\HeaderA{KellyRatio}{calculate Kelly criterion ratio (leverage or bet size) for a strategy}{KellyRatio}
\keyword{ts}{KellyRatio}
\keyword{multivariate}{KellyRatio}
\keyword{distribution}{KellyRatio}
\keyword{models}{KellyRatio}
\begin{Description}\relax
Kelly criterion ratio (leverage or bet size) for a strategy.
\end{Description}
\begin{Usage}
\begin{verbatim}
KellyRatio(R, Rf = 0, method="half")
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{R}] a vector of returns to perform a mean over 
\item[\code{Rf}] risk free rate, in same period as your returns 
\item[\code{method}] method=half will use the half-Kelly, this is the default
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
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: \dQuote{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

\deqn{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.
\end{Details}
\begin{Value}
Kelly Ratio or Bet/Leverage Size
\end{Value}
\begin{Author}\relax
Brian G. Peterson
\end{Author}
\begin{References}\relax
Thorp, Edward O. (1997; revised 1998). The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market.
\url{http://www.bjmath.com/bjmath/thorp/paper.htm} \\
\url{http://en.wikipedia.org/wiki/Kelly_criterion}
\end{References}
\begin{Examples}
\begin{ExampleCode}
    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])
\end{ExampleCode}
\end{Examples}

