TreynorRatio: calculate Treynor Ratio or modified Treynor Ratio of excess...

In braverock/PerformanceAnalytics: Econometric Tools for Performance and Risk Analysis

calculate Treynor Ratio or modified 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, 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:

TreynorRatio = \frac{\overline{(R_{a}-R_{f})}}{\beta_{a,b}}

ModifiedTreynorRatio = \frac{r_p - r_f}{\sigma_s}

Author(s)

Peter Carl, Matthieu Lestel

References

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

See Also

SharpeRatio SortinoRatio CAPM.beta

Examples

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['2002',1], managers['2002',8], modified = TRUE))
print(TreynorRatio(managers['2002',1:5], managers['2002',8], modified = TRUE)) 

braverock/PerformanceAnalytics documentation built on Dec. 16, 2024, 12:56 p.m.