What is the expected return to a portfolio of 25% Stock X and 75% Stock Y?
r
i
=
0.0290 + 0.908Forex +
1.292Default
+
0.9180Size
28
Stock
a
i
b
i,m
b
i,s
b
i,v
X
0.05
1.1
1.4
.6
Y
0.02
0.8
1.2
1.0
ARBITRAGE PRICING THEORY
The APT, as it is known, describes the expected return to an asset as a
linear function of the risk of the asset with respect to a set of factors.
•
The APT is an equilibrium model
where the
s represent factor sensitivities and the
s represent risk premiums.
•
The APT relies on three assumptions:
1.
A factor model describes asset returns.
2.
There are many assets, so investors can form welldiversified portfolios that
eliminate assetspecific risk.
3.
No arbitrage opportunities exist among welldiversified portfolios.
•
In contrast to multifactor models, the APT models the expected return in
equilibrium (the first term of the equation), in essence restricting the first term
in the general multifactor expression to the APT value for that term.
•
29
ARBITRAGE PRICING THEORY
Focus On: Calculations
•
You are considering purchasing shares in Cleveland Corp., and you believe the
APT with three priced risk factors is an accurate description of the expected
return to Cleveland Corp. The first risk factor, Macro, has a risk premium of 3%
and Cleveland Corp. has a
for this risk factor of 1.1. The second risk factor,
Term, has a risk premium of 2% and Cleveland has a
of 0.74. Finally, the last
risk factor, Inflation, has a risk premium of 1.3% and Cleveland has a
of 0.27.
•
If the current riskfree rate is 3.5%, what is the APT threefactor expected
return to Cleveland Corp. shares?
•
30
THE APT AND ARBITRAGE
Focus On: Calculations
•
Consider the following stock returns and factor sensitivities for a single factor
APT.
•
Can we combine X and Y to achieve an arbitrage possibility with Z?

What weights create a portfolio with equal sensitivities so that the sensitivity
of the portfolio = the sensitivity of Z?

Is the expected return to this portfolio the same as the expected return to Z?
31
Stock
Expected Return
Sensitivity
X
0.10
1.625
Y
0.14
2.625
Z
0.11
2.375
THE APT AND ARBITRAGE
Focus On: Calculations

What weights create a portfolio with equal sensitivities so that the sensitivity
of the portfolio = the sensitivity of Z?

Is the expected return to this portfolio the same as the expected return to Z?

No. Therefore, if we go short Z, we can use the proceeds to go long X
and Y in weights 25% and 75%, respectively. We will generate a riskfree
profit of 2% = 13% – 11%.
•
32
FUNDAMENTAL FACTOR MODELS
In contrast to macroeconomic models, fundamental models use expected
returns (instead of surprises) as factors.
•
Because the expected returns no longer have an expected value of zero, as do the
surprises in macroeconomic factor models, the intercept,
a
i
, is no longer an expected
return but the intercept term from a regression.
•
The
b
i
terms are typically factor sensitivities that have been standardized by the
sensitivity across all stocks.
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 Spring '09
 JAMESOWENS
 Standard Deviation, Capital Asset Pricing Model, Corporate Finance, CML, Modern portfolio theory, Cleveland Corp.