Since the ASX200 index is not traded, you wish to construct a portfolio out of the 12 stocks that tracks the index as close as possible (in some sense). Your boss asks you to propose at least two different methods for constructing such a tracker portfolio. After some careful research you come up with two possible methods and to implement these you must perform the following tasks (Hintyou will need to use Solver):

2. (a)

Report the weights (in the 12 stocks) of the portfolio whose variance is minimised but whose exposure to the index is exactly one, i.e. that has P = 1. You should describe in words what you have done in Excel and report the value of your portfolios (minimised) variance.

(b) Report the weights (in the 12 stocks) of the portfolio that minimises the Root-Mean- Square Error (RMSE) of the difference in weekly returns between the portfolio and the ASX200 index. More specifically, let r1, . . . , rT be the vector-valued sample returns of the 12 stocks, for t = 1,...,T weeks. Similarly, let rI,1,...,rI,T denote the sample returns of the index. Then you want to find the vector of portfolio weights that solves

Note you should use the variance-covariance matrix to calculate the portfolios variance.

Again you should describe in words what you have done in Excel as well as report theminimum value of the RMSE achieved.

(c) You are also interested in knowing if all 12 stocks are required for your tracker portfolio in (b). To investigate this, report the value of the minimised RMSE achieved if the top six capitalised stocks were used to construct the tracker portfolio (instead of the top 12). Comment briefly on your results.

(d) Report the expected return, variance, beta and R2 for your three tracker portfolios con- structed above; i.e. the trackers in (a), (b) and (c). Which method do you recommend to your boss and why?

You present this evidence to your boss, who, after careful consideration, decides to implement the tracking portfolio you constructed in 2(b).