PerformanceAnalytics (version 1.4.3541)

DRatio: d ratio of the return distribution

Description

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

Usage

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

Examples

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

data(managers)
print(DRatio(managers['1996']))
print(DRatio(managers['1996',1])) #expected 0.0725