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Chapter 11

Chapter 11. Arbitrage Pricing Theory. Arbitrage Pricing Theory. Developed by Ross (1976,1977) Has three major assumption : Capital markets are perfectly competitive Investors always prefer more wealth to less wealth with certainty

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Chapter 11

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  1. Chapter 11 ArbitragePricing Theory Chapter 10-Bodie-Kane Marcus

  2. Arbitrage Pricing Theory • Developed by Ross (1976,1977) • Has three major assumption : • Capital markets are perfectly competitive • Investors always prefer more wealth to less wealth with certainty • The stochastic process generating asset returns can be expressed as a linear functions of a set of K factors (or indexes) Source: Reilly Brown

  3. 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 Chapter 10-Bodie-Kane Marcus

  4. Arbitrage Pricing Theory • Fama and French demonstrates: • Value stocks (with high book value-to market price ratios) tend to produce larger risk adjusted returns than growth stock (with low book to market price ratios • Value Stocks : stocks that appear to be undervalued for reasons besides earning growth potential. These stock are ussually identified based on high dividend yields, low P/E ratios or low P/B ratios • Growth stock : stock issue that generates a higher rate of return than other stocks in the market with similar risk characteristic Source: Reilly Brown

  5. Price to Book (MRQ) Chapter 10-Bodie-Kane Marcus

  6. Arbitrage Example 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 Chapter 10-Bodie-Kane Marcus

  7. Arbitrage Portfolio Mean S.D. Correlation Portfolio A,B,C 25.83 6.40 0.94 D 22.25 8.58 Chapter 10-Bodie-Kane Marcus

  8. E( R) * P * D St.Dev. Short (jual) 3 shares of D and buy 1 of A, B & C to form P (portofolio) You earn a higher rate on the investment Arbitrage Action and Returns Chapter 10-Bodie-Kane Marcus

  9. APT Reilly Brown Chapter 10-Bodie-Kane Marcus

  10. Expected Return Equation Reilly Brown p.284

  11. Security Valuation with APT • Stocks : A,B,C • Two common systematic risk factors: (1&2) • The zero beta return (0) • E(RA) = (0.80)1 +(0.90) 2 • If 1= 4%; 2= 5% • E(RA) = (0.80) (4%) +(0.90) (5%)=7.7%=0.077 • PA= $35 → E(PA)= $35 (1 + 0.077) =$37.7 • If next year Stock Price A = $ 37.20 • So, Intrinsic value ($ 37.7) > Market Price ($37.2)→ Overvalued → sell Stock A Reilly Brown

  12. Arbitrage Reilly Brown

  13. Arbitrage Reilly Brown

  14. Arbitrage • Net Profit : Sell A (2 shares) Buy B(1) Buy C(1) • 2(35) - 2(37.2)+(37.8-35)+(38.5-35) • =$1.90 Reilly Brown

  15. APT & Well-Diversified Portfolios rP = E (rP) + bPF + eP F = some factor For a well-diversified portfolio eP approaches zero Similar to CAPM Chapter 10-Bodie-Kane Marcus

  16. E(r)% E(r)% F F Portfolio Individual Security Portfolio &Individual Security Comparison Simpangan (risiko) portofoliolebihkecildaripadaaset individual

  17. Disequilibrium Example E(r)% 10 A D 7 6 C 4 Risk Free Beta for F .5 1.0 Chapter 10-Bodie-Kane Marcus

  18. Disequilibrium Example • Short (jual) 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% Chapter 10-Bodie-Kane Marcus

  19. APT with Market Index Portfolio E(r)% M [E(rM) - rf] Market Risk Premium Risk Free Beta (Market Index) 1.0 Chapter 10-Bodie-Kane Marcus

  20. 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 Chapter 10-Bodie-Kane Marcus

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