SPY and XIU are ETFs tracking the S&P 500 and S&P/TSX 60 index, which are often used
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
SD=0.28
XIU:
E(r)= 0.18
SD: 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:
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.
Probability & Statistics For Engineers & Scientists
ISBN: 9780131877115
8th Edition
Authors: Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying Ye