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Standard deviations of stocks

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Suppose the expected returns and standard deviations of stocks A and B are
E(RA) = 0.17
E(RB) = 0.27
StdDevA = 0.12, and
StdDevB = 0.21, respectively

a. Calculate the expected return and standard deviation of a portfolio that is composed of 35 percent A and 65 percent B when the correlation between the returns on A and B is 0.6.

b. Calculate the standard deviation of a portfolio that is composed of 35 percent A and 65 percent B when the correlation coefficient between the returns on A and B is -0.6.

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

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Standard deviations of stocks are emphasized.

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a. The expected return of a two-stock portfolio, where 'wa' is the weight of stock A (in this case 0.35) and 'wb' is the weight of stock B (in this case 0.65) is:

Exp Ret of Portfolio = wa*E(RA) + wb*E(RB) = 0.35*0.17 + 0.65*0.27 = 0.235

So the expected return is 0.235, or 23.5%

The Variance of a two-stock portfolio (the standard deviation will simply be the square root of the variance) is:

Variance = (wa^2)*Variance(A) + (wb^2)*Variance(B) + 2*wa*wb*Covariance(A, B)
[the symbol ^ means "to the power of "]

So we first find the variance ...

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