Suppose that you have the following utility function:

U$=$E$($r$)(1)/(2)$ A$\backslash$sigma $2$ 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 $0\mathrm{.}35\%$ 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$)=0\mathrm{.}070584$

$\backslash$sigma $=0\mathrm{.}173687$

ETFCDA :

E$($r$)=0\mathrm{.}073763$

$\backslash$sigma $=0\mathrm{.}16816$

Covariance between ETFUS and ETFCDA $=0\mathrm{.}02397$

Answer the following questions using Excel:

Draw the opportunity set offered by these two securities $($with increments of $0\mathrm{.}01$ in weight$).$ Hint: In Excel, calculate the portfolio$$s expected return and standard deviation for different weights on each ETF. Then use Excel$$s Create Chart command, under the Insert Charts menu.

What is the optimal portfolio of ETFUS and ETFCDA?

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.