Problem D - Markowitz Portfolio Model (25 points)

You are managing a index fund represented by 6 stock investments (investments of your choosing).

1. Acquire at least 2 years of historical daily time series data (e.g. finance.yahoo.com) for the applicable investments and estimate the annual return for each investment (using Adjusted Close price). Estimate the annual return by taking the average of the daily percentage change in closing stock price times 250. 250 represents the typical number of trading days in a year.
2. Create a line plots of the daily percentage change (properly labeled) that includes all 6 series. If you want to impress me, using a moving average to understand trend.
3. Create a variance-covariance matrix (based on daily percentage change).
4. Build a Markowitz Portfolio Model. Identify/describe the Objective Function, Decision Variables, and Constraints.
5. Solve and answer the question of how much of each investment should the portfolio represent with a 5% desired return, 10%, 15%, and 20%. The following table may help.
6. Create an Efficient Frontier chart and describe the chart (ideally, describe to someone in your life (e.g. significant other, parent, child, friend, etc). what the chart means).

Desired return	Stock 1	Stock 2	Stock 3	Stock 4	Stock 5	Stock 6	Variance	Calculated Return
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%

Tips/Tricks:

• Use as much stock/investment history as you want to use (does not need to be only 2 years). If you have a 401K/IRA, maybe use those investments (Index funds, bonds, etc.).
• Pay particular attention to whether a feasible solution is found as you increase the Desired Return. In the above table, simply note that the calculated return is "feasible solution cannot be found".
• Do not pick a stock/invesment that calculates with a negative return (e.g. PG&E) as the objective is to not lose money (why would someone pick a stock that is anticipated to have a negative return).
• The above table is for guidance only. Use hire desired return amounts is appropriate.