SPY and XIU are ETFs tracking the S&P 500 and S&P/TSX 60 index, which are often used as proxies for the US 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) = 0.36

0.26

XIU:

E(r) = 0.44

0.28

Covariance between= 0.0568

Suppose that you have $5 million to invest for one year and you want to invest this money into SPY, XIU and the Canadian one-year T-bill. Assume that the interest rate of the one-year T-Bill is 6% per annum.

Suppose that you have the following utility function:

U=E(r)