Kelly criterion ratio (leverage or bet size) for a strategy.
KellyRatio(R, Rf = 0, method = "half")
| R | a vector of returns to perform a mean over |
|---|---|
| Rf | risk free rate, in same period as your returns |
| method | method=half will use the half-Kelly, this is the default |
The Kelly Criterion was identified by Bell Labs scientist John Kelly, and applied to blackjack and stock strategy sizing by Ed Thorpe.
The Kelly ratio can be simply stated as: “bet size is the ratio of edge over odds.” Mathematically, you are maximizing log-utility. As such, the Kelly criterion is equal to the expected excess return of the strategy divided by the expected variance of the excess return, or $$leverage=\frac{(\overline{R}_{s}-R_{f})}{StdDev(R)^{2}}$$
As a performance metric, the Kelly Ratio is calculated retrospectively on a particular investment as a measure of the edge that investment has over the risk free rate. It may be use as a stack ranking method to compare investments in a manner similar to the various ratios related to the Sharpe ratio.
Thorp, Edward O. (1997; revised 1998). The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market. http://www.bjmath.com/bjmath/thorp/paper.htm http://en.wikipedia.org/wiki/Kelly_criterion
data(managers) KellyRatio(managers[,1,drop=FALSE], Rf=.04/12)#> HAM1 #> Kelly Ratio 5.929483KellyRatio(managers[,1,drop=FALSE], Rf=managers[,10,drop=FALSE])#> HAM1 #> Kelly Ratio 6.010854KellyRatio(managers[,1:6], Rf=managers[,10,drop=FALSE])#> HAM1 HAM2 HAM3 HAM4 HAM5 HAM6 #> Kelly Ratio 6.010854 4.069873 3.458124 1.376354 0.3876476 7.948295