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Question

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

    Standard Deviation = 0.28


XIU:

E(r)= 0.18

    Standard Deviation = 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) - ½ Aσ2  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).

2.      What is the optimal portfolio of SPY and XIU?

3.      Determine your optimal asset allocation among SPY, XIU, and T-Bill, in percentage and in dollar amounts. 

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