PerformanceAnalytics (version 1.1.0)

AppraisalRatio: Appraisal ratio of the return distribution

Description

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

Run this code
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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