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Week 7_MPT and CAPM_Note by Wang

Week 7_MPT and CAPM_Note by Wang - MPT and CAPM An MGT 330...

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MPT and CAPM An MGT 330 supplement note Kevin Q. Wang This is an entirely optional, very mathematical note on the modern portfolio theory (MPT) and the capital asset pricing model (CAPM). It is for those who cannot live without math. That is, if you don’t feel you have learned anything without seeing a mathematical derivation, then the note is for you. This note presents (i) how to get the tangency portfolio, (ii) an elegant result of the portfolio theory, and (iii) how to establish the CAPM. Notations Suppose we have n risky assets with returns ˜ r 1 , · · · , ˜ r n , and a riskless asset. The riskless rate is r f . Let w be the n × 1 vector of weights on the n risky assets, i.e., w = ( w 1 · · · w n ) 0 , and let µ denote the n × 1 vector of expected excess returns on the risky assets, i.e., µ = ( µ 1 · · · µ n ) 0 , where µ i = E r i ) r f . Let V be the n × n variance-covariance matrix of the n risky returns. The Tangency Portfolio The mean-variance optimization problem is as follows. We need to fi
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