306 - CAPM 3/28/11 4:00 PM CAPM:Capitalassetpricingmodel...

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CAPM 3/28/11 4:00 PM CAPM: Capital asset pricing model -beta: measure of risk -security market line -CAPM -practical details BETA -regression analysis: Ri-rf= Bi(Rm-rf) + Epsilon i -Ri= return on stock I / Rm= return on market / rf= risk free rate / Ei= error term Ri-rf= excess returns above the risk free rate for the stock Rm-rf= excess returns for the market -The regression asks: “Does this stock have high returns when the market goes  up and low returns when the market goes down?” If yes, B is high If no, B is low B measures the comovement of the stocks with the market as a whole But the market as a whole only respond to systematic risk So B is a measure of the stock’s systematic risk
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B high==== high systematic risk Why take an rf? We want only risk concerns not TUM Examples: -Risk free asset? B=0 because no risk implies no systematic risk -Market portfolio? B=1 because the market has one unit of systematic risk by  construction -Most stocks have Bs fairly close to 1 -Possible to have a stock with B=0? Yes No systematic risk does not mean no risk B=0 just means an asset ignores the market on average -Possible to have a stock with B<0? Yes -Portfolios: Stocks          Standard deviation         B            C                    20%                             1.25 K                    30%                              .95 K has more total risk because greater standard deviation C has more systematic risk because greater B C has greater expected returns
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The systematic risk does”add” like expected return, so we can easily compute  portfolio Bs: Bport= sum (Wi Bi) = 2/3 (.95) + 1/3 (1.25) = 1.05 Let’s say we have a stock with B=1.5 and access to T-bills (B=0) How do we construct a portfolio with B=1? 2/3 in stocks and 1/3 in T-bills What if we borrow? Start with $100 and borrow $50. Invest all $150 in the stock  (B=1.5) Wstock=1.5      Wbond=-.5 So Bport= 1.5(1.5) + (-5)(0) = 2.25 Ex: vanilla home mortgage: 80% loan, 20% down payment        For every $1 we start with, we borrow $4 and the total $5 goes in to                     the house So Whome=5    Wloan=4 If the B on the property is 1.1 then the B of the home + mortgage= 1.1*5+0(- 4)=5.5 SECURITY MARKET LINE (SML) -rewards/risk plot for an asset
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2 Assets:  Stock C with B=1.25  E(R)=14% Risk free with B=0 and rf=5% ----Plot to a graph let say we want a portfolio with B=.625. How do we get this? Split the portfolio between C and T-bills
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This note was uploaded on 09/11/2011 for the course BUAD 306 taught by Professor Selvili during the Spring '07 term at USC.

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306 - CAPM 3/28/11 4:00 PM CAPM:Capitalassetpricingmodel...

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