PerformanceAnalytics (version 2.0.8)

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

Author

Matthieu Lestel

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
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]))