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Chapter 11

Arbitrage Pricing 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 .

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Chapter 11

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  1. Arbitrage Pricing Theory and Multifactor Models of Risk and Return Chapter 11

  2. 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

  3. 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

  4. 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.

  5. 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

  6. Multifactor SML Models E(r) = rf + BGDPRPGDP + BIRRPIR BGDP = Factor sensitivity for GDP RPGDP = Risk premium for GDP BIR = Factor sensitivity for Interest Rate RPIR = Risk premium for GDP

  7. Arbitrage Pricing Theory • Arbitrage - arises if an investor can construct 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.

  8. APT & Well-Diversified Portfolios rP = E (rP) + bPF + eP F = some factor For a well-diversified portfolio: eP approaches zero Similar to CAPM

  9. Portfolios and Individual Security E(r)% E(r)% F F Individual Security Portfolio

  10. Disequilibrium Example E(r)% 10 A D 7 6 C Risk Free 4 Beta for F .5 1.0

  11. 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%

  12. APT with Market Index Portfolio E(r)% M [E(rM) - rf] Market Risk Premium Risk Free Beta (Market Index) 1.0

  13. APT and CAPM Compared • APT applies to well diversified portfolios and not necessarily to individual stocks. • With APT it is possible for some individual stocks to be mispriced - not lie on the SML. • APT is more general in that it gets to an expected return and beta relationship without the assumption of the market portfolio. • APT can be extended to multifactor models.

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