## Correlation coefficient, Applied Statistics

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Consider three stocks A, B and C costing \$100 each. The annual returns on the three stocks have mean \$5 and variance \$10.

a. Suppose that the returns on the three stocks are i.i.d.    Find the means and variance of the returns on Portfolio I, consisting of 3 units of A, and Portfolio II, consisting of 1 units each of A, B and C?

b. Suppose the returns from A and B have a correlation coefficient of -0.8 but they are uncorrelated with returns from C. Find the means and variances of the returns on the two portfolios.

c. Suppose the returns from A, B, and C are perfectly correlated (each pair have a correlation =1).  Find the means and variances of the returns on the two portfolios.  Is there any benefit to diversification in this case?

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