Mr x who has mean variance preferences considers the

14. Mr. X, who has mean-variance preferences, considers the following two funds:
Sure-thing fund: Expected Return=16%, Standard Deviation of Return=15%
Sure-bet fund: Expected Return=12%, Standard Deviation of Return=8%
The correlation between the funds’ returns is 0.7, and T-bill rate is 8%. Mr. X forms portfolio Y
using the two funds, and then combines Y with T-bills. The weights of the funds within Y are:
a. 43.56% in Sure-thing fund and 56.44% in Sure-bet fund
b. 56.44% in Sure-thing fund and 43.56% in Sure-bet fund
c. 39.62% in Sure-thing fund and 60.38% in Sure-bet fund
d. 60.38% in Sure-thing fund and 39.62% in Sure-bet fund
e. 50.00% in Sure-thing fund and 50.00% in Sure-bet fund
15. For the portfolio Y in the previous question (the portfolio formed by Mr. X), the standard deviation of
portfolio Y’s return is:

Foundations of Finance: Practice Midterm Examination Prof. Alex Shapiro
16. Mrs. R is using a model of expected returns, where the expected return next year depends on the
current value of the variable TRM (which measures a yield spread, defined as the yield on a 30-year
T-bond minus the yield on a 1-year T-note). Given the value of TRM, the expected one-year return
on stock i is
γ
i
+ δ
i
TRM,
where TRM is in percentage points.
For (risky) stocks A , B , and C , Mrs. R finds that γ
A
= 1%, γ
B
= 2%, γ
C
= 3%, δ
A
= 2, δ
B
= 1,
When T-bond’s annual yield is 6% and T-note’s annual yield is 5%, based on Mrs. R’s model, the
expected returns on A and B satisfy:
δ
C
= 3.
B
A
B
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17. Use the data in the previous question, and note that our risk averse Mrs. R (who uses the above model
for conditional expectations) realizes that she has mean-variance preferences. She also has an
investment horizon of one year and wants to construct a portfolio from either (i) 1-year T-notes and
stock A only, or (ii) 1-year T-notes and stock C only.
C
C
C
C
to

Foundations of Finance: Practice Midterm Examination Prof. Alex Shapiro
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