Full points to whoever shows all work

(Tracking) Suppose that it is impractical to use all the assets that are incorporated into a specified portfolio (such as a given efficient portfolio). One alternative is to find the portfolio, made up of a given set of n stocks, that tracks the specified portfolio most closely-in the sense of minimizing the variance of the difference in returns. Specifically, suppose that the target portfolio has (random) rate of return rM. Suppose that there are n assets with (random) rates of return r1,r2, . . . , rn. We wish to find the portfolio rate of return r = alpha 1r1 + alpha 2r2 + . . . + alpha nrn (with alpha i = 1) minimizing var(r - rM). Find a set of equation for the alpha i's. (Tracking) Suppose that it is impractical to use all the assets that are incorporated into a specified portfolio (such as a given efficient portfolio). One alternative is to find the portfolio, made up of a given set of n stocks, that tracks the specified portfolio most closely-in the sense of minimizing the variance of the difference in returns. Specifically, suppose that the target portfolio has (random) rate of return rM. Suppose that there are n assets with (random) rates of return r1,r2, . . . , rn. We wish to find the portfolio rate of return r = alpha 1r1 + alpha 2r2 + . . . + alpha nrn (with alpha i = 1) minimizing var(r - rM). Find a set of equation for the alpha i's