Systematic risk of the return distribution

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, ...)

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

scale

number of periods in a year (daily scale = 252, monthly scale = 12, quarterly scale = 4)

...

any other passthru parameters

Details

$$\sigma_s = \beta * \sigma_m$$

where \(\sigma_s\) is the systematic risk, \(\beta\) is the regression beta, and \(\sigma_m\) is the market risk

References

Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.75

Author

Matthieu Lestel

Examples

data(portfolio_bacon)
print(SystematicRisk(portfolio_bacon[,1], portfolio_bacon[,2])) #expected 0.013
#> [1] 0.132806

data(managers)
print(SystematicRisk(managers['2002',1], managers['2002',8]))
#> [1] 0.1103665
print(SystematicRisk(managers['2002',1:5], managers['2002',8]))
#>                                           HAM1       HAM2       HAM3      HAM4
#> Systematic Risk to SP500 TR (Rf = 0) 0.1103665 0.02041913 0.08939036 0.1651298
#>                                            HAM5
#> Systematic Risk to SP500 TR (Rf = 0) 0.02013523