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Global Fund Managers (GFM), the world's leading company in the management of investment funds and pensions, has just hired you to be part of its team of equity portfolio managers in Latin America. Your first task is to prepare a report. In the attached file sent by the quantitative analysis team, you will find monthly closing prices of the top 10 shares out of the 15 in the S & P / BVL PERU SELECT INDEX1 portfolio, as well as the closing values of the S & P / BVL PERU SELECT INDEX. The analysis period is from January 2017 to September 2021. As part of the report, you have to:

1. Present a graph in which it can be seen the relationship between the annual return2 and the risk of the annual return3 of each of the selected stocks. Is there a relationship between the risk and return of the stocks? (1.5 marks)

2. Present the Correlation Matrix, and the VARCOVAR matrix of the monthly returns of the shares that are part of the study. Identify the 3 pairs of shares with the highest correlations and the 3 pairs of shares with the lowest correlations. In case you find any negative correlation, you must specify the name of the shares. (1.5 marks)

3. Estimate the efficient frontier using only the shares that are part of the study, calculating for each efficient portfolio: i) the annual return, ii) the risk and iii) the weights of each share. The weight of each share (Wi) can only be greater than or equal to zero and less than or equal to 1 (restriction to short term sales). It is important that you estimate no less than 20 efficient portfolios so that you can have a complete outlook of the efficient frontier and be able to present a graph. What is the global minimum variance portfolio? And what is the maximum return portfolio? (4 marks) One of the members of the GFM quantitative analysis team, graduated from Universidad del Pacfico, was the one who sent you the email with the closing prices. In the email he indicated the following: Once the variance and covariance matrix has been calculated, I suggest that you first find the portfolio with the global minimum variance, and second, the efficient portfolio with the maximum expected return. When you have these two portfolios, the one with the minimum variance and the one with the maximum expected return, you should be able to find the rest of the portfolios. Solver could be a useful tool to do your job ... "

4. If the risk-free rate is 2%, what would be the optimal risky portfolio? (1 mark)

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