bodie kane-ch.10 arbitrage pricing theory
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Transcript bodie kane-ch.10 arbitrage pricing theory
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
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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
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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
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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
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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
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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