1. Markowitz Portfolio Optimisation. [30 Marks]

Lisa is considering two risky funds, the S&P 500 index fund and a corporate bond fund, plus Treasury bills (T-Bills). The information of the funds and T-bills are as follows:

	Expected Return	Standard Deviation
S&P 500	16%	20%
Corporate Bond Fund	10%	15%
T-bills	6%	0

The correlation between the S&P 500 index fund and the corporate bond fund is 0.4.

If Lisa has a risk aversion of A = 5 when applying to return on wealth, what are the investment proportions in the T-bills and each of the two risky funds? Calculate the expected return and standard deviation of the completed portfolio.