A long time ago I wrote a note on position sizing, before I knew that the problem had been analyzed already. This note explains in very simple terms the analytic solution to the problem I solved earlier with Monte Carlo estimation. 


Once again, I had to copy and paste screenshots to keep the formulas so it's a little hard to read. Here's this note is in pdf format, if that's easier.



There has been a lot of research on generalizations of the Kelly Criterion, which should be easy to find.

6 comments:

Anonymous said...

Ernie Chan said on his blog post on Kelly's Criterion that to be safe you should take divide the fraction by 2. This would significantly reduce your chance of error.

Max Dama said...

Anon,

Obviously it's not a good idea to choose a random number, say 2, and use that as another parameter. Better to optimize that amount you change the Kelly estimate via backtesting or other outside knowledge of how accurate your accuracy estimate will be.

Regards,
Max

Anonymous said...

Can you tell me what is the relationship between the Kelly ratio and Optimal f? Are they the same thing? (PS. Nice work on the derivation.)

Max Dama said...

Anon,

I'm assuming you're referring to Ralph Vince's optimal f. Yes, Kelly and optimal f are the same. However optimal f is more general since it doesn't require the amount won and lost to be equal like Kelly does.

Regards,
Max

manaau said...

Thanks a lot, that's a gem, you might want to put your name on the pdf. I'm curious how the formula is composed when win and loss sizes are different, say if the win rate is 2x losses and wins are .9x losses - would this give .66 x .9 or .59 in place of the .65 given in the example? Thanks and regards

Max Dama said...

Manaau,

Thanks for the compliment. There's tons of literature on the Kelly criterion. One good easy to read author to look up is Ziemba. Google Scholar is a good resource.

Regards,
Max