Systematic risk as defined by Bacon(2008) is the product of beta by market risk. Be careful ! It's not the same definition as the one given by Michael Jensen. Market risk is the standard deviation of the benchmark. The systematic risk is annualized
SystematicRisk(Ra, Rb, Rf = 0, scale = NA, ...)
| 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 |
| scale | number of periods in a year (daily scale = 252, monthly scale = 12, quarterly scale = 4) |
| … | any other passthru parameters |
$$\sigma_s = \beta * \sigma_m$$
where \(\sigma_s\) is the systematic risk, \(\beta\) is the regression beta, and \(\sigma_m\) is the market risk
Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.75
data(portfolio_bacon) print(SystematicRisk(portfolio_bacon[,1], portfolio_bacon[,2])) #expected 0.013#> [1] 0.132806data(managers) print(SystematicRisk(managers['1996',1], managers['1996',8]))#> [1] 0.02626834print(SystematicRisk(managers['1996',1:5], managers['1996',8]))#> HAM1 HAM2 HAM3 HAM4 #> Systematic Risk to SP500 TR (Rf = 0) 0.02626834 0.0802869 0.08824707 0.06878241 #> HAM5 #> Systematic Risk to SP500 TR (Rf = 0) NA