Martin ratio of the return distribution

To calculate Martin ratio we divide the difference of the portfolio return and the risk free rate by the Ulcer index

MartinRatio(R, Rf = 0, ...)

Arguments

R

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

Rf

risk free rate, in same period as your returns

...

any other passthru parameters

Details

$$Martin ratio = \frac{r_P - r_F}{\sqrt{\sum^{n}_{i=1} \frac{{D'_i}^2}{n}}}$$

where \(r_P\) is the annualized portfolio return, \(r_F\) is the risk free rate, \(n\) is the number of observations of the entire series, \(D'_i\) is the drawdown since previous peak in period i

References

Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.91

Author

Matthieu Lestel

Examples

data(portfolio_bacon)
print(MartinRatio(portfolio_bacon[,1])) #expected 1.70
#>             portfolio.monthly.return....
#> Ulcer Index                      1.70772

data(managers)
print(MartinRatio(managers['1996']))
#>                           HAM1     HAM2     HAM3     HAM4 HAM5 HAM6 EDHEC LS EQ
#> Martin Ratio (Rf = 0) 15.49888 16390.63 19.24429 13.67313   NA   NA          NA
#>                       SP500 TR  US 10Y TR US 3m TR
#> Martin Ratio (Rf = 0) 14.81878 0.01003279      Inf
print(MartinRatio(managers['1996',1])) 
#>                 HAM1
#> Ulcer Index 15.49888