Compute the mean, variance and Sharpe ratio of eight firms
Please download daily price data of eight stocks contained in Don Jones Industrial Average index fromJanuary 4th, 2016 to December 30th, 2019 using Yahoo Finance. Assume a risk-free rate of 125 basispoints. Use the “adjusted close” price when calculate returns.
(a) For all eight fifirms compute the mean, variance and Sharpe ratio (both daily and annual).
(b) Compute the daily correlation matrix and variance-covariance matrix of the eight stocks.
(c) Comment on the performance of two of the eight fifirms vis-`a-vis the DJIA index over the past fouryears. Did these two stocks outperform or underperform DJIA index? How were the two stockscorrelated with the index, positively or negatively?
(d) Choose two stocks from the eight stocks. Draw the investment opportunity set with two stocks.
(e) Draw the minimum variance frontier by creating portfolios of the eight stocks with short saleconstraint. Here you should use Excel solver to come up with at least 8 portfolios including theglobal minimum risk portfolio. [Hint: add constraints that all weights are greater than zero orturn on the “making unconstrained variables non-negative” option in Excel solver. ]
(f) Draw the minimum variance frontier by creating portfolios of the eight stocks without short saleconstraint. Again use at least 8 portfolios to plot the frontier. How does the frontier changecompared with the result in question (e)?
(g) Plot the two stocks opportunity set you got in question (d) and the minimum variance frontierin question (f) in one picture. Does a eight-asset portfolio provide more diversifification benefifitaccording to your result?
(h) Calculate the risk contribution of the eight stocks in the global minimum variance portfolio withshort sale constraint. Which stock has the highest contribution to the portfolio variance?
(i) Compute the weight of the optimal risky portfolio without short sale constraint. Comparing theSharpe ratio of the optimal portfolio and the eight stocks.