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13 Pages

### Chap10

Course: FIN 320, Fall 2008
School: Wisconsin
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Word Count: 374

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Pricing Arbitrage Theory and Multifactor Models of Risk and Return Chapter 11 Single Factor Model Returns on a security come from two sources Common macro-economic factor Firm specific events Possible common macro-economic factors Gross Domestic Product Growth Interest Rates Single Factor Model Equation Ri = E(ri) + Betai (F) + ei Ri = Return for security i Betai = Factor sensitivity or factor loading or...

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Pricing Arbitrage Theory and Multifactor Models of Risk and Return Chapter 11 Single Factor Model Returns on a security come from two sources Common macro-economic factor Firm specific events Possible common macro-economic factors Gross Domestic Product Growth Interest Rates Single Factor Model Equation Ri = E(ri) + Betai (F) + ei Ri = Return for security i Betai = Factor sensitivity or factor loading or factor beta F = Surprise in macro-economic factor (F could be positive, negative or zero) ei = Firm specific events Multifactor Models Use more than one factor in addition to market return Examples include gross domestic product, expected inflation, interest rates etc. Estimate a beta or factor loading for each factor using multiple regression. Multifactor Model Equation Ri = E(ri) + BetaGDP (GDP) + BetaIR (IR) + ei Ri = Return for security i BetaGDP= Factor sensitivity for GDP BetaIR = Factor sensitivity for Interest Rate ei = Firm specific events Multifactor SML Models E(r) = rf + GDPRPGDP + IRRPIR GDP = Factor sensitivity for GDP RPGDP = Risk premium for GDP IR = Factor sensitivity for Interest Rate RPIR = Risk premium for GDP Arbitrage Pricing Theory Arbitrage - arises if an investor construct can a zero investment portfolio with a sure profit. Since no investment is required, an investor can create large positions to secure large levels of profit. In efficient markets, profitable arbitrage opportunities will quickly disappear. APT & Well-Diversified Portfolios rP = E (rP) + PF + eP F = some factor For a well-diversified portfolio: eP approaches zero Similar to CAPM Portfolios and Individual Security E(r)% E(r)% F Portfolio Individual Security F Disequilibrium Example E(r)% 10 7 6 Risk Free 4 .5 1.0 D C A Beta for F Disequilibrium Example Short Portfolio C Use funds to construct an equivalent risk higher return Portfolio D. D is comprised of A & Risk-Free Asset Arbitrage profit of 1...

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