Question

- Suppose the expected returns and standard deviations of stocks
A and B are E(R
_{A}) 0.15, E(R_{B}) 0.25, σ_{A}0.40, and σ_{B}0.65, respectively.

a. Calculate the expected return and standard deviation of a portfolio that is composed of 40 percent A and 60 percent B when the correlation between the returns on A and B is 0.5.

b. Whether the risk (standard deviation) of the portfolio will decrease or increase if the correlation between the returns on A and B decreases and becomes negative?

Answer #1

Given about two stocks,

E(R_{A}) = 0.15,

E(R_{B}) = 0.25,

σ_{A} = 0.40,

σ_{B} = 0.65

Corr(A,B) = 0.5

a). W_{A} = 0.40

W_{B} = 0.60

Expected return of portfolio is E(R_{P}) =
W_{A}*E(R_{A}) + W_{B}*E(R_{B}) =
0.4*15 + 0.6*25 = 21%

standard deviation of the portfolio is SD_{p} =
SQRT((W_{A}*σ_{A})^{2} + (WB*σ_{B})^{2} +
2*W_{A}*σ_{A}*WB*σ_{B}*Corr(A,B))

SD_{p} = SQRT((0.4*40)^{2} +
(0.6*65)^{2} + 2*0.4*40*0.6*65*0.5) = 45.70% or 0.4570

b). As, correlation decreases and moves to negative, third term of the formula also turn negative. This will decrease the risk of the portfolio.

Suppose the expected returns and standard deviations of stocks
A and B are E( RA ) = 0.15, E(
RB ) = 0.21, σ A = 0.48, and σ B =
0.72, respectively.
Required:
(a)
Calculate the expected return and standard deviation of a
portfolio that is composed of 42 percent A and 58 percent
B when the correlation between the returns on A
and B is 0.46. (Round your answers to 2 decimal
places. (e.g., 32.16))
Expected return
%...

Suppose the expected returns and standard deviations of Stocks
A and B are E(RA) = .080,
E(RB) = .140, σA = .350, and
σB = .610.
a-1. Calculate the expected return of a portfolio
that is composed of 25 percent A and 75 percent B
when the correlation between the returns on A and
B is .40. (Do not round intermediate calculations.
Enter your answer as a percent rounded to 2 decimal places, e.g.,
32.16.)
Expected return 12.5 %
a-2....

Suppose the expected
returns and standard deviations of Stocks A and B are
E(RA) = .100, E(RB) = .160,
σA = .370, and σB = .630.
a-1.
Calculate the expected
return of a portfolio that is composed of 45 percent Stock A and 55
percent Stock B when the correlation between the returns on A and B
is .60. (Do not round intermediate calculations and enter
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
composed of 39 percent Stock A and 61 percent Stock B when the
correlation between the returns on A and B is .54. (Do not round
intermediate calculations and enter your answer as a percent
rounded to 2 decimal places, e.g., 32.16.)
a-2. Calculate...

Suppose the expected returns and standard deviations of Stocks A
and B are E(RA) = .098,
E(RB) = .158, σA = .368, and
σB = .628.
a-1.
Calculate the expected return of a portfolio that is composed of
43 percent Stock A and 57 percent Stock B when the correlation
between the returns on A and B is .58. (Do not round
intermediate calculations and enter 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) = .089, E(RB) = .149, σA = .359, and σB = .619.
a-1. Calculate the expected return of a portfolio that is composed
of 34 percent Stock A and 66 percent Stock B when the correlation
between the returns on A and B is .49. (Do not round intermediate
calculations and enter your answer as a percent rounded to 2
decimal places, e.g., 32.16.) a-2. Calculate...

Q9. The expected returns and standard deviations for stocks A
and B are rA=14% and rB=19%, respectively, and A=23% and B=34%,
respectively. The correlation of the returns on the two stocks is
AB=0.3. (a) What is the expected return, rP, and standard
deviation, P, of a portfolio with weights of wA=0.60 and wB=0.40
in stocks A and B, respectively? (b) Suppose now ?? = 3%, and ?? =
7%, the portfolio had zero risk, that is suppose ?? = 0...

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...

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...

2. What is the portfolio expected return and standard deviation?
$4000 market value in stock A with E(RA) = 12% and $6000 market
value in stock B with E(RB) = 9%. The standard deviations (σ) and
correlation (ρ) are: σA = 25% σB = 20% ρAB = 0.5
For a 2 stock portfolio,
σ2port = wA2 σ2A + wB2 σ2B + 2 wA wB ρAB σA σB
σport = (wA2 σ2A + wB2 σ2B + 2 wA wB ρAB σA...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 13 minutes ago

asked 35 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago