c.
This statement is correct.
5.
Substituting the portfolio returns and betas in the expected returnbeta relationship,
we obtain two equations with two unknowns, the riskfree rate (r
f
) and the factor
risk premium (RP):
12 = r
f
+ (1.2
×
RP)
9 = r
f
+ (0.8
×
RP)
Solving these equations, we obtain:
r
f
= 3% and RP = 7.5%
6.
a.
Shorting an equallyweighted portfolio of the ten negativealpha stocks and
investing the proceeds in an equallyweighted portfolio of the ten positive
alpha stocks eliminates the market exposure and creates a zeroinvestment
portfolio.
Denoting the systematic market factor as R
M
, the expected dollar
return is (noting that the expectation of nonsystematic risk,
e
, is zero):
$1,000,000
×
[0.02 + (1.0
×
R
M
)]
−
$1,000,000
×
[(–0.02) + (1.0
×
R
M
)]
= $1,000,000
×
0.04 = $40,000
The sensitivity of the payoff of this portfolio to the market factor is zero
because the exposures of the positive alpha and negative alpha stocks cancel
out.
(Notice that the terms involving R
M
sum to zero.)
Thus, the systematic
component of total risk is also zero.
The variance of the analyst’s profit is not
zero, however, since this portfolio is not well diversified.
For n = 20 stocks (i.e., long 10 stocks and short 10 stocks) the investor will
have a $100,000 position (either long or short) in each stock.
Net market
exposure is zero, but firmspecific risk has not been fully diversified.
The
variance of dollar returns from the positions in the 20 stocks is:
20
×
[(100,000
×
0.30)
2
] = 18,000,000,000
The standard deviation of dollar returns is $134,164.
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b.
If n = 50 stocks (25 stocks long and 25 stocks short), the investor will have a
$40,000 position in each stock, and the variance of dollar returns is:
50
×
[(40,000
×
0.30)
2
] = 7,200,000,000
The standard deviation of dollar returns is $84,853.
Similarly, if n = 100 stocks (50 stocks long and 50 stocks short), the investor
will have a $20,000 position in each stock, and the variance of dollar returns is:
100
×
[(20,000
×
0.30)
2
] = 3,600,000,000
The standard deviation of dollar returns is $60,000.
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
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 Spring '13
 Ohk
 Arbitrage, Capital Asset Pricing Model, Financial Markets, Modern portfolio theory

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