TreynorRatio {PerformanceAnalytics} R Documentation

## 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})}}{β_{a,b}}

Treynor ratio

Peter Carl

### References

`SharpeRatio` `SortinoRatio` `CAPM.beta`

### Examples

```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])

```

[Package PerformanceAnalytics version 0.9.9-5 Index]