You have 3 billion dollars in the fund, which you can invest inany combination of Australian stocks, US stocks, and AustralianTreasury. The idea is to use your knowledge of portfolio theory tomake an argument for having an internationally diversifiedportfolio, rather than just holding domestic assets. The data aremonthly returns and the relevant sample statistics are summarizedin the following table:
| Stock | E[R] | Var(R] | Cov(Aus, US) |
| Aus Index | 0.00959 | 0.00222 | 0.00088 |
| US Index | 0.00727 | 0.00348 | |
| Aus Treasury | 0.00300 | 0.00000 | |
1. Using the results of portfolio theory and the estimatesabove, compute the tangency mutual fund (portfolio) betweenAustralian and US stocks (i.e., the optimal split betweenAustralian and US stocks). Find the tangency portfolio using theSolver in Excel. Paste the table used with Solver to your Worddocument and discuss your findings.
Suppose you would like to achieve an average return of 0.5% permonth in excess of the T-bill rate with the smallest possible risk.What is the optimal split between Australian stocks, US stocks, andT-bills? That is, how much of the $3 billion should you invest ineach country and how much should you borrow or lend? What is thestandard deviation of this portfolio?
After a bad year on the US stock market, some people try toinfluence you to divest (i.e., sell all of) the holdings of USstocks. How much should you invest in Australian stocks and T-billsalone to obtain the same level of risk as you obtained in part 2.?(Hint: you want the standard deviation of the divested portfolio tobe the same as the nondivested portfolio.)
What would be the cost in terms of expected monthly return fromdivesting in the US stocks? What would be the cost in terms ofannual return (note: the returns are continuously compounded)? Whatwould be the cost in dollar terms on the $3 billion portfolio eachyear?
