Question

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 values. Describe the steps.

c. Write all the steps (i.e., the first method used in the example shown in videos/Excel) used in finding variance-covariance matrix directly from returns. Which steps can be skipped in Excel? Write the steps in plain English.

d. What are the diagonal entries of a variance-covariance matrix? If you have two assets with correlation of 0.65 and variances of 0.03 and 0.04, what would be the entries in the variance-covariance matrix (write in terms of (1,1), (1,2), (2,1), (2,2) where the first value refers to row number and the second value refers to column number)? Show how you found those values.

e. What is the difference between minimum variance frontier and efficient frontier?

Answer #1

A.

the variance of asset A is 0.04 and variance of asset B is 0.02, the correlation between the two assets is =

0.015/((0.04)^0.5*(0.02)^0.5)=0.53

Co-relation=Covariance(X,Y)/(S.D of X*S.D of Y)

[S.D (Standered Deviation=square root of variance]

B.

If we invest 25% in asset A and B , and rest 75% on risk free invest then we can generate 10% return from the portfolio.

Let assume A&B total contain x% and risk free asset hold 100-x%

then,

x%*15%+(100-x%)*3%=10%

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...

5. Variance Covariance Matrix and Asset
Allocation Model (Markowitz Portfolio Model): Suppose the variance
covariance matrix for two stocks is given as:
Stock 1
Stock 2
Stock 1
0.025
0.015
Stock 2
0.030
The expected rate of returns on Stocks 1 and 2 are 10% and 12%,
respectively. The average return to risk-free treasury is 5%. Given
that the objective of the investor is a minimum-risk portfolio,
find the optimum weights of each stock in the portfolio.

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...

There are three distinct frontier
portfolios, A, B and C.
Portfolio
Expected Returns
Standard Deviation
A
0.4
0.40
B
0.2
0.30
C
0.3
0.25
Compute, ρAB, the correlation between frontier
portfolios A and B.
Calculate the expected return on the global minimum variance
portfolio.
Calculate the maximum possible Sharpe Ratio from these frontier
portfolios, when the risk free rate is 2% per annum.
d. Explain, illustrating with graphs, the difference between the
portfolio frontier when there is a risk free...

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.

Problem 11-18 Minimum Variance Portfolio (LO4, CFA4)
Asset K has an expected return of 14 percent and a standard
deviation of 33 percent. Asset L has an expected return of 8
percent and a standard deviation of 14 percent. The correlation
between the assets is 0.52. What are the expected return and
standard deviation of the minimum variance portfolio?

Suppose Asset A has an expected return of 10% and a standard
deviation of 20%. Asset B has an expected return of 16% and a
standard deviation of 40%. If the correlation between A and B is
0.35, what are the expected return and standard deviation for a
portfolio consisting of 30% Asset A and 70% Asset B?
Plot the attainable portfolios for a correlation of 0.35. Now
plot the attainable portfolios for correlations of +1.0 and
−1.0.
Suppose a...

The variance of a 2-asset portfolio has been calculated to be
.0225, meaning its standard deviation is .15 (for 15%) its expected
return is 10%. This portfolio also has a covariance of 0.1 with the
broad market. The standard deviation of the market portfolio is
10%. You are looking to add a third asset to the portfolio and are
choosing amongst three assets to add. Which assets, if any, would
lower the SYSTEMATIC risk of your portfolio. (Assume equally
weighted...

The variance of a 2-asset portfolio has been calculated
to be .0225, meaning its standard deviation is .15 (or 15%). Its
expected return is 10%. This portfolio also has a covariance of .01
with the broad market. The standard deviation of the market
portfolio is 10%. You are looking to add a third asset to the
portfolio and are choosing amongst three assets to add. Which
asset(s), if any, would lower the SYSTEMATIC risk of your
portfolio. (Assume equally-weighted portfolios...

The variance of a 2-asset portfolio has been calculated to be
.0225, meaning its standard deviation is .15 (or 15%). Its expected
return is 10%. This portfolio also has a covariance of .01 with the
broad market. The standard deviation of the market portfolio is
10%. You are looking to add a third asset to the portfolio and are
choosing amongst three assets to add. Which asset(s), if any, would
lower the SYSTEMATIC risk of your portfolio. (Assume
equally-weighted portfolios...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 26 minutes ago

asked 33 minutes ago

asked 40 minutes ago

asked 50 minutes ago

asked 52 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago