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CAPM - Capital Asset Pricing Model 1 Estimating return on...

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) Emma Rasiel, 2009 1 Capital Asset Pricing Model 2 Estimating return on an individual security The Single Index Model r i - r f = β i (r m - r f ) + e i or equivalently Use “excess Returns” rather than total returns: (why?and what is R i ?) component of return due to market factor component of return due to firm-specific factor (assume e i uncorrelated w/ r m ) We will test a Single Factor Regression model of security returns using historic data, where the factor is a market index such as the S&P 500. R i = β i R m + e i Why a single factor (rather than multiple factors)? Why pick “the market” rather than other factors? Why should firm-specific component be uncorrelated with market factor?

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) Emma Rasiel, 2009 3 Link between CAPM and the CML E[r m ] - r f σ m r f E[r C ] σ C σ m E[r m ] Capital Market Line (CML) M The slope of the CML = We know that all investors' portfolios (i) Are made up of some combination of the riskless asset and M , the market portfolio (ii) Lie on the CML. Hence the risk-reward tradeoff for all investors is given by: this is sometimes referred to as the Market Price of Risk E[r m ] - r f σ m E[r C ] = r f + σ C (E[r m ] - r f ) σ m 4 Link between CAPM and the CML r f E[r i ] β 1 E[r m ] Security Market Line (SML) M E[r i ] = r f + β i (E[r m ] – r f ) If all investors have well diversified portfolios (so that idiosyncratic risk is diversified away), then the only source of risk is market risk (or beta risk). If we want to price a new security to add to our well-diversified portfolio, we care only about its beta risk.
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