Which pair(s), if any, of expected returns and standard deviations
on the
red line
can be obtained by investing in the two risky assets A & B and in
the riskless asset? Give an intuitive answer. Try to explain why you
believe in your result?
Kathrin Glau, Financial Mathematics III, Semester B 2018
435
Portfolio of Two Risky & One Riskless Asset
%
2
(

1
,
1)
The point (0
, μ
rf
) that represents the riskless asset in the graph is
attainable. This is the only attainable point on the red line
....
Why?
...
Let us first look at another case:
Kathrin Glau, Financial Mathematics III, Semester B 2018
436
Portfolio of Two Risky & One Riskless Asset
%
2
(

1
,
1)
Example Exam Question V.107
0
B
A
0
mu
rf
B
A
(
A
,
A
)
(
B
,
B
)
riskless asset
Which point(s) on the red line are attainable?
Which pair(s), if any, of expected returns and standard deviations
on the
red line (segment)
can be obtained by investing in the two risky assets A
& B and in the riskless asset? Why?
Kathrin Glau, Financial Mathematics III, Semester B 2018
437
Portfolio of Two Risky & One Riskless Asset
%
2
(

1
,
1)
0
B
A
0
mu
rf
B
A
(
A
,
A
)
(
B
,
B
)
riskless asset
Which point(s) on the red line are attainable?
All points on the red line are attainable.
The line represents all portfolios obtained by investing a portion in asset
A and a portion in the riskless asset.
We have already seen that such portfolios are represented by straight
lines connecting the pairs of the two assets.
Kathrin Glau, Financial Mathematics III, Semester B 2018
438
Portfolio of Two Risky & One Riskless Asset
%
2
(

1
,
1)
Example Exam Question V.108
0
B
A
0
rf
B
A
(
A
,
A
)
(
B
,
B
)
riskless asset
Which point(s) on the red line are attainable?
Which pair(s), if any, of expected returns and standard deviations
on the
red line (segment)
can be obtained by investing in the two risky assets A
& B and in the riskless asset? Why?
Kathrin Glau, Financial Mathematics III, Semester B 2018
439
Portfolio of Two Risky & One Riskless Asset
%
2
(

1
,
1)
0
B
A
0
rf
B
A
(
A
,
A
)
(
B
,
B
)
riskless asset
Which point(s) on the red line are attainable?
All points on the red line are attainable.
The line represents all portfolios obtained by investing a portion in asset
B and a portion in the riskless asset.
Kathrin Glau, Financial Mathematics III, Semester B 2018
440
Portfolio of Two Risky & One Riskless Asset
%
2
(

1
,
1)
Example Exam Question V.109
0
B
=0.05
A
=0.07
0
mu
rf
B
=0.07
A
=0.1
(
A
,
A
)
(
B
,
B
)
riskless asset
Which point(s) on the red line are attainable?
Which pair(s), if any, of expected returns and standard deviations
on the
red line (segment)
can be obtained by investing in the two risky assets A
& B and in the riskless asset? Why?
Kathrin Glau, Financial Mathematics III, Semester B 2018
441
Portfolio of Two Risky & One Riskless Asset
%
2
(

1
,
1)
0
B
=0.05
A
=0.07
0
mu
rf
B
=0.07
A
=0.1
(
A
,
A
)
(
B
,
B
)
riskless asset
Which point(s) on the red line are attainable?
All points on the red line are attainable.
The blue star represents a portfolio obtained by investing a portion
x
A
in
the asset A and the rest in asset B. We call this portfolio
P
AB
(
x
A
).
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 Normal Distribution, Variance, Probability theory, Kathrin Glau