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.

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