Specific risk is the standard deviation of the error term in the regression equation.
SpecificRisk(Ra, Rb, Rf = 0, ...)Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.75
data(portfolio_bacon)
print(SpecificRisk(portfolio_bacon[,1], portfolio_bacon[,2])) #expected 0.0329
#> [1] 0.03293109
data(managers)
print(SpecificRisk(managers['1996',1], managers['1996',8]))
#> [1] 0.04977046
print(SpecificRisk(managers['1996',1:5], managers['1996',8]))
#> HAM1 HAM2 HAM3 HAM4 HAM5
#> Specific Risk = 0.04977046 NA 0.06225051 0.0857627 NA