Equity X is the stock of a company that produces confectionary. Equity Y is the stock of company that manufactures sports cars. The table below presents the share price returns to Equity X and Equity Y depending on the state of the economy.

State of the economy	Probability of state of the economy	Return on Equity X (%)	Return on Equity Y (%)
Bear	0.30	7.2	-5.2
Normal	0.50	8.6	14
Bull	0.20	13.2	17.1

The market risk premium is 8 percent and the T-bill rate is 3 percent. The market returns are 11% percent.

Questions:

1. Calculate the expected returns and standard deviations for both Equity X and for Equity Y. Explain your workings.

2. Calculate the covariance and the correlation coefficient between the returns on Equity X and the returns on Equity Y. Explain your workings.

3. Calculate b (beta or systematic risk) for both Equity X and Equity Y. Discuss what the systematic risk reflects. Explain your workings.

4. Explain which stock a risk-averse investor should select for their portfolio. Would they prefer Equity X or Equity Y? Assume that this investor does not keep a well-diversified portfolio.

5. With reference to your answers above, explain how a typical risk-averse investor with a well-diversified portfolio would evaluate Equity X and Equity Y as investment propositions.

6. Based on the expected return and standard deviation of Equity X and Y, form a portfolio that invests equally in Equity X and Equity Y and estimates the risk of this portfolio. Are there diversification benefits? Explain.