problem: 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, find out the tangency portfolio. You have to report

(a)                Weights of the individual stocks in the tangency portfolio;

(B)                Expected returns and volatilities of the individual stocks;

(c)                Variance-covariance matrix;

(d)                Expected return and volatility of the tangency portfolio;

(e)                Sharpe ratio of the tangency portfolio;

Use solver to find out 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 exs" 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