Fama beta of the return distribution

Fama beta is a beta used to calculate the loss of diversification. It is made so that the systematic risk is equivalent to the total portfolio risk.

FamaBeta(Ra, Rb, ...)

Arguments

Ra

an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns
Rb

return vector of the benchmark asset
…

any other passthru parameters

Details

$$\beta_F = \frac{\sigma_P}{\sigma_M}$$

where \(\sigma_P\) is the portfolio standard deviation and \(\sigma_M\) is the market risk

References

Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.78

Examples


data(portfolio_bacon)
print(FamaBeta(portfolio_bacon[,1], portfolio_bacon[,2])) #expected 1.03
#>                              portfolio.monthly.return....
#> portfolio.monthly.return....                     1.030395

data(managers)
print(FamaBeta(managers['1996',1], managers['1996',8]))
#>           HAM1
#> HAM1 0.5351217
print(FamaBeta(managers['1996',1:5], managers['1996',8]))
#>                 HAM1 HAM2     HAM3     HAM4 HAM5
#> Fama Beta  0.5351217   NA 1.007084 1.037632   NA