The covariance is the measure of risk added by asset

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Unformatted text preview: (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 : > 1 riskier than average σi ,m βi ≡ 2 = 1 average risk σm < 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: Financial Economics 7/ 17 CAPM Generalization: General Motivation The functional form of our CAPM result E (ri ) = rf + β [E (rm ) − rf ] , lends itself to the...
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