Appraisal ratio of the return distribution
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"),
...
)Ra |
an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns |
Rb |
return vector of the benchmark asset |
Rf |
risk free rate, in same period as your returns |
method |
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 = Jensen's alpha / specific risk
Modified Jensen's alpha = Jensen's alpha / beta
Alternative Jensen's alpha = Jensen's alpha / systematic risk
where alpha is the Jensen's alpha, σ_{epsilon} is the specific risk, σ_S is the systematic risk.
Matthieu Lestel
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 print(AppraisalRatio(portfolio_bacon[,1], portfolio_bacon[,2], method="modified")) print(AppraisalRatio(portfolio_bacon[,1], portfolio_bacon[,2], method="alternative")) data(managers) print(AppraisalRatio(managers['1996',1], managers['1996',8])) print(AppraisalRatio(managers['1996',1:5], managers['1996',8]))
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