CAPM and Risky Arbitrage - WhatWeWillLearn This lecture...

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The CAPM and Risky Arbitrage Professor David McLean Alberta School of Business
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What We Will Learn This lecture will cover the following: The CAPM assumptions The resulting equilibrium conditions Capital Market Line (CML) Security Market Line (SML) Hedging and Risky Arbitrage 2
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The CAPM The CAPM is the lynchpin of modern finance theory It relies on mean-variance efficiency, which we covered in the last lecture The CAPM has many applications, such as estimating discount rates and evaluating mutual fund performance In this lecture we will learn a little bit about the assumptions that underlie the CAPM, but focus more on its applications 3
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The CAPM Assumptions Individual investors are price takers; trading does not impact prices Investors are rational; they desire mean-variance efficiency Investments are limited to financial assets, like stocks and bonds Ignore taxes and transaction costs, although we can include those and the effects are the same Investors have the same expectations of risk and returns 4
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CAPM Equilibrium Conditions All investors hold the same portfolio of risky assets; the market portfolio The market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value The market portfolio is on the efficient frontier and, moreover, it is the optimal risk portfolio 5
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Optimal Risky Portfolio Recall that in class we learned that all mean- variance optimizing investors should hold some combination of the optimal risky (tangency) portfolio and the risk free asset How to calculate the optimal P: Find wi that results in the highest the slope of the CAL (that is to maximize the reward – to – variability ratio) 6 p f p p i w r ) E(r S Max
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CAL becomes the CML In the CAPM, the market portfolio (M) is the optimal risky portfolio So now the Capital Allocation Line (CAL) is the Capital Market Line (CML) In the CAPM every investor holds some combination of M and the risk free asset These combinations are plotted on the CML 7
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The Capital Market Line E(r) E(rM) rf M CML m 8
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CML Slope and Market Risk  Premium M = The market portfolio
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