TreynorRatio: calculate Treynor Ratio or modified Treynor Ratio of excess... In PerformanceAnalytics: Econometric Tools for Performance and Risk Analysis

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

 `1` ```TreynorRatio(Ra, Rb, Rf = 0, scale = NA, modified = FALSE) ```

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) `modified` a boolean to decide whether to return the Treynor ratio or Modified Treynor ratio

Details

To calculate modified Treynor ratio, we divide the numerator by the systematic risk instead of the beta.

Equation:

(mean(Ra-Rf))/(Beta(Ra,Rb))

ModifiedTreynorRatio = (Rp - Rf)/sytematic risk

Author(s)

Peter Carl, Matthieu Lestel

References

http://en.wikipedia.org/wiki/Treynor_ratio, Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.77

`SharpeRatio` `SortinoRatio` `CAPM.beta`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```data(portfolio_bacon) data(managers) round(TreynorRatio(managers[,1], managers[,8], Rf=.035/12),4) round(TreynorRatio(managers[,1], managers[,8], Rf = managers[,10]),4) round(TreynorRatio(managers[,1:6], managers[,8], Rf=.035/12),4) round(TreynorRatio(managers[,1:6], managers[,8], Rf = managers[,10]),4) round(TreynorRatio(managers[,1:6], managers[,8:7], Rf=.035/12),4) round(TreynorRatio(managers[,1:6], managers[,8:7], Rf = managers[,10]),4) print(TreynorRatio(portfolio_bacon[,1], portfolio_bacon[,2], modified = TRUE)) #expected 0.7975 print(TreynorRatio(managers['1996',1], managers['1996',8], modified = TRUE)) print(TreynorRatio(managers['1996',1:5], managers['1996',8], modified = TRUE)) ```