=0%) 2.2574000 2.1903000 Worst Drawdown 0.2480087 0.2579846 Calmar Ratio 3.2341613 3.0463063
Thanks for reading.
NOTE: I am currently looking for my next full-time opportunity, preferably in New York City or Philadelphia relating to the skills I have demonstrated on this blog. My LinkedIn profile can be found here. If you know of such opportunities, do not hesitate to reach out to me.
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