a.
Suppose asset A has an expected return of 10 percent and a standard deviation of
20 percent.
Asset B has an expected return of 16 percent and a standard
deviation of 40 percent.
If the correlation between A and B is 0.4, what are the
expected return and standard deviation for a portfolio comprised of 30 percent
asset A and 70 percent asset B?
Answer:
%.
2
.
14
142
.
0
)
16
.
0
(
7
.
0
)
1
.
0
(
3
.
0
rˆ
)
w
1
(
rˆ
w
rˆ
B
A
A
A
P
309
.
0
)
4
.
0
)(
2
.
0
)(
4
.
0
)(
7
.
0
)(
3
.
0
(
2
)
4
.
0
(
7
.
0
)
2
.
0
(
3
.
0
)
W
1
(
W
2
)
W
1
(
W
2
2
2
2
B
A
AB
A
A
2
B
2
A
2
A
2
A
p
b.
Plot the attainable portfolios for a correlation of 0.4.
Now plot the attainable
portfolios for correlations of +1.0 and -1.0.
Answer:
AB
= +0.4:
Attainable Set of
Risk/Return Combinations
0%
5%
10%
15%
20%
0%
10%
20%
30%
40%
Risk,
p
Expected return
Mini Case:
5 - 8
MINI CASE

AB
= +1.0:
Attainable Set of Risk/Return
Combinations
0%
5%
10%
15%
20%
0%
10%
20%
30%
40%
Risk,
p
Expected return
AB
= -1.0:
Attainable Set of Risk/Return
Combinations
0%
5%
10%
15%
20%
0%
10%
20%
30%
40%
Risk,
p
Expected return
Mini Case:
5 - 9

c.
Suppose a risk-free asset has an expected return of 5 percent.
By definition, its
standard deviation is zero, and its correlation with any other asset is also zero. Using
only asset A and the risk-free asset, plot the attainable portfolios.
Answer:
Attainable Set of Risk/Return
Combinations with Risk-Free Asset
0%
5%
10%
15%
0%
5%
10%
15%
20%
Risk,
p
Expected return
Mini Case:
5 - 10

d.
Construct a reasonable, but hypothetical, graph which shows risk, as measured
by portfolio standard deviation, on the x axis and expected rate of return on the
y axis.
Now add an illustrative feasible (or attainable) set of portfolios, and show
what portion of the feasible set is efficient.
What makes a particular portfolio
efficient?
Don't worry about specific values when constructing the graph—
merely illustrate how things look with "reasonable" data.
Answer:
The figure above shows the
feasible
set of portfolios.
The points B, C, D, and E
represent single securities (or portfolios containing only one security).
All the other
points in the shaded area, including its boundaries, represent portfolios of two or more
securities.
The shaded area is called the
feasible, or attainable, set
.
The boundary AB defines the
efficient set
of portfolios, which is also called the
efficient frontier
.
Portfolios to the left of the efficient set are not possible because
they lie outside the attainable set.
Portfolios to the right of the boundary line (interior
portfolios) are inefficient because some other portfolio would provide either a higher
return with the same degree of risk or a lower level of risk for the same rate of return.
e.
Now add a set of indifference curves to the graph created for part B. What do
these curves represent?
What is the optimal portfolio for this investor?
Finally,
add a second set of indifference curves which leads to the selection of a different
optimal portfolio.
Why do the two investors choose different portfolios?

#### You've reached the end of your free preview.

Want to read all 18 pages?

- Spring '16
- Wiyada
- Management, Pricing, Capital Asset Pricing Model, SML