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Suppose you are a US investor looking for international diversification opportunities. Your investment advisor offers you an international equity index that expects annual returns of 18%, but the volatility of these returns is 48%. This international index comprises other developed countries as well as some emerging economies. The expected returns, volatility, and correlations are provided below:
Risk-Free Rate
US Equity Index Returns (annual)
International Equity Index Returns (annual)
Expected Returns
3%
8%
18%
Std. Deviation (Volatility)
0%
48%
Correlation US Equity Index
0
1
0.4
Correlation International Equity Index
d. Suppose your investment advisor suggests adding the risk-free asset to the portfolio. In other words, your investment advisor recommends you to have a portfolio with three assets: risk-free rate, US equity index, and the International Equity Index. Using the following weights of the risk-free asset as the initial guess, estimate the portfolios that maximize the Sharpe ratios of those portfolios.
Risk-free asset
US Equity index returns (Weight)
International Equity index returns (Weight)
Portfolio Standard Deviation
Slope of CAL (Sharpe Ratio)
100%
2
80%
3
60%
4
40%
5
20%
6
e. Finally, suppose you do not use the weights for the risk-free asset in part d, but any other number you want to assume (as long as the weights of the 3-assets add up to 1). Find a portfolio that maximizes the Sharpe ratio?
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