Risk Decomposition: Variance or Standard Deviation—A Reexamination and Extension

This paper reexamines and extends the work of Ben Horim and Levy [1], which argued that risk decomposition should be based on standard deviation rather than on variance. Their analysis showed that decomposition of variance is wrong when β < 0 and that, in general, this procedure produces incorrect estimates of undiversifiable risk. This paper shows that these conclusions also apply to the no-risk-free asset extended CAPM if risk is adjusted for the unavoidable risk associated with the global minimum variance portfolio.