Maximize the sharpe ratios of portfolios

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Reference no: EM133060570

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%

18%

48%

Correlation US Equity Index

0

1

0.4

Correlation International Equity Index

0

0.4

1

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)

Expected Returns

Portfolio Standard Deviation

Slope of CAL (Sharpe Ratio)

1

100%

 

 

 

 

 

2

80%

 

 

 

 

 

3

60%

 

 

 

 

 

4

40%

 

 

 

 

 

5

20%

 

 

 

 

 

6

0%

 

 

 

 

 

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?

Reference no: EM133060570

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