Stock X  Expected Return 14%
Stock Y Expected Return 18%
Stock X Standard Deviation 40%
Stock Y Standard Deviation 54%
Correlation(X,Y) = .25
Mean is 15.6%
What is the standard deviation for a portfolio with 60% in stock x and
40% invested in stock Y?
Please show me how to calculate the answer

Hello snowbear!
The formulas used to compute the answer are the following. Let X and Y
be random variables, and let a and b be numbers. Then,

1) Var(X) = SD(X)^2   (SD is standard deviation)

2) Var(aX+bY)=a^2*Var(X)+b^2*Var(Y)+2*a*b*Cov(X,Y) (Cov is covariance)

3) Correlation(X,Y)=    Cov(X,Y)
                     -------------
                      SD(X)*SD(Y)

In order to compute the answer to your question, let us first
calculate the variance of the stocks. Using formula (1), we get:

Var(X)=40^2=1600
Var(Y)=54^2=2916

Next, we calculate the covariance between X and Y, that is, Cov(X,Y).
Since we know the correlation and the standard deviations, we can use
formula (3) to compute Cov(X,Y):

Cov(X,Y)=Correlation(X,Y)*SD(X)*SD(Y)
        =0.25*40*54
        =540

Finally, we use formula (2) to compute your answer. The portfolio can
be thought as a random variable, given by

0.6*X + 0.4*Y  (60 percent X plus 40 percent Y)

Therefore, using formula (2) and the results we already know:

Var(0.6*X+0.4*Y)=0.6^2*Var(X)+0.4^2*Var(Y)+2*0.6*0.4*Cov(X,Y)
                =0.36*1600 + 0.16*2916 + 2*0.6*0.4*540
                =1301.76

So 1301.76 is the variance of the returns of the portfolio. Then, the
standard deviation of the returns of the portfolio is given by the
square root of 1301.76, which is 36.07. The answer is then that the
standard deviation is 36.07%.

I hope this was clear enough. If there is anything unclear about my
answer, please let me know through a clarification request. Otherwise,
I await your rating and final comments.


Best wishes!
elmarto