Problem Set 6 (Answer Key)
ECN 134
Financial Economics
Prof. Farshid Mojaver
Part A: Risk Aversion
Consider a portfolio that offers an expected rate of return of 12% and a standard deviation of 18%.
Tbills offer a riskfree 7% rate of return. What is the maximum level of risk aversion for which the
risky portfolio is still preferred to bills?
Answer)
When we specify utility by U =
E(r) – 0.5A
σ
2
, the utility level for Tbills is:
0.07
The utility level for the risky portfolio is: U = 0.12 – 0.5A(0.18)
2
= 0.12 – 0.0162A
In order for the risky portfolio to be preferred to bills, the following inequality must hold:
0.12 – 0.0162A > 0.07
⇒
A < 0.05/0.0162 = 3.09
1.
When an investment advisor attempts to determine an investor's risk tolerance, which factor would
they be
least
likely to assess?
A.
the investor's prior investing experience
B.
the investor's degree of financial security
C.
the investor's tendency to make risky or conservative choices
D.
the level of return the investor prefers
E.
the investor's feeling about loss
Assume an investor with the following utility function: U = E(r)  3/2(s
2
).
2.
To maximize her expected utility, she would choose the asset with an expected rate of return of
_______ and a standard deviation of ________, respectively.
A.
12%; 20%
B.
10%; 15%
C.
10%; 10%
D.
8%; 10%
E.
none of the above
U = 0.10  3/2(0.10)
2
= 8.5%; highest utility of choices.
U = E(r)  (A/2)s
2
, where A = 4.0.
3
. Based on the utility function above, which investment would you select?
A.
1
B.
2
C.
3
D.
4
E.
cannot tell from the information given
U(c) = 0.21  4/2(0.16)
2
= 15.88 (highest utility of choices).
4.
Which investment would you select if you were risk neutral?
A.
1
B.
2
C.
3
D.
4
E.
cannot tell from the information given
If you are risk neutral, your only concern is with return, not risk.
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View Full Document5
. An investor invests 30 percent of his wealth in a risky asset with an expected rate of return of 0.13
and a variance of 0.03 and 70 percent in a Tbill that pays 6 percent. His portfolio's expected return
and standard deviation are __________ and __________, respectively.
A.
0.114; 0.128
B.
0.087;0.063
C.
0.295; 0.125
D.
0.081; 0.052
E.
none of the above
E(r
P
) = 0.3(13%) + 0.7(6%) = 8.1%; s
P
= 0.3(0.03)
1/2
= 5.19%.
6
. What percentages of your money must be invested in the risky asset and the riskfree asset,
respectively, to form a portfolio with an expected return of 0.09?
A.
85% and 15%
B.
75% and 25%
C.
67% and 33%
D.
57% and 43%
E.
cannot be determined
9% = w
1
(12%) + (1  w
1
)(5%); 9% = 12%w
1
+ 5%  5%w
1
; 4% = 7%w
1
; w
1
= 0.57; 1  w
1
= 0.43;
0.57(12%) + 0.43(5%) = 8.99%.
Your client, Bo Regard, holds a complete portfolio that consists of a portfolio of risky assets (P) and
TBills. The information below refers to these assets.
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 Spring '10
 FARSHIDMOJAVER
 Capital Asset Pricing Model, Modern portfolio theory, Risk premium

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