Q1.
You are trying to develop a strategy for investing in t different stocks. The
anticipated annual return for a $1,000 investment in each stock under four different
economic conditions has the following probability distribution:
Probabilities &
Outcomes:
P
X
Y
recession
0.1
100
50
slow growth
0.3
0
150
moderate growth
0.3
80
20
fast growth
0.3
150
100
a.
Compute the expected return for X and Y.
b.
Compute the standard deviation for X and Y.
c.
Compute the covariance of X and Y.
d.
Would you invest in X or Y? Explain.
(a)
E
(
X
) =
(
29
1
N
i
i
i
X P X
=
∑
= 59
E
(
Y
) =
(
29
1
N
i
i
i
Y P Y
=
∑
= 14
(b)
X
σ
=
(
29
(
29
2
1
N
i
i
i
X
E X
P X
=

∑
= 78.6702
Y
σ
=
(
29
(
29
2
1
N
i
i
i
Y
E Y
P Y
=

∑
= 99.62
(c)
σ
XY
=
(
29
(
29
(
29
1
N
i
i
i
i
i
X
E X
Y
E Y
P X Y
=


∑
= 6306
(d)
Stock
X
gives the investor a lower standard deviation while yielding a higher
expected return so the investor should select stock
X
.
Q2.
Half the portfolio assets are invested in X and half in Y.
E(X)=$105, E(Y)=$35
,
14,725,
11,025
X
Y
σ
σ
=
=
,
σ
XY
=
12,675

.Calculate the portfolio expected return and
risk if
a.
30% of the portfolio assets are invested in X and 70%
in Y.
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 Spring '11
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 Accounting, Investing, Mean, Probability theory, bank account, Poisson probabilities table

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