4. Your aunt is a typical mean-variance investor with a home bias, currently invested 100% in a diversified Spanish equity portfolio with expected re- turn of 12.46% and volatility of 15.76%. She is considering changing 20% of her portfolio. One option is fund N, an investment fund that invests in Spanish start-ups, with an expected return of 14.69% and a volatility of 32.5%. Based on historical data, she has determined its correlation with his current portfolio to be 0.7274. She is also considering the Exotic fund, which invests in several emerging markets. The expected return on the fund is only 12%; it has 34% volatility and a correlation of 0.2 with her portfolio. The correlation of the Exotic fund with the fund is 0.15. Assume that the risk-free rate is 5%. If your aunt is interested in improving the Sharpe ratio of her portfo- lio, will she invest a positive amount in one of the funds? Which one? Carefully explain your reasoning (HINT: Remember, the Sharpe ra- tio is computed as the extra return of the portfolio with respect to the risk-free rate and over the standard deviation of the portfolio).

4. Your aunt is a typical mean-variance investor with a home bias, currently invested 100% in a diversified Spanish equity portfolio with expected return of 12.46% and volatility of 15.76%. She is considering changing 20% of her portfolio. One option is fund N~, an investment fund that invests in Spanish start-ups, with an expected return of 14.69% and a volatility of 32.5%. Based on historical data, she has determined its correlation with his current portfolio to be 0.7274 . She is also considering the Exotic fund, which invests in several emerging markets. The expected return on the fund is only 12%; it has 34% volatility and a correlation of 0.2 with her portfolio. The correlation of the Exotic fund with the N fund is 0.15 . Assume that the risk-free rate is 5%. - If your aunt is interested in improving the Sharpe ratio of her portfolio, will she invest a positive amount in one of the funds? Which one? Carefully explain your reasoning (HINT: Remember, the Sharpe ratio is computed as the extra return of the portfolio with respect to the risk-free rate and over the standard deviation of the portfolio)