Chapter 11
Arbitrage
Pricing Theory
1
Chapter 10-Bodie-Kane Marcus
Arbitrage Pricing Theory
 Developed by Ross (1976,1977)
 Has three major assumption :
1.
2.
3.
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
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
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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
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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
Stock Price$ Return%
A
10
25.0
B
10
20.0
C
10
32.5
D
10
22.5
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Chapter 10-Bodie-Kane Marcus
Standard
Dev.%
29.58
33.91
48.15
8.58
Arbitrage Portfolio
Mean
Portfolio
A,B,C
D
7
S.D.
25.83
6.40
22.25
8.58
Chapter 10-Bodie-Kane Marcus
Correlation
0.94
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
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Chapter 10-Bodie-Kane Marcus
APT
Reilly Brown
9
Chapter 10-Bodie-Kane Marcus
Expected Return Equation
E ( Ri )  0  1bi1  2 bi 2
 w  0 [i.e., no net wealth invested]
 w b  0 for all K factors [ no systematic risk]
 w R  0 [i.e., the actual portfolio return is positive]
i
i
i
i ij
i
i
i
w i  the percentage investment in security i
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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
→ 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
 PA= $35
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Reilly Brown
Arbitrage
Stock
INTRINSIC
Price ($)
MARKET
Price ($)
A
37.7
37.2
B
C
12
37
38.4
CONDITION
ACTIO
N
SELL
IV >MV
OVER
VALUED
IV < MV
UNDER
VALUED
PUR
CHASE
IV < MV
UNDER
VALUED
PUR
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
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Reilly Brown
APT & Well-Diversified Portfolios
rP = E (rP) + bPF + eP
F = some factor
For a well-diversified portfolio
eP approaches zero
Similar to CAPM
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Chapter 10-Bodie-Kane Marcus
Portfolio &Individual Security
Comparison
E(r)%
E(r)
%
F
F
Portfolio
Individual Security
Simpangan (risiko) portofolio lebih kecil dari pada aset individual
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E(r)%
10
7
A
D
6
C
4 Risk Free
.5
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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%
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Chapter 10-Bodie-Kane Marcus
APT with Market Index Portfolio
E(r)%
M
[E(rM) - rf]
Market Risk Premium
Risk Free
1.0
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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
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Chapter 10-Bodie-Kane Marcus