Chapter 7 Capital Asset Pricing and Arbitrage Pricing theory I Capital Asset Pricing Model CAPM for a security to its reisk as measured by beta model that relates the required rate of return Investors cannot effect prices by their indivudal trades a Assupmtions i ii All investors want same holding period iii Have access to unlimited risk free borrowing iv No taxes nor transaction costs v Rational investors who want highest returns vi All investors analyze securities the same way b Equilibirium i All investors hold Portfolio M 1 this intersects at tangent point wher CAL is Tangent to Efficency Fronteir 2 Risk Premium a E rM rf A 2 M i is the standard deviation of the return of the market portofolio ii A scale factor representing the degree of risk c Mutual Fund Theorm be satisfied by a single mutual fund all investors desire the same risky portfolio and can i Technical Side efficent mutual fund created by an efficient manager ii Personal Side The amount of risk and risk free asset determines an investors risk tolerance iii PASSIVE STRATEGY d Risk Premium of Market Portfolio i E rM rf 1 proportional to 2 2 see example on page 193 M e Expected Returns on Individual Securities i The Ratio of risk premium of an asset is proportional to its beta ii The securities expected esxcess return risk premium E r rf will be protional to its beta iii E rD rf BD E rM rf rf BD Risk Premium 1 E rD expected return of security D 2 3 BD Beta of security D 4 E rM expected return of Market rf risk free rate iv Beta of a portfolio is the weighted average of the individual Betas f Security Market Line SML return beta relationship of the CAPM graphical representation of the expected i Graphs individual assets risk premiums as a function of asset risk 1 opposed to CML which graphs risk premiums of whole ii Alpha the aabnormal rate of return on a security in excess of what would be predicted by an equilibrium model such as the CAPM 1 overpriced stocks have negatinve alpha are priced below portfolios the CAPM CAPM 2 Underpriced stocks have a positive alpha placed above the 3 E rD D rf BD E rM rf D rf BD Risk Premium 4 Used to determine if Capital Projects should be calculated 5 Can find return if return is greater than IRR Reject II CAPM and the Index Model a Limitations i Relies on theoretical market portfolio ii Expected as opposed to actual returns b Index Model i rit rft i Bi rMt tft eit rit the holding Period return HPR on asset I in period t 1 2 i y intercept of line that relates assets i reaized excess return to the realized excess return of the index 3 Bi slop of line that relates assets i realized excess return to the realized excess return of the index rm index return 4 5 eit firm specific risk effects durin holding period t a over a long period of time e 0 b thus i E rit rft i Bi rMt tft
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