Question

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 E[Ra] and E[Rb].

(b) The variance of the portfolio may be greater than σA.

(c) There are only gains from diversification if ρA,B 6= 1.

(d) With the proper weights, a portfolio of zero variance can be formed

Answer #1

(a) **False -** Assuming E[Ra] > E[Rb], and
w_{a} > w_{b}, the expected return of this
portfolio will be more inclined towards E[Ra] and will be greater
than average of E[Ra] and E[Rb].

(b) **True -** given that ρ_{A,B} > 0,
The variance of the portfolio will lie between σA < σB and hence
might be greater than σA.

(c) **False -** we have to look for gain per unit
of risk which is not possible with the given data.

(d) **False -** since ρ_{A,B} > 0.

Please do rate me and mention doubts, if any, in the comments section.

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...

Suppose the expected returns and standard deviations of stocks
A and B are E(RA) 0.15, E(RB) 0.25,
σA 0.40, and σB 0.65, respectively.
a. Calculate the expected return and
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and 60 percent B when the correlation between the returns on A and
B is 0.5.
b. Whether the risk (standard
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correlation between the returns on A and B...

Suppose the expected
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a-1.
Calculate the expected
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your answer as a percent rounded to 2 decimal places, e.g.,
32.16.)
a-2....

Suppose the expected returns and standard deviations of Stocks A
and B are E(RA) = .094, E(RB) = .154, σA = .364, and σB = .624.
a-1. Calculate the expected return of a portfolio that is
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intermediate calculations and enter your answer as a percent
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a-2. Calculate...

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σB = .628.
a-1.
Calculate the expected return of a portfolio that is composed of
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intermediate calculations and enter your answer as a percent
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a-2....

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Suppose the expected returns and standard deviations of stocks
A and B are E( RA ) = 0.15, E(
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0.72, respectively.
Required:
(a)
Calculate the expected return and standard deviation of a
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14)
Two assets have the following expected returns and standard
deviations when the risk-free rate is 5%:
Asset A E(rA) = 10%
σA = 20%
Asset B E(rB) = 15%
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An investor with a risk aversion of A = 3 would find that
_________________ on a risk-return basis.
Multiple Choice
only asset A is acceptable
only asset B is acceptable
neither asset A nor asset B is acceptable
both asset A and asset B are acceptable

Consider the risky portfolios with expected returns and standard
deviations of returns as given in the table below. Which of the
statements about the portfolios that follow is true?
Portfolio
Expected Return
Standard Deviation
A
10%
5%
B
21%
11%
C
18%
23%
D
24%
16%
Group of answer choices
Portfolio C dominates portfolio A.
Portfolio B dominates portfolio C.
Portfolio B dominates portfolio A.
Portfolio D dominates portfolio B.

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