Chapter 11 Arbitrage Pricing Theory 1 Chapter 10

Chapter 11 Arbitrage Pricing Theory 1 Chapter 10 -Bodie-Kane Marcus

Arbitrage Pricing Theory �Developed by Ross (1976, 1977) �Has three major assumption : Capital markets are perfectly competitive 2. Investors always prefer more wealth to less wealth with certainty 3. The stochastic process generating asset returns can be expressed as a linear functions of a set of K factors (or indexes) 1. Source: Reilly Brown 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 3 Chapter 10 -Bodie-Kane Marcus

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 4

Price to Book (MRQ) TLKM BUMI BBRI SULI PTSP HMSP 5 Chapter 10 -Bodie-Kane Marcus COMPANY INDUSTRY 4. 34 2. 91 4. 12 1. 04 2. 58 2. 17 0. 94 2. 45 1. 00 0. 72 2. 36 0. 16

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 6 Chapter 10 -Bodie-Kane Marcus

Arbitrage Portfolio Mean Portfolio A, B, C 0. 94 D 7 S. D. Correlation 25. 83 22. 25 Chapter 10 -Bodie-Kane Marcus 8. 58 6. 40

Arbitrage Action and Returns 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 8 Chapter 10 -Bodie-Kane Marcus

APT Reilly Brown 9 Chapter 10 -Bodie-Kane Marcus

Expected Return Equation 10 Reilly Brown p. 284

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 11 Reilly Brown

Arbitrage Stock INTRINSIC Price ($) MARKET Price ($) A 37. 7 37. 2 CONDITION IV >MV B C 12 37 38. 4 OVER VALUED ACTION SELL IV < MV PUR UNDER VALUED CHASE 37. 8 38. 5 Reilly Brown

Arbitrage 13 Stock Weight Sell / buy Current Price Value A -1 Sell 2 shares $ 35 $ 70 B 0. 5 Buy 1 share $ 35 -$ 35 C 0. 5 Buy 1 share $ 35 -$ 35 Reilly Brown

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 14 Reilly Brown

APT & Well-Diversified Portfolios r. P = E (r. P) + b. PF + e. P F = some factor For a well-diversified portfolio e. P approaches zero Similar to CAPM 15 Chapter 10 -Bodie-Kane Marcus

Portfolio &Individual Security Comparison E(r)% F F Portfolio Individual Security Simpangan (risiko) portofolio lebih kecil dari pada aset individual 16

Disequilibrium Example E(r)% 10 7 A D 6 C 4 Risk Free. 5 17 Chapter 10 -Bodie-Kane Marcus 1. 0 Beta for F

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% 18 Chapter 10 -Bodie-Kane Marcus

APT with Market Index Portfolio E(r)% M [E(r. M) - rf] Market Risk Premium Risk Free 1. 0 19 Chapter 10 -Bodie-Kane Marcus Beta (Market Index)

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 20 Chapter 10 -Bodie-Kane Marcus