Over the period of time 2009–2018, the return (per dollar invested) on Maura stock was 0.013469 per month, the return on Ward was 0.013543 per month, and the return on Goldsmith was 0.006504 per month. Under certain assumptions, including that whatever underlying process generated the past set of observations will continue to hold in the present and near future, we can estimate the expected return for a stock portfolio containing these assets in some combination. Suppose we have a portfolio that has 20% of our total wealth in Maura, 30% in Ward, and 50% in Goldsmith stock. Use the following steps to estimate the portfolio’s historical return, which can be used to estimate the future return.
(a) Write a 1 × 3 matrix that defines the decimal part of our total wealth in Maura, in Ward, and in Goldsmith.
(b) Write a 3 × 1 matrix that gives the monthly returns from each of these companies.
(c) Find the historical return of the portfolio by computing the product of these two matrices.
(d) What is the expected monthly return of the stock portfolio, as a percent?