B
AYLOR
U
NIVERSITY
H
ANKAMER
S
CHOOL OF
B
USINESS
D
EPARTMENT OF
F
INANCE
,
I
NSURANCE
&
R
EAL
E
STATE
Dr. Garven
Name ___SOLUTIONS_________
Problem Set #4
1.
Consider two risky prospects,
X
l
and
X
2
, with payoffs given by:
1
0 with probability .25
10 with probability .50
20 with probability .25
X
and
2
0 with probability 1/3
10 with probability 1/3
20 with probability 1/3
X
Assume that your initial wealth (
W
0
) is $0, and your utility
U
(
W
) =
W
.
A.
Is either prospect preferred to the other according to first or second order stochastic
dominance?
SOLUTION:
The FOSD rule says that investment
i
First Order Stochastic Dominates
investment
j
if
F
(
X
js
)
F
(
X
is
) for all
s.
Computing cumulative probabilities across the various
states for
X
1
and
X
2
, we find the following:
Payoffs
F
(
X
1s
)
F
(
X
2s
)
$0
25.00%
33.33%
$10
75.00%
66.67%
$20
100.00%
100.00%
Since
F
(
X
1s
) is not greater than or equal to
F
(
X
2
s
) for all
s
, it follows that there is no first order
stochastic dominance.
Next, we consider whether there is second order stochastic dominance (SOSD).
The SOSD rule
states that
F
(
X
is
) Second Order Stochastic Dominates
F
(
X
js
) if
1
(
)
(
)
0.
n
js
is
s
F X
F X
X
s
f
(
X
1s
)
F
(
X
1s
)
1
1
(
)
n
s
s
F X
f
(
X
2s
)
F
(
X
2s
)
2
1
(
)
n
s
s
F X
1
1
(
)
n
s
s
F X

2
1
(
)
n
s
s
F X
$0 25.00%
25.00%
25.00%
33.33%
33.33%
33.33%
8.33%
$10 50.00%
75.00%
100.00%
33.33%
66.67%
100.00%
0.00%
$20 25.00% 100.00%
200.00%
33.33% 100.00%
200.00%
0.00%
Since
1
2
1
(
)
(
)
0
n
s
s
s
F X
F X
, this means that there is no second order stochastic dominance.
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P
ROBLEM
S
ET
#4
SOLUTIONS
2
B.
Is either prospect preferred to the other according to the meanvariance rule?
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 Spring '09
 Finance, Derivatives, Utility, Options, initial wealth, order stochastic dominance

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