PerformanceAnalytics (version 1.0.4.4)

TreynorRatio: calculate Treynor Ratio of excess return over CAPM beta

Description

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).

Usage

TreynorRatio(Ra, Rb, Rf = 0, scale = NA)

Arguments

Ra

an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns

Rb

return vector of the benchmark asset

Rf

risk free rate, in same period as your returns

scale

number of periods in a year (daily scale = 252, monthly scale = 12, quarterly scale = 4)

Details

Equation: $$\frac{\overline{(R_{a}-R_{f})}}{\beta_{a,b}}$$

References

http://en.wikipedia.org/wiki/Treynor_ratio

See Also

SharpeRatio SortinoRatio CAPM.beta

Examples

data(managers)
round(TreynorRatio(managers[,1,drop=FALSE], managers[,8,drop=FALSE], Rf=.035/12),4) 
round(TreynorRatio(managers[,1,drop=FALSE], managers[,8,drop=FALSE], Rf = managers[,10,drop=FALSE]),4) 
round(TreynorRatio(managers[,1:6], managers[,8,drop=FALSE], Rf=.035/12),4) 
round(TreynorRatio(managers[,1:6], managers[,8,drop=FALSE], Rf = managers[,10,drop=FALSE]),4)
round(TreynorRatio(managers[,1:6], managers[,8:7,drop=FALSE], Rf=.035/12),4) 
round(TreynorRatio(managers[,1:6], managers[,8:7,drop=FALSE], Rf = managers[,10,drop=FALSE]),4)