8. (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 / Suppose that there are n assets with (random) rates of return 12. We wish to find thei portfolio rate of return (with 1) minimizing var(FM)

(a) Find a set of equations for the a's.

(b) Although this portfolio tracks the desired portfolio most closely in terms of variance, it may sacrifice the mean Hence a logical approach is to minimize the variance of the tracking error subject to achieving a given mean return. As the mean is varied, this results in a family of portfolios that are efficient in a new sense-say, tracking efficient. Find the equation for the a's that are tracking efficient