AppraisalRatio | R Documentation |
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 = \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.
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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