Appraisal ratio is the Jensen's alpha adjusted for specific risk. The numerator is divided by specific risk instead of total risk.
Usage
AppraisalRatio(
Ra,
Rb,
Rf = 0,
method = c("appraisal", "modified", "alternative"),
...
)Arguments
- 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
Details
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.
References
Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.77
Examples
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