Jensen's alpha of the return distribution

The Jensen's alpha is the intercept of the regression equation in the Capital Asset Pricing Model and is in effect the exess return adjusted for systematic risk.

CAPM.jensenAlpha(Ra, Rb, Rf = 0, ...)

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
…

any other passthru parameters

Details

$$\alpha = r_p - r_f - \beta_p * (b - r_f)$$

where \(r_f\) is the risk free rate, \(\beta_r\) is the regression beta, \(r_p\) is the portfolio return and b is the benchmark return

References

Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.72

Examples


data(portfolio_bacon)
print(SFM.jensenAlpha(portfolio_bacon[,1], portfolio_bacon[,2])) #expected -0.014
#> [1] -0.01416944

data(managers)
print(SFM.jensenAlpha(managers['1996',1], managers['1996',8]))
#> [1] 0.08077871
print(SFM.jensenAlpha(managers['1996',1:5], managers['1996',8]))
#>                                      HAM1 HAM2      HAM3       HAM4 HAM5
#> Jensen's Alpha (Risk free = 0) 0.08077871   NA 0.2196026 0.06063837   NA