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Chapter 11

Chapter 11. Arbitrage Pricing Theory. 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

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Chapter 11

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  1. Chapter 11 ArbitragePricing Theory 11-1

  2. 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 11-2

  3. Arbitrage Example from Text pp. 308-310 Current Expected Standard Stock Price$ Return% Dev.% A 10 25.0 29.58 B 10 20.0 33.91 C 10 32.5 48.15 D 10 22.5 8.58 11-3

  4. Arbitrage Portfolio Mean S.D. Correlation Portfolio A,B,C 25.83 6.40 0.94 D 22.25 8.58 11-4

  5. E. Ret. * P * D St.Dev. Short 3 shares of D and buy 1 of A, B & C to form P You earn a higher rate on the investment than you pay on the short sale Arbitrage Action and Returns 11-5

  6. APT & Well-Diversified Portfolios rP = E (rP) + bPF + eP F = some factor For a well-diversified portfolio eP approaches zero Similar to CAPM 11-6

  7. E(r)% E(r)% F F Portfolio Individual Security Portfolio &Individual Security Comparison 11-7

  8. Disequilibrium Example E(r)% 10 A D 7 6 C Risk Free 4 Beta for F .5 1.0 11-8

  9. 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% 11-9

  10. APT with Market Index Portfolio E(r)% M [E(rM) - rf] Market Risk Premium Risk Free Beta (Market Index) 1.0 11-10

  11. 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 11-11

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