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Lecture 15
Empirical Survey and Application: APT
Suppose well diversified portfolios X, Y, and Z have expected returns described
by the APT
E[R
n
] = a + b
1n
f
1
+ b
2n
f
2
+ b
3n
f
3
Where E[R
n
] is the expected return of nth stock.
F
k
= the kth nondiversifiable economy wide risk component
a
= the riskfree rate
The betas of stocks X, Y, Z and a fourth stock, Stock A, can be found in the
following table.
Stock
Expected
Return
b
1n
b
2n
b
3n
X
.1
1
0
0
Y
.15
0
1
0
Z
.1
0
0
1
A
?
1
1
1
What is the expected return of stock A?
To find the expected return of A note that the expected return must satisfy a
NO
ARBITRAGE
condition. The noarbitrage condition is that the expected return of
stock’s X,Y,Z, and A should satisfy E[R
n
] = a + b
1n
f
1
+ b
2n
f
2
+ b
3n
f
3
and there
should be no way to combine X,Y,Z,A into an
arbitrage portfolio.
Arbitrage Portfolio:
A portfolio that has 1) zero cost 2) zero risk 3) positive
return.
In equilibrium we cannot have expected returns that present arbitrage
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 Winter '08
 CHABOT

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