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H AAS S CHOOL OF B USINESS UGBA 103 U NIVERSITY OF C ALIFORNIA AT B ERKELEY A VINASH V ERMA B RIEF T EACHING N OTE AND H OMEWORK 7 Let us first note that squared correlation, commonly referred to as “R-squared,” between returns on S ecurity i and those on the market portfolio measures the percentage of the total risk of the security that cannot be diversified away. To elaborate, we can decompose the total risk of S ecurity i, denoted 2 i σ , into two components in the following equation: σ β σ σ ε i iM M i 2 2 2 2 = + . The first term on the RHS is the systematic or the undiversifiable risk, and the second term is the unsystematic or diversifiable risk. It follows that the percentage of the undiversifiable risk to the total is: 2 2 2 i M iM σ σ β . Now, by definition: M i iM im M i iM iM σ σ ρ σ σ σ σ ρ * * * = ; And, again by definition: β σ σ iM iM M 2 . Substituting for iM σ from the first expression in the numerator of the second, we get: i M iM iM σ σ β ρ Squaring both sides shows us that R-squared is indeed the fraction of the total risk of a security that is systematic. Conversely, the fraction of the total risk
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