1. Suppose the expected returns and standard deviations of stocks A and B are 

E(RA) = 0.15, E(RB) = 0.25, sA = 0.1, and sB = 0.2, 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.   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 and B is _0.5.

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

Hi!!

a.)
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.) this part is solved in the same way:

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.)
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.




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

Regards.
livioflores-ga

Thank you very much.