In this project you will use your many skills to create multiple portfolios, using the Standard and Poor's Mid Cap 400 as your dataset.

First, construct an index fund using a stratified sample of 100 stocks from the Mid Cap 400. Follow the selection process we used in class, sorting by size and P/B. Be sure to use the random numbers in your data file as the random numbers to select your stocks. Use the weight of the 20th largest stock as your threshold for stocks that have to be selected, as discussed in class.

Note: Stocks with no P/B value should be treated as extreme growth stocks.

2. Be within 10% of the average market cap, average P/B and sector weights. What is your minimized tracking error value?

Now change your range from 10% to 5% and reoptimize. What is your new optimized tracking error? Is the new value larger or smaller? Explain your result (put it directly on your Excel sheet).

Now switch to an "index-plus" portfolio. The goal here is to be mindful of tracking error, but to also try to add some utility by overweighting the portfolio with stocks that have positive alphas 2. Be within 10% of the average market cap, average P/B and sector weights. What is the maximized value of your utility function? 

Now remove the restriction of all weights being greater than or equal to zero and reoptimize. What is your new maximized utility value, and which stock have the biggest positive and negative weights?

Be sure that your sampling technique is correct. Errors in sampling will cause more errors in your later analysis.