Suppose the expected returns and standard deviations of stocks A & B
are E(RA)=0.15,
E(RB) = 0.25, ?B = 0.2, respectfully

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 & B is 0.5

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

c. How does the correlation between the returns on A & B affect the
standard deviation
of the portfolio?

Hi!!

IMPORTANT NOTE:
You are missing the STD of the stock A, I will suppose that it is
0.10; I think that you also forgot a minus sign in the statement of
part b) (correlation must be -0.5), if not the problem is the same
than the part a) and the part c) results not related to this problem.
If they are not the case and my assumptions make difficult the
understanding of the solution, just let me know using the
clarification feature.


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 & B is 0.5

If we call:
E(RP) = expected return on the portfolio
E(RA) = expected return on Stock A
E(RB) = expected return on Stock B 
WA = weight of Stock A in the portfolio
WB =  weight of Stock B in the portfolio

E(RP) = (WA)*[E(RA)] + (WB)*[E(RB)] =
      = (0.40)*(0.15) + (0.60)*(0.25)
      = 0.21  or  21%


Variance = (WA)^2*(STDA)^2 + (WB)^2*(STDB)^2 +
           + 2*(WA)*(WB)*(STDA)*(STDB)*[Correlation(RA, RB)] =
         = (0.40)^2*(0.10)^2 + (0.60)^2*(0.20)*2 +
           + 2*(0.40)*(0.60)*(0.10)*(0.20)*(0.5) =
         = 0.0208

STDP = sqrt(Variance) = sqrt(0.0208) = 0.1442 or 14.42%





b.) Calculate the standard deviation of a portfolio that is composed
of 40 percent A and 60 percent B when the correlation coefficient
between the returns on A & B is 0.5

In this case we have that: 

Variance = (WA)^2*(STDA)^2 + (WB)^2*(STDB)^2 +
           + 2*(WA)*(WB)*(STDA)*(STDB)*[Correlation(rA, rB)] =
         = (0.40)^2*(0.10)^2 + (0.60)^2*(0.20)*2 +
           + 2*(0.40)*(0.60)*(0.10)*(0.20)*(-0.5) =
         = 0.0112

STDP = sqrt(Variance) = sqrt(0.0112) = 0.1058 or 10.58%



c.) How does the correlation between the returns on A & B affect the
standard deviation of the portfolio?

As Stock A and Stock B become more negatively correlated, the standard
deviation of the portfolio decreases. That is the portfolio become
less volatile or more predictible in its return rate.
For example if the correlation is zero the STDP is 12.65% and if it is
-1 we will have a STDP equal to 8%.
To make a more predictible portfolio you need to use stocks that are
negative correlated, this will balance the uncertainty.

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I hope that this helps you. Feel free to request for a clarification
if you need it.

Regards.
livioflores-ga

Thank you so much. I really appreciate the help.