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# Calculate the Standard Deviation of a Two-stock Portfolio

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Let X and Y be two stocks with the following features:

- 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?

#### Solution Preview

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)
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SD(X)*SD(Y)

In ...

#### Solution Summary

The solution carefully explains all the concepts, the logic while showing the formulas and the calculations to arrive at the answers.

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