Prospect ratio of the return distribution

Prospect ratio is a ratio used to penalise loss since most people feel loss greater than gain

ProspectRatio(R, MAR, ...)

Arguments

R

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

the minimum acceptable return
…

any other passthru parameters

Details

$$ProspectRatio(R) = \frac{\frac{1}{n}*\sum^{n}_{i=1}(Max(r_i,0)+2.25*Min(r_i,0) - MAR)}{\sigma_D}$$

where \(n\) is the number of observations of the entire series, MAR is the minimum acceptable return and \(\sigma_D\) is the downside risk

References

Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.100

Examples

data(portfolio_bacon)
MAR = 0.05
print(ProspectRatio(portfolio_bacon[,1], MAR)) #expected -0.134
#> [1] -0.1347065

data(managers)
MAR = 0
print(ProspectRatio(managers['1996'], MAR))
#>                                HAM1     HAM2     HAM3      HAM4 HAM5 HAM6
#> Prospect ratio (MAR = 0%) 0.9737463 442.1359 1.725605 0.5960639   NA   NA
#>                           EDHEC LS EQ  SP500 TR  US 10Y TR US 3m TR
#> Prospect ratio (MAR = 0%)          NA 0.7975008 -0.7234556      Inf
print(ProspectRatio(managers['1996',1], MAR))
#> [1] 0.9737463