SPY and XIU are ETFs tracking the S&P 500 and S&P/TSX 60 index, which are often used as proxies for the U.S. and Canadian stock markets, respectively. From a set of their historical data, the annual expected returns and standard deviations of those two ETFs and their covariance are estimated as follows:

SPY:

E(r)= 0.15

=0.28

XIU:

E(r)= 0.18

=0.32

Covariance between SPY and XIU = 0.0618

Suppose that you have $10 million to invest for one year and you want to invest that money into SPY, XIU, and the Canadian one-year T-bill. Assume that the interest rate of the one-year T-Bill is 3% per annum.

Suppose that you have the following utility function:

U=E(r) A² and A=3

Answer the following questions using Excel:

1. Draw the opportunity set offered by these two securities (with an increment of 0.01 in weight).