The Vanguard European stock fund, Pacific stock fund, and Exxon Mobil reported the following historical dividend-adjusted prices:
(a) Compute the means and covariances of the rates of return on these three assets.
(b) Draw the efficient frontier if you can only invest in VEURX and VPACX.
(c) Now add Exxon Mobil. Use Excel to draw 1,000 random numbers in two columns, called wE and wP. (Create one formula, and copy it into all of the cells.) Each of these 2,000 cells should use the formula 'rand()*3-1'. Create a new column that is 1.0 minus wE and wP, and call it wX.
Now consider these random numbers as investment weights in VEURX, VPACX, and XOM. Compute the risk and reward for each of these portfolios (one portfolio is three numbers: one wE, one wP, and one wX), using the standard deviation and expected rate of return formulas. Finally create an x-y plot that shows, for each of your wE, wP, and wX portfolios, the riskreward combinations. What doesthe plot look like?
(d) If the risk-free rate stood at 5% per annum, what would be the tangency portfolio?