https://docs.google.com/spreadsheets/d/1kqaJ9-BNujzYzNyOUm3pSHgE0vGdpih4D7ZvT5WhLqI/edit#gid=0

1) Use 5 points to draw the efficient frontier using these portfolios

2) The investment firm RMF has taken long position in Amazon (AMZN). They are concerned about the future volatility of the stock, and have approached you to create a hedge portfolio, with the objective of minimizing future volatility. To create the hedge you must work within the following parameters:

- You will have $10M of capital available to you

- You must hold $7M worth of Amazon shares. Calculate the number of shares to the nearest whole number based on stock prices available on the last day of the data.

- You can supplement these shares with either short or long holdings chosen from any or all of the following five securities mentioned above (Nasdaq 100 Trust (QQQ), S&P Depository Receipts (SPY), Verizon (VZ), Microsoft (MSFT), Wal-Mart (WMT)

- You can use up to 50% of the value of the long positions as collateral to finance purchases or satisfy short margin requirements

- All short positions require 50% margin (lower margin requirements apply for short positions that hedge long investments)

Calculate min variance portfolio with the above constraints. What are some of the limitations of using the min-variance weights that you calculated. What qualitative adjustments would you make based on your outlook for volatility and correlations for these stocks?