d ratio of the return distribution

The d ratio is similar to the Bernado Ledoit ratio but inverted and taking into account the frequency of positive and negative returns.

DRatio(R, ...)

Arguments

R

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

...

any other passthru parameters

Details

It has values between zero and infinity. It can be used to rank the performance of portfolios. The lower the d ratio the better the performance, a value of zero indicating there are no returns less than zero and a value of infinity indicating there are no returns greater than zero.

$$DRatio(R) = \frac{n_{d}*\sum^{n}_{t=1}{max(-R_{t},0)}}{n_{u}*\sum^{n}_{t=1} {max(R_{t},0)}}$$

where \(n\) is the number of observations of the entire series, \(n_{d}\) is the number of observations less than zero, \(n_{u}\) is the number of observations greater than zero

References

Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.95

Author

Matthieu Lestel

Examples

data(portfolio_bacon)
print(DRatio(portfolio_bacon[,1])) #expected 0.401
#> [1] 0.4013329

data(managers)
print(DRatio(managers['1996']))
#>               HAM1         HAM2       HAM3      HAM4 HAM5 HAM6 EDHEC LS EQ
#> d ratio 0.07248996 0.0001052632 0.03085081 0.1383098  NaN  NaN         NaN
#>           SP500 TR US 10Y TR US 3m TR
#> d ratio 0.04607631  1.361501        0
print(DRatio(managers['1996',1])) #expected 0.0725
#> [1] 0.07248996