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, ...)
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 |
systematic risk = beta * market risk
where σ_s is the systematic risk, β is the regression beta, and σ_m is the market risk
Matthieu Lestel
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 data(managers) print(SystematicRisk(managers['1996',1], managers['1996',8])) print(SystematicRisk(managers['1996',1:5], managers['1996',8]))
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