Question

There are 2 assets. Asset 1: Expected return 7.5%, standard deviation 9% Asset 2: Expected return 11%, standard deviation 12%. You are not sure about the correlation between 2 assets. You hold 30% of your portfolio in asset 1 and 70% in asset 2.

What is the highest possible variance of your portfolio?

Hint 1: Think how the portfolio variance depends on the correlation between 2 assets.

Hint 2: Think which values the correlation between Asset 1 and Asset 2 can get.

Answer #1

Let the correlation between the two assets be denoted by p. Further, asset correlation can take values only between -1 and +1.

The variance of a portfolio of two assets is given by the following relationship:

V(p) = [{w(1) x sd(1)}(2) + {w(2) x sd(2)}^(2) + 2 x w(1) x w(2) x sd(1) x sd(2) x p]

As is clearly observable the correlation is directly related to the portfolio's variance and consequently the portfolio will possess the highest variance only when its correlation is +1.

V(p) = [{0.3 x 9}(2) + {0.7 x 12}^(2) + 2 x 0.3 x 0.7 x 9 x 12 x (+1)] = 123.21

Consider the following two assets:
Asset A:
expected return is 4% and standard deviation of return is 42%
Asset B:
expected return is 1.5% and standard deviation of return is
24%
The
correlation between the two assets is 0.1.
(1)
Compute the expected return and the standard deviation of return
for 4 portfolios with different weights w on asset A (and therefore
weight 1-w on B): w=-0.5, w=0.3, w=0.8, w=1.3.
(2)
Then sketch a portfolio frontier with the 4 portfolios,...

Consider a portfolio that consist of 2 assets A and B;
Asset
Expected Return
Standard Deviation
Correlation
A
20%
10%
B
40%
20%
A&B
-1
Compute the asset weights (WA and WB) so that an investor
obtains a zero risk portfolio. Show all your workings and
calculations.

Asset K has an expected return of 19 percent and a standard
deviation of 34 percent. Asset L has an expected return of 7
percent and a standard deviation of 18 percent. The correlation
between the assets is 0.43. What are the expected return and
standard deviation of the minimum variance portfolio? (Do not round
intermediate calculations. Enter your answers as a percent rounded
to 2 decimal places.)
Expected return%
Standard deviation%

Asset K has an expected return of 11 percent and a standard
deviation of 26 percent. Asset L has an expected return of 9
percent and a standard deviation of 21 percent. The correlation
between the assets is 0.21. What are the expected return and
standard deviation of the minimum variance portfolio?
Expected return%
Standard deviation%

The domestic asset has an expected return of 9% and standard
deviation of 25%
The foreign asset has an expected return of 15% and standard
deviation of 35%
The correlation between two asset is 0.40. Assuming the
portfolio has 30% invested in the domestic asset and the reminder
in the foreign asset.
1. calculate the portfolio's expected return and standard
deviation. SHOW YOUR WORK
rp=................%
op=................%

given expected return for asset 1=12%,expected return for asset
2=16%,stander deviation for asset 1=4%, stander deviation for asset
2=6%,and correlation between asset 1 and 2=0.60,find out the
portfolio return and portfolio stander deviation if the weight of
asset 1 and asset 2 are
a.0.50 and 0.50
b. 0.30 and 0.70

You have the following assets available to you to invest in:
Asset
Expected Return
Standard Deviation
Risky debt
6%
0.25
Equity
10%
.60
Riskless debt
4.5%
0
The coefficient of correlation between the returns on the risky
debt and equity is 0.72
2D. Hector has a coefficient of risk aversion of 1.8. What
percentage of his assets should he invest in the risky
portfolio?
2E. What would the expected return be on Hector’s
portfolio?
2F. What would the standard deviation...

The expected return of Asset A and Asset B are 15% and 20%
respectively, and the standard deviation of the two assets are 20%
and 30% respectively. The correlation coefficient between the two
assets is zero. Suppose you form a portfolio using the two assets,
and the expected return of your portfolio is 22.5%. Find out the
standard deviation of your portfolio.

You are constructing a portfolio from two assets. The first
asset has an expected return of 7.7% and a standard deviation of
7.8%. The second asset has an expected return of 10.2% and a
standard deviation of 12.6%. You plan to invest 41% of your money
in the first asset, and the rest in asset 2. If the assets have a
correlation coefficient of -0.61, what will the standard deviation
of your portfolio be?

Asset 1 has a standard deviation of returns equal to 4% per
year, and an expected return of 2.5% per year. Asset 2 has a
standard deviation of returns equal to 25% per year, and an
expected return of 6% per year. The correlation between the two
assets is 0.2. What is the standard deviation of a portfolio that
has 50% in asset 1 and 50% in asset 2?.

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