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")
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 = (mean(R)-Rf=0)/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.
Brian G. Peterson
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)
KellyRatio(managers[,1,drop=FALSE], Rf=managers[,10,drop=FALSE])
KellyRatio(managers[,1:6], Rf=managers[,10,drop=FALSE])Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.