# Numerical Optimization - Computational Questions

Use the data in the Excel file for the following questions.

## Excel Questions

1. Find the portfolio that maximizes Sharpe ratio. Assume no short sells are allowed. Also, you cannot invest more than 30% combined in assets 1 and 3. For every dollar invested in asset 2, you must invest at least 2 dollars in asset 4.

2. Find portfolio that maximizes (Sharpe-4*Skew), where Sharpe is the portfolio's Sharpe ratio and Skew is the portfolio's skewness. Assume no short selling.

3. Currently 40% of your portfolio is invested in asset 1, 50% is invested in asset 2, and 10% is invested in asset 3. The portfolio is currently worth $100. You just received$20 from your paycheck. You want to invest the additional $20, but you cannot alter how the original$100 is invested. When you invest your additional $20, your new portfolio will be worth$120. What's the optimal investment weights that maximizes the new portfolio's Sharpe ratio when you invest the additional \$20? Assume no short selling.