Question

Assume that we have 3 Stocks A, B & C.

	A	B	C
Expected return	8%	12%	6%
Variance	0.012	0.028	0.009

If the covariance between stock A & B return is equal to 0.009159, stock A & C return is equal to -0.005146 and stock B & C return 0.01572

Required

1. Calculate the Standard Deviation for stock A, B & C. which stock is risky and why?
2. Calculate the correlation between every two stocks. What is the indication of it?
3. Calculate the expected return and expected risk for a portfolio that consists of 30% of stock A and 70% 0f stock B, and a portfolio that consists of 60% of stock A and 40% of stock C.
4. Does the diversification effect work for both portfolios? Why?

Answer 1

Stock B has the highest risk because it has the highest standard deviation compared to the other stocks. A high standard deviation indicates that the firm's return is less stable.

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Correlation coefficient indicates the strength of relationship between two variables and also the direction of relationship.

Between stock A and stock B, the degree of relationship between the two stocks is not very high. However a positive relationship exists between the two stocks which indicates that as the returns for stock A increases, the returns for stock B also increases.

Between stock A and stock C, again the degree of relationship is not very high. A negative relationship exists between the two stocks which indicates that as the returns for stock A increases, the returns for stock B decreases.

Between stock B and C, the correlation coefficient indicates that the degree of relationship is very high. The correlation coefficient between the two stocks is positive which indicates that the returns move in the same direction. If returns for stock B increases, then returns for stock C also increases.

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Expected return for a two stock portfolio = E(R1) W(R1) + E(R2) W(R2)

Expected return for a portfolio that contains 30% stock A and 70% stock B = 0.30 0.08 + 0.70 0.12 = 10.8%

Expected risk for a portfolio that contains 30% stock A and 70% stock B = 13.65%

Expected return for a portfolio that contains 60% of stock A and 40% of stock C = 0.60 0.08 + 0.40 0.06

Expected return for a portfolio that contains 60% of stock A and 40% of stock C = 7.2%

Expected risk for a portfolio that contains 60% stock A and 40% stock C = 10.34%

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As observed from the above calculations, we observe that by diversifying the investment in two stocks, we can obtain a portfolio with a lower expected risk. Therefore the diversification effect works for both the portfolios.