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, ...)
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 |
epsilon_r = r_p - alpha_r - beta_r * b
where α_r is the regression alpha, β_r is the regression beta, r_p is the portfolio return and b is the benchmark return
Matthieu Lestel
Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.71
data(portfolio_bacon) print(SFM.epsilon(portfolio_bacon[,1], portfolio_bacon[,2])) #expected -0.013 data(managers) print(SFM.epsilon(managers['1996',1], managers['1996',8])) print(SFM.epsilon(managers['1996',1:5], managers['1996',8]))
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