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, ...)
R |
an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns |
... |
any other passthru parameters |
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) = nd*sum (t=1..n)(max(-R(t),0)) / nu*sum(t=1..n)(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
Matthieu Lestel
Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.95
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
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