Question

Suppose John wishes to construct his portfolio with Stock X and Y, but he is not decided on the weights. Jane wishes to construct her portfolio with Stock Y and Z, also undecided on the weights.

	Stock X	Stock Y	Stock Z
Expected Return	0.06	0.18	0.12
Standard Deviation	0.10	0.30	0.20
Covariance between X and Y	-0.027
Covariance between Y and Z		0.054

• Compute the correlation coefficients for John's and Jane's portfolios.
• Which person has a greater chance to achieve greater risk diversification? Why?
• What other factor(s) may affect the degree of risk diversification?

Answer 1

1.

We can compute correlation coefficient of two stock with following equation:

Thus,

Correlation coefficients for John's Portfolio:

Correlation coefficients for Jane's Portfolio:

2.

John has greater chance of to greater risk diversification because Stock X and Stock Y have negative coefficient of correlation. Stocks with negative correlation can diversify greater amount of unsystematic risk.

3.

We have to choose optimal weights to minimize the risk of portfolio. If two stocks are perfectly negative correlated then portfolio risk can be diversified to zero risk.

There are some other factors for diversification of risk:

• Assets class: Equity, Bond, commodity etc
• Industrial diversification
• Geographical diversification
• Time diversification