Regression epsilon of the return distribution

The regression epsilon is an error term measuring the vertical distance between the return predicted by the equation and the real result.

CAPM.epsilon(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

$$\epsilon_r = r_p - \alpha_r - \beta_r * b$$

where \(\alpha_r\) is the regression alpha, \(\beta_r\) 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.71

Examples


data(portfolio_bacon)
print(SFM.epsilon(portfolio_bacon[,1], portfolio_bacon[,2])) #expected -0.013
#> [1] -0.01313932

data(managers)
print(SFM.epsilon(managers['1996',1], managers['1996',8]))
#> [1] 0.07425366
print(SFM.epsilon(managers['1996',1:5], managers['1996',8]))
#>                                          HAM1      HAM2      HAM3       HAM4
#> Regression epsilon (Risk free = 0) 0.07425366 0.5399193 0.2048063 0.05570592
#>                                    HAM5
#> Regression epsilon (Risk free = 0)   NA