Tangency Portfolio Problem. Question: Collect 10 years of monthly returns for four stocks. Sample of ten years of monthly data should be a pretty reasonable estimate of expected returns, variances, and covariance.
[A] Using this information, calculate the tangency portfolio. You have to report
(a) Corresponding weights of the Tangency and T-Bill portfolios;
(b) Expected return and volatility of the complete portfolio.
Apply solver to calculate the tangency portfolio in M.S. Excel. Print and submit two Excel spreadsheets: one with the starting values for portfolio weights, another with the optimal portfolio weights. The Excel Spreadsheet Tangency Portfolio.xls with similar problem is placed on ANGEL in the "Excel Examples" folder. You can use it as a template for this problem. This problem aims at demonstrating that the concepts we discussed in class hold in a more general setting than just a two-stock market. If you like, you can easily make the tangency using 5 & more stocks.
Suggestion: Apply vector formulation; it is very easy to compute portfolio's variance! If ω is the N Χ 1 vector of portfolio weights and Ω is the N Χ N variance-co variance matrix, then the portfolio variance is