\HeaderA{TreynorRatio}{calculate Treynor Ratio of excess return over CAPM beta}{TreynorRatio}
\keyword{ts}{TreynorRatio}
\keyword{multivariate}{TreynorRatio}
\keyword{distribution}{TreynorRatio}
\keyword{models}{TreynorRatio}
\begin{Description}\relax
The Treynor ratio is similar to the Sharpe Ratio, except it uses beta as the volatility measure (to divide the investment's excess return over the beta).
\end{Description}
\begin{Usage}
\begin{verbatim}
TreynorRatio(Ra, Rb, Rf = 0, scale = NA)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{Ra}] an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns 
\item[\code{Rb}] return vector of the benchmark asset 
\item[\code{Rf}] risk free rate, in same period as your returns 
\item[\code{scale}] number of periods in a year (daily scale = 252, monthly scale = 12, quarterly scale = 4) 
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
Equation:
\deqn{\frac{\overline{(R_{a}-R_{f})}}{\beta_{a,b}}}{}
\end{Details}
\begin{Value}
Treynor ratio
\end{Value}
\begin{Author}\relax
Peter Carl
\end{Author}
\begin{References}\relax
\url{http://en.wikipedia.org/wiki/Treynor_ratio}
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{SharpeRatio}{SharpeRatio}}
\code{\LinkA{SortinoRatio}{SortinoRatio}}
\code{\LinkA{CAPM.beta}{CAPM.beta}}
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
data(managers)
TreynorRatio(managers[,1,drop=FALSE], managers[,8,drop=FALSE], Rf=.035/12) 
TreynorRatio(managers[,1,drop=FALSE], managers[,8,drop=FALSE], Rf = managers[,10,drop=FALSE]) 
TreynorRatio(managers[,1:6], managers[,8,drop=FALSE], Rf=.035/12) 
TreynorRatio(managers[,1:6], managers[,8,drop=FALSE], Rf = managers[,10,drop=FALSE])
TreynorRatio(managers[,1:6], managers[,8:7,drop=FALSE], Rf=.035/12) 
TreynorRatio(managers[,1:6], managers[,8:7,drop=FALSE], Rf = managers[,10,drop=FALSE])

\end{ExampleCode}
\end{Examples}

