Appraisal ratio is the Jensen's alpha adjusted for specific risk. The numerator is divided by specific risk instead of total risk.
AppraisalRatio(
Ra,
Rb,
Rf = 0,
method = c("appraisal", "modified", "alternative"),
...
)an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns
return vector of the benchmark asset
risk free rate, in same period as your returns
is one of "appraisal" to calculate appraisal ratio, "modified" to calculate modified Jensen's alpha or "alternative" to calculate alternative Jensen's alpha.
any other passthru parameters
Modified Jensen's alpha is Jensen's alpha divided by beta.
Alternative Jensen's alpha is Jensen's alpha divided by systematic risk.
$$Appraisal ratio = \frac{\alpha}{\sigma_{\epsilon}}$$
$$Modified Jensen's alpha = \frac{\alpha}{\beta}$$
$$Alternative Jensen's alpha = \frac{\alpha}{\sigma_S}$$
where \(alpha\) is the Jensen's alpha, \(\sigma_{epsilon}\) is the specific risk, \(\sigma_S\) is the systematic risk.
Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.77
data(portfolio_bacon)
print(AppraisalRatio(portfolio_bacon[,1], portfolio_bacon[,2], method="appraisal")) #expected -0.430
#> [1] -0.4302756
print(AppraisalRatio(portfolio_bacon[,1], portfolio_bacon[,2], method="modified"))
#> [1] -0.01418576
print(AppraisalRatio(portfolio_bacon[,1], portfolio_bacon[,2], method="alternative"))
#> [1] -0.1066928
data(managers)
print(AppraisalRatio(managers['1996',1], managers['1996',8]))
#> [1] 1.623025
print(AppraisalRatio(managers['1996',1:5], managers['1996',8]))
#> HAM1 HAM2 HAM3 HAM4 HAM5
#> Appraisal ratio (Risk free = 0) 1.623025 NA 3.527723 0.7070483 NA