Question

(i)

The expected returns on two distinct risky assets A and B are correlated and a portfolio consisting of A and B has zero variance of expected return. What can be said about the correlation between the expected returns of risky assets A and B?

(ii)

An investor constructs an efficient portfolio that invests 150% of his investment in the tangent portfolio of risky asset and is short in the risky free asset for the rest. What can be said about the standard deviation of the efficient portfolio?

Answer #1

I) when the standard deviation of two assets is zero, it means that both the assets will have similar rate of return and it will mean that the asset will be perfectly correlated to each other because it is a positive correlation when the the return of one stock is completely replicated by another stock. It will mean that both the assets are perfectly positively correlated and they will have a correlation of +1.

Ii) standard deviation of this portfolio would be relatively low because it is mostly focusing into investment at the tangency point, which is also known as Efficient market portfolio so at these points the deviation from the mean would be lowest.

A and B are two risky assets. Their expected returns are E[Ra],
E[Rb], and their standard deviations are σA,σB. σA< σB and asset
A and asset B are positively correlated (ρA, B > 0). Suppose
asset A and asset B are comprised in a portfolio with positive
weight in both and please check all the correct answers below.
() There are only gains from diversification if ρA, B is not
equal to 1.
() The portfolio may have a zero...

Mark all the correct statements.
When two assets are not correlated, it is possible to create a
portfolio with them that will have zero standard deviation.
When two assets' correlation is +1, the minimum variance
portfolio (allowing no short selling) consists of 100% from the
asset with the lesser variance.
Even very risk averse investors prefer the Optimum Risky
Portfolio to the Minimum Variance Portfolio.
Given a 50-50% investment into two predetermined risky assets,
the lower their correlation, the lower...

Suppose that assets 1 and 2 are 24% correlated and have the
following expected returns and standard deviations:
Asset
E(R)
σ
1
14%
9%
2
8%
4%
a) Calculate the expected return and standard deviation for a
portfolio consisting of equal weights in assets 1 and 2.
b) What are the weights of a minimum variance portfolio
consisting of assets 1 and 2? What is the expected return and
standard deviation of this portfolio?
c) Has there been an improvement...

Consider two risky securities, A and B. They have expected
returns E[Ra], E[Rb], standard deviations σA, σB. The standard
deviation of A’s returns are lower than those of B (i.e. σA < σB
and both assets are positively correlated (ρA,B > 0). Consider a
portfolio comprised of positive weight in both A and B and circle
all of the true statements below (there may be multiple true
statements).
(a) The expected return of this portfolio cannot exceed the
average of...

Assume two risky assets A and B with correlation ρ=-1.00.Their
respective returns and volatilities are,
Asset
Expected Return (%)
Volatility
A
7.00
0.0010
B
5.00
0.0005
Compute the return and volatility of the minimum-variance
portfolio.
Select one:
a. Return: 5.67%; volatility: 0.0%
b. No answer
c. Return: 7.12%; volatility: 0.0%.
d. Return: 7.12%; volatility: 3.21%.
e. Return: 5.67%; volatility: 3.21%.

There are two risky securities A and B that are perfect
negatively correlated. The expected return and standard deviation
of A and B are E(rA), E(rB), , . How much is the standard deviation
of the minimum variance portfolio that includes these two
securities?

Risky Asset A and Risky Asset B are combined so that the new
portfolio consists of 70% Risky Asset A and 30% Risky Asset
B. If the expected return and standard deviation of
Asset A are 0.08 and 0.16, respectively, and the expected return
and standard deviation of Asset B are 0.10 and 0.20, respectively,
and the correlation coefficient between the two is 0.25: (13
pts.)
What is the expected return of the new portfolio consisting of
Assets A & B...

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%. If Drew invests 30% money in Gamiori and the
remaining in Origami, what is the standard deviation of his
portfolio?

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...

Which of the following statements about a portfolio is(are)
correct A portfolio of two assets with perfectly positively
correlated returns will have an overall risk below that of the
least risky asset B. A portfolio of two assets with perfectly
negatively correlated

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