Notice that, when the number of stocks increases by a factor of 5 (i.e., from 20
to 100), standard deviation decreases by a factor of
5 = 2.23607 (from
$134,164 to $60,000).
7
a.
)
e
(
2
2
M
2
2
σ
+
σ
β
=
σ
881
25
)
20
8
.
0
(
2
2
2
2
A
=
+
×
=
σ
500
10
)
20
0
.
1
(
2
2
2
2
B
=
+
×
=
σ
976
20
)
20
2
.
1
(
2
2
2
2
C
=
+
×
=
σ
b.
If there are an infinite number of assets with identical characteristics, then a
welldiversified portfolio of each type will have only systematic risk since the
nonsystematic risk will approach zero with large n.
The mean will equal that
of the individual (identical) stocks.
c.
There is no arbitrage opportunity because the welldiversified portfolios all
plot on the security market line (SML).
Because they are fairly priced, there
is no arbitrage.
8.
a.
A long position in a portfolio (P) comprised of Portfolios A and B will offer
an expected returnbeta tradeoff lying on a straight line between points A and
B.
Therefore, we can choose weights such that
β
P
=
β
C
but with expected
return higher than that of Portfolio C.
Hence, combining P with a short
position in C will create an arbitrage portfolio with zero investment, zero beta,
and positive rate of return.
b.
The argument in part (a) leads to the proposition that the coefficient of
β
2
must be zero in order to preclude arbitrage opportunities.
103
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9.
The APT factors must correlate with major sources of uncertainty, i.e., sources of
uncertainty that are of concern to many investors.
Researchers should investigate
factors that correlate with uncertainty in consumption and investment opportunities.
GDP, the inflation rate, and interest rates are among the factors that can be expected
to determine risk premiums.
In particular, industrial production (IP) is a good
indicator of changes in the business cycle.
Thus, IP is a candidate for a factor that
is highly correlated with uncertainties that have to do with investment and
consumption opportunities in the economy.
10.
Any pattern of returns can be “explained” if we are free to choose an indefinitely
large number of explanatory factors.
If a theory of asset pricing is to have value, it
must explain returns using a reasonably limited number of explanatory variables
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 Spring '13
 Ohk
 Arbitrage, Capital Asset Pricing Model, Financial Markets, Modern portfolio theory

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