You are a pension fund manager and are considering investing in three assets: an equity shares fund, a bond fund, and treasury bills. The T-bills has an expected return of 4%. You would like to build a portfolio with 70% risky assets and 30% risk-free assets. You have sourced the following information with respect to the equity shares fund and the bond fund:

Scenario	Probability	Equity fund Rate of Return	Bond fund Rate of Return
Severe recession	0.10	-3.4%	-13%
Mild recession	0.20	-14%	19%
Normal growth	0.40	19%	12%
Boom	0.30	24%	-8%

3.1 Calculate the values of mean return and standard deviation for the equity fund.

3.2 Calculate the values of mean return and standard deviation for the bond fund.

3.3 Calculate the correlation coefficient between the stock and bond funds.

3.4 What would be the expected returns and risk aversion for the portfolio if you split the investment in the bond and the equity fund equally? Would this be the optimal asset allocation? Why or why not?

3.5 Which of the following would make for the greatest increase in the portfolios Sharpe ratio? a) An increase of 1% in expected return b) A decrease of 1% in the risk-free rate c) A decrease of 1% in the standard deviation