Applying the Kelly Criterion to Dollar and Contract Positions

Summary

The document asks how to express Kelly sizing in absolute dollars rather than as a fraction of bankroll. It points to the standard Kelly formula and argues that knowing the bankroll lets a trader translate a fractional allocation into an amount. It also mentions Optimal F, a modified sizing approach that works in dollars or contracts, and refers readers to worked examples and spreadsheet implementations.

The discussion gives no derivation, worked calculation, or comparison of the methods. It therefore offers a starting point rather than enough detail to apply either approach. In particular, it does not explain the assumptions behind Kelly sizing, how to estimate its inputs, or how to adjust for estimation error and risk tolerance. Readers should consult the cited treatments before using the suggestions to size a position.

Key ideas

• A fractional Kelly allocation can be translated into dollars when the bankroll is known.
• Optimal F is presented as a modified approach for sizing in dollars or contracts.
• The discussion provides references rather than a derivation or worked example.
• The document does not address estimation uncertainty or practical risk controls.

Tags

# Absolute Dollar Form Of Kelly Criterion


# Absolute Dollar Form Of Kelly Criterion












Is there a absolute dollar form of the Kelly equation $f=\frac{m}{s^2}$? (i.e. one that does not use percent returns).

## Answer by Matt Wolf (score 1)

https://quant.stackexchange.com/a/4604

Well, the first formula on the wiki page gives you a straight forward answer in absolute terms (you do know your bankroll so its pretty much absolute):

http://en.wikipedia.org/wiki/Kelly_criterion

Simple as that, sometimes it does not pay but only causes headaches to overcomplicate things :-)

Happy Thanksgiving!!!

Update as requested by OP:

http://www.math.washington.edu/~morrow/336_10/papers/jane.pdf

and here an application using R

http://braverock.com/brian/R/PerformanceAnalytics/html/KellyRatio.html

## Answer by n.e.w (score 1)

https://quant.stackexchange.com/a/4658

See Ralph Vince's excellentbook: Handbook of Portfolio Mathematics where he goes through explicit, worked examples of using an appropriate modified-Kelly system in dollar / contract terms (Optimal F). He even gives Excel examples for the programmatically uninitiated.

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.