Using Python:

Instructions:

• Download the monthly returns of the Fama-French 12 industry portfolios from Kenneth French's website from the beginning of 1960 to the end of 2020.
• Assume the risk-free rate is zero.
• Starting from December 1990, estimate the covariance matrix and expected returns every month using data from January 1960 through that month (rolling window estimation).
• Form the tangency portfolio of the 12 industries every month from January 1991 through December 2020 using the estimates from the previous step. Here are a few examples of the timing of the estimates and the tangency portfolios:
  • Use the data from 1960/1 to 1990/12 to estimate the covariance matrix and the expected returns. Hold the corresponding tangency portfolio over January 1991.
  • Use the data from 1960/1 to 1991/1 to estimate the covariance matrix and the expected returns. Hold the corresponding tangency portfolio over February 1991.
  • Use the data from 1960/1 to 1991/2 to estimate the covariance matrix and the expected returns. Hold the corresponding tangency portfolio over March 1991.
  • Use the data from 1960/1 to 2020/10 to estimate the covariance matrix and the expected returns. Hold the corresponding tangency portfolio over November 2020.
  • Use the data from 1960/1 to 2020/11 to estimate the covariance matrix and the expected returns. Hold the corresponding tangency portfolio over December 2020.
• Calculate the returns of your tangency portfolio as well as an equally weighted portfolio of the 12 industries over the same period, that is, from January 1991 until December 2020.
• Calculate the Sharpe ratio for
  • Your tangency portfolio, and
  • The equally weighted portfolio.
• Explain the results and include:
  • A table of summary statistics for your monthly industry return data.
  • A summary statistic table and a graph of the weights of the industries in your tangency portfolio.
  • A table and a figure describing monthly returns of your tangency portfolio.
  • A table comparing the Sharpe ratios of the tangency and the equally weighted portfolio.