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CHAPTER TWELVE

CHAPTER TWELVE. ARBITRAGE PRICING THEORY. Background. Estimating expected return with the Asset Pricing Models of Modern Finance CAPM Strong assumption - strong prediction. Expected Return. Expected Return. B. C. x. x. x. x. x. x. Market Index. x. x. x. x. x. x. x. x.

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CHAPTER TWELVE

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  1. CHAPTER TWELVE ARBITRAGE PRICING THEORY

  2. Background • Estimating expected return with the Asset Pricing Models of Modern Finance • CAPM • Strong assumption - strong prediction

  3. Expected Return Expected Return B C x x x x x x Market Index x x x x x x x x x x x A x x x x x x x Market Beta Risk (Return Variability) Market Index on Efficient Set Corresponding Security Market Line

  4. Expected Return Expected Return Risk (Return Variability) Market Beta Market Index Inside Efficient Set Corresponding Security Market Cloud Market Index

  5. FACTOR MODELS • ARBITRAGE PRICING THEORY (APT) • is an equilibrium factor model of security returns • Principle of Arbitrage • the earning of riskless profit by taking advantage of differentiated pricing for the same physical asset or security • Arbitrage Portfolio • requires no additional investor funds • no factor sensitivity • has positive expected returns • Example …

  6. Expected Return 35% F E D 25% C 15% B A 5% -3 -1 -5% 1 3 Interest Rate Beta -15% Curved Relationship Between Expected Return and Interest Rate Beta

  7. The Arbitrage Pricing Theory • Two stocks • A: E(r) = 4%; Interest-rate beta = -2.20 • B: E(r) = 26%; Interest-rate beta = 1.83 • Invest 54.54% in E and 45.46% in A • Portfolio E(r) = .5454 * 26% + .4546 * 4% = 16% • Portfolio beta = .5454 * 1.83 + .4546 * -2.20 = 0 • With many combinations like this, you can create a risk-free portfolio with a 16% expected return.

  8. The Arbitrage Pricing Theory • Two different stocks • C: E(r) = 15%; Interest-rate beta = -1.00 • D: E(r) = 25%; Interest-rate beta = 1.00 • Invest 50.00% in E and 50.00% in A • Portfolio E(r) = .5000 * 25% + .4546 * 15% = 20% • Portfolio beta = .5000 * 1.00 + .5000 * -1.00 = 0 • With many combinations like this, you can create a risk-free portfolio with a 20% expected return. Then sell-short the 16% and invest the proceeds in the 20% to arbitrage.

  9. The Arbitrage Pricing Theory • No-arbitrage condition for asset pricing • If risk-return relationship is non-linear, you can arbitrage. • Attempts to arbitrage will force linearity in relationship between risk and return.

  10. Expected Return 35% F E 25% D 15% C 5% B A -3 -1 1 3 -5% Interest Rate Beta -15% APT Relationship Between Expected Return and Interest Rate Beta

  11. FACTOR MODELS • ARBITRAGE PRICING THEORY (APT) • Three Major Assumptions: • capital markets are perfectly competitive • investors always prefer more to less wealth • price-generating process is a K factor model

  12. FACTOR MODELS • MULTIPLE-FACTOR MODELS • FORMULA ri = ai + bi1 F1 + bi2 F2 +. . . + biKF K+ ei where r is the return on security i b is the coefficient of the factor F is the factor e is the error term

  13. FACTOR MODELS • SECURITY PRICING FORMULA: ri = l0 + l1 b1 + l2 b2 +. . .+ lKbK where ri = rRF +(d1-rRF )bi1 + (d2- rRF)bi2+ . . . +(d-rRF)biK

  14. FACTOR MODELS where r is the return on security i l0 is the risk free rate b is the factor e is the error term

  15. FACTOR MODELS • hence • a stock’s expected return is equal to the risk free rate plus k risk premiums based on the stock’s sensitivities to the k factors

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