Miss Maple is considering two securities, A and B with the relevant
information given:
State of Econ     Probability   return on Sec A     return on Sec B
Bear                  0.4          3.0%                6.5%
Bull                  0.6         15.0                 6.5

a. Calulate the expected return and standard deviation of each of the
two securities.
b. Suppose Miss Maple invested $2500 in security A and $3500 in
security B. Calulate the expected return and standard deviation of her
portfolio.

Solution
a.Expected Return(A)=0.4*3%+0.6*15% = 10.20%

Expected Return (B)=0.4*6.5%+0.6*6.5%=6.5%

Variance(A)= Prob(bear)*(Return(bear)-Expected return(A))^2 +
                       Prob(bull)*(Return(bull)-Expected return(A))^2

Standard Deviation(A)= SquareRooT(Variance)=5.88%

Similarly for B
Standard Deviation(B)=0

b.Expected Return of Portfolio=Weightage of A *Expected Return(A)+
                                Weightage of B *Expected Return(B)  

Where weight of A =Investment in A/Total portfolio Size
                  = 2500/(2500+3500)
                  =0.4167

Similary Weight of B=0.5833

So Expected return of Portfolio=0.4167*10.2%+0.5833*6.5%
                               = 8.04%

Variance of Portfolio = {Weightage of A *Standard Deviation(A)}^2+
                                {Weightage of B *Standard Deviation(B)}^2+
                         2* Weight A*Weight B*Standard Dev(A)*Standard
Dev(B)*Correlation coefficient(A,B)

Since Standard deviation(B)=0 so the last two terms of the above
equation equal zero

So, Variance of Portfolio=(0.4167*5.88%)^2
                         = 0.06%
So, Standard Deviation =2.45%

So Expected return of Portfolio=8.04%
Standard deviation of Portfolio=2.45%