calculate Kelly criterion ratio (leverage or bet size) for a strategy

Kelly criterion ratio (leverage or bet size) for a strategy.

KellyRatio(R, Rf = 0, method = "half")

Arguments

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

Details

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.

References

Thorp, Edward O. (1997; revised 1998). The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market. https://en.wikipedia.org/wiki/Kelly_criterion

no longer online, but can be found at archive.ph /h1LuS

Author

Brian G. Peterson

Examples

    data(managers)
    KellyRatio(managers[,1,drop=FALSE], Rf=.04/12)
#>                 HAM1
#> Kelly Ratio 5.929483
    KellyRatio(managers[,1,drop=FALSE], Rf=managers[,10,drop=FALSE])
#>                 HAM1
#> Kelly Ratio 6.010854
    KellyRatio(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