HAASSCHOOLOFBUSINESSUGBA 103UNIVERSITYOFCALIFORNIAATBERKELEYAVINASHVERMABRIEFTEACHINGNOTEANDHOMEWORK7Let us first note that squared correlation, commonly referred to as “R-squared,” between returns on Security iand 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 Security i,denoted 2iσ, into two components in the following equation: σβσσεiiMMi2222=+.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:222iMiMσσβ.Now, by definition: MiiMimMiiMiMσσρσσσσρ***=⇒≡;And, again by definition:βσσiMiMM≡2.Substituting for iMσfrom the first expression in the numerator of the second, we get: iMiMiMσσβρ≡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
This is the end of the preview.
access the rest of the document.