Consider data in the  dataset  included  in  the  file  ’data  for  exam  2021.xls’. This  file  is  divided up into 4 worksheet: i) stocks daily; ii) stocks monthly; iii) funds daily; iv) funds monthly. The worksheet with stocks, include a selection of stocks from the Italian Stock Market starting from January 1st, 2015 until June 14th, 2021. The daily worksheet includes daily prices adjusted for dividends, while the monthly worksheet includes monthly prices for the same sample of securities, adjusted for dividends, starting from Jan 1st, 2015 and ending on June 1st 2021.

The worksheet identified with funds, contains a sample of investment funds sold in the Euro Area and managed by some of the most famous and respected investment firms: both in daily and in monthly frequency, for the same sample size considered also for stocks.

1. Focus first on the two worksheet on stocks. Compute returns for both daily and monthly Compute mean, standard deviation, variance, skewness and kurtosis for stocks at daily and monthly frequency. Show the results in a table and comment.
2. Compute the variance-covariance matrix and the correlation

1. Select a sample made of 10-12 securities. You should motivate your choice of securities. The choice can be made, for example, on the basis of the correlation structure of the variance- covariance Explain and justify your choices.
2. Plot the behavior of the security prices you have chosen, both in daily and monthly frequency during the entire lenght of the sample
3. Compute the Mean Variance optimal portfolio allocation for the sample of securities chosen by you both in daily and monthly Discuss.
4. Compute the same asset allocation after imposing non-negativity constraint on portfolio
5. Given previous results, compute mean, standard deviations, variance, skewness and kurtosis of your optimal mean-variance portfolios, both for daily and monthly frequency. Provide the necessary intuition by making extensive
6. Plot the efficient frontier for both daily and monthly Discuss.

1. Consider an index representative of the Italian stock market, such as FTSE Italia All Market, given in the two distinct worksheets, one for the daily and one for monthly version. The index is here collected in its Total Return version. Compute all the statistics relative to that index (mean, standard deviation, variance, kurtosis and skewness). Discuss the differences between such statistics for the index and those you found for your
2. Compute the beta for each security included in your portfolio and the beta for your portfolio as
3. Given a return for a Risk-Free security equal to 0.5 per cent (0.005), compute the Security Market Line (SML)for two (2) securities of your portfolio and for your portfolio as well. Verify for the two chosen securities if the SML is verified., for both daily and monthly frequency.