Suppose you can only invest in the stock markets of two countries: US and China. The US has an expected return of 5.0% and a standard deviation of 15.0%. China has an expected return of 7.0% and a standard deviation of 22.0%. The correlation between the returns in the two markets is 0.3. The risk-free rate is 3.0%. What is the maximum Sharpe ratio you can obtain (rounded to the nearest 0.001)

The maximum Sharpe ratio you can obtain is 0.182.

Explanation:

Sharpe ratio = (Stock's expected return - Risk-free rate) / Standard Deviation …………… (1)

Therefore, we have:

Sharpe ratio of the US stock market = (5.0% - 3.0%) / 15.0% = 0.133

Sharpe ratio of China stock market = (7.0% - 3.0%) / 22.0% = 0.182

Since you can only invest in the stock markets of US and China, and the Sharpe ratio of China stock market of 0.182 is greater than the Sharpe ratio of the stock market of 0.133, this implies that the maximum Sharpe ratio you can obtain is 0.182.

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