Question

A market consists of four risky assets with the following characteristics: Asset 1: Mean return = 5, Risk (i.e, Standard Deviation) = 10 Asset 2: Mean return = 10, Risk = 20 Asset 3: Mean return = 15, Risk = 30 Asset 4: Mean return = 20, Risk = 40 The returns of Asset 1 have 20% correlation with returns of all the other assets. The returns of Asset 2 have 10% correlation with returns of Asset 3 and Asset 4. The returns of the other two assets are mutually independent.1. Calculate and write down the variance-covariance matrix of the 4 risky assets. 2.Calculate and write down the Lagrangian function used for the portfolio optimization procedure. 3.Write down the 4+2 equation system used for the portfolio optimization procedure 4. From part 3, translate the 4+2 equation system into the matrix form: ?? = ?, and write down the coefficient matrix ?, the unknown vector ?, and the vector ?, respectively

Answer #1

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
2A. Using the Markowitz portfolio optimization method, what
would the composition of the optimal risky portfolio of these
assets be? 10 points
2B. What would the expected return be on this optimal
portfolio? 2 points
2C. What would the standard deviation of this optimal
portfolio be? 3 points

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
2A. Using the Markowitz portfolio optimization method, what
would the composition of the optimal risky portfolio of these
assets be?
Please show work

a. If variance of asset A is 0.04 and variance of asset B is
0.02, what is the correlation between the two assets? Assume
covariance between the 2 assets to be 0.015. Show how you found the
values.
b. Suppose a portfolio has expected return of 15% and volatility
of 30%. How can you combine this portfolio with the risk-free asset
to create a portfolio with 10% expected return? Risk-free asset has
expected return of 3%. Show how you found the...

You have performed the
James optimization on a portfolio with 3 assets whose risk/return
characteristics are summarized in the table below:
Asset
1
Asset
2
Asset
3
E[r]
5.00%
10.00%
15.00%
s.d.
10.00%
15.00%
20.00%
The ‘bordered matrix’
for the optimal risky portfolio based on these three assets is
given below:
Bordered
matrix
W1
W2
W3
-1.522
1.585
0.938
W1
-1.522
0.0232
-0.0261
-0.0044
W2
1.585
-0.0261
0.0565
-0.0033
W3
0.938
-0.0044
-0.0033
0.0352
Please, find the optimal risky portfolio’s...

You have performed the
XXXX optimization on a portfolio with 3 assets whose risk/return
characteristics are summarized in the table below:
Asset
1
Asset
2
Asset
3
E[r]
5.00%
10.00%
15.00%
s.d.
10.00%
15.00%
20.00%
The ‘bordered matrix’
for the optimal risky portfolio based on these three assets is
given below:
Bordered
matrix
W1
W2
W3
-1.522
1.585
0.938
W1
-1.522
0.0232
-0.0261
-0.0044
W2
1.585
-0.0261
0.0565
-0.0033
W3
0.938
-0.0044
-0.0033
0.0352
1)Find the optimal risky portfolio’s expected...

You have performed the XXXX optimization on a portfolio with 3
assets whose risk/return characteristics are summarized in the
table below:
Asset 1
Asset 2
Asset 3
E[r]
5.00%
10.00%
15.00%
s.d.
10.00%
15.00%
20.00%
The ‘bordered matrix’ for the optimal risky portfolio based on
these three assets is given below:
Bordered matrix
W1
W2
W3
-1.522
1.585
0.938
W1
-1.522
0.0232
-0.0261
-0.0044
W2
1.585
-0.0261
0.0565
-0.0033
W3
0.938
-0.0044
-0.0033
0.0352
1)Find the optimal risky portfolio’s expected...

1.)In a universe with just two assets, a risky asset and a
risk-free asset, what is the slope of the Capital Allocation Line
if the Expected return of the risky asset is 12.16% and the
standard deviation of the returns of the risky asset is 19.25%. The
return on the risk-free asset is 3.88%
2.)Peter Griffin calculates that his portfolio's risk, as
measured by the standard deviation, is 21.96%. His portfolio is
made up of many stocks from just two...

a) Calculate the expected return andstandard deviation of a portfolio invested in the
following two risky assets.SecurityWE(r)σA40%1018.63B60%58.27Correlation coefficient ρ= -
0.49b) Calculate the expected return of a
complete portfolio invested equally in the risky portfolio
calculated previously (a) and risk-free asset with 4% return.
Compare your results?

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...

Drew can design a risky portfolio based on two risky assets,
Origami and Gamiori. Origami has an expected return of 13% and a
standard deviation of 20%. Gamiori has an expected return of 6% and
a standard deviation of 10%. The correlation coefficient between
the returns of Origami and Gamiori is 0.30. The risk-free rate of
return is 4%. What is the portfolio weight of Origami in the
optimal risky portfolio?

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