Suppose that you have the following utility function:

U=E(r) A² and A=3

Suppose that you have $10 million to invest for one year and you want to invest that money into ETFs tracking the S&P 500 (US) and S&P/TSX 60 (Canada) index, which are often used as proxies for the US and Canadian stock markets, respectively, and the Canadian one-year T-bill. Assume that the interest rate of the one-year T-bill is 0.35% per annum.

You have found two ETFs that you are interested in. From a set of their historical data between 2001 and 2019, you have estimated the annual expected returns, standard deviations, and covariance as follows:

ETFUS :

E(r)= 0.070584

= 0.173687

ETFCDA :

E(r)= 0.073763

= 0.16816

Covariance between ETFUS and ETFCDA = 0.02397

Answer the following questions using Excel:

1. Draw the opportunity set offered by these two securities (with increments of 0.01 in weight). Hint: In Excel, calculate the portfolio expected return and standard deviation for different weights on each ETF. Then use Excels Create Chart command, under the Insert Charts menu.
2. What is the optimal portfolio of ETFUS and ETFCDA?
3. Determine your optimal asset allocation among ETFUS , ETFCDA , and T-bill, in percentage and in dollar amounts.

Note: Include your answer to this problem in the same Word file as your other answers. Also submit an Excel file to show your work.