# J hawkins econ 136 financial economics 2 17 capm and

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Unformatted text preview: f asset i to a market portfolio 2 2 σm = wi2 σi2 + (1 − wi )2 σm + 2wi (1 − wi ) σi ,m 0 X \$ \$ 2wi X2 \$\$ 1 2 = w i2 + \$\$\$ i )2 σm + \$\$(1 \$\$i )σi ,m σ (1 − w 2wi \$ − w i 2 = σm + 2wi σi ,m Portfolios III: R. J. Hawkins Econ 136: Financial Economics 2/ 17 CAPM and β Intuition Add a small amount wi of asset i to a market portfolio 2 2 σm = σm + 2wi σi ,m . The covariance is the measure of risk added by asset i . The covariance is a percentage value. Normalizing by dividing by the variance of the market portfolio we deﬁne the β of asset i : &gt; 1 riskier than average σi ,m βi ≡ 2 = 1 average risk σm &lt; 1 safer than average Portfolios III: R. J. Hawkins Econ 136: Financial Economics 3/ 17 CAPM, Risk Decomposition, and Diversiﬁcation 2 σi ,i = 40% and σi ,j = 15% ¯ ¯ VARIANCE OF PORTFOLIO (%) 40 30 Idiosyncratic Risk (diversifiable) 20 10 Total Risk Systematic Risk (not diversifiable) 0 0 5 10 15 20 25 NUMBER OF SECURITIES Portfolios III: R. J. Hawkins Econ 136:...
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