1. Arbitrage Pricing Theory
Chapter 11
Arbitrage Pricing 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) TLKM 4.34 0.94 BUMI 2.91 2.45 BBRI 4.12 1.00 SULI
COMPANY
INDUSTRY
TLKM
4.34
0.94
BUMI
2.91
2.45
BBRI
4.12
1.00
SULI
1.04
0.72
PTSP
2.58
2.36
HMSP
2.17
0.16
Chapter 10-Bodie-Kane Marcus

6. Arbitrage Example
Current Expected Standard Stock Price$ Return% Dev.% A B C D
Chapter 10-Bodie-Kane Marcus

7. Arbitrage Portfolio
Mean S.D. Correlation Portfolio A,B,C D
Chapter 10-Bodie-Kane Marcus

8. Arbitrage Action and Returns
E( R)
St.Dev.
* P
* D
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
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= $ → E(PA)= $35 ( ) =$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 A 37.7 37.2 IV >MV B 37 37.8 C 38.4 38.5 Stock OVER
INTRINSIC Price ($)
MARKET Price ($)
CONDITION
ACTION A
37.7
37.2
IV >MV
OVER
VALUED
SELL B 37
37.8
IV < MV
UNDER
PUR
CHASE C
38.4
38.5
Reilly Brown

13. Arbitrage A -1 Sell 2 shares B 0.5 Buy 1 share C Stock Weight
Sell / buy
Current Price
Value A -1
Sell
2 shares
$ 35
$ 70 B
0.5
Buy
1 share
-$ 35 C
Reilly Brown

14. Arbitrage Net Profit : Sell A (2 shares) Buy B(1) Buy C(1)
2(35) - 2(37.2)+( )+( )
=$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. Portfolio &Individual Security Comparison
E(r)%
Individual Security F
E(r)%
Portfolio
Simpangan (risiko) portofolio lebih kecil dari pada aset 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