There are 3 short questions in question 3, which will use the ‘Out-of-Sample Data’ will be used for Question 3 and the Question 2’s answer, that will show you in the files.

Since the tracker portfolio is a passive strategy, your boss moves you on to other projects. However, over 12 months have now passed and your boss asks you to look into the performance of the tracker portfolio. The portfolio was constructed on November 3, 2017 using the portfolio weights found in 2(b) and with an investment amount of $1,000,000. You should assume that this was done without any transaction costs at the prices quoted on that date in the ‘Out-of-Sample’ tab and that any fraction of a share can be purchased. You should also assume that the portfolio was held, without any further transactions, until November 9, 2018 (i.e., the portfolio was not re-balanced). To assess the performance of the tracking portfolio you need to perform the following tasks:

3. (a) Calculate and report a time-series plot of the tracker portfolio value from Nov 3, 2017, to Nov 9, 2018, along with the performance of the ASX200 index, clearly indicating which series is which. You should also normalise the values of both time series so that their values are 100 on Nov 3, 2017.

(b) Report the simple annualised return of the tracker portfolio and the ASX200 index over the investment period.

(c) Using the weekly simple returns for the tracker portfolio and the index, report the beta, R2 , and RMSE for the tracker portfolio over the investment period. Comment on how close these values are to the values found for the tracker portfolio ‘in sample’ from Questions 2.

**Question 2**

- Report the weights (in the 10 stocks) of the portfolio whose variance is minimisedbut whose exposure to the index is exactly one, i.e., that has βP = 1. You shoulddescribe in words what you have done in Excel and report the value of your portfolio’s(minimised) variance.

Portfolio’s (minimised) variance is 0.0168081

** **

Workings in Excel

- Input randomly the weights of the 10 assets to ensure the sum of the weight is 1.
- Calculating the expected return, variance, beta and R
^{2}with proper formula. - Run the solver

Target cell: variance to minimise

Variable cells: portfolio weights

Constraints: sum of portfolio weights = 1 & portfolio beta = 1

** **

- Report the weights (in the 10 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,…r
_{T}be the vector-valued sample returns of the twelve stocks, for t = 1,… T Similarly, let rI,1,…rI,Tdenote the sample returns of the index. Then you want to find the vector of portfolio weights that solvesthe following minimisation problem:

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

** **

Minimum value of the RMSE achieved is 0.00546416

** **

Workings in Excel

- Input randomly the weights of the ten assets to ensure the sum of the weight is 1.
- Calculating the RMSE with proper formula.
- Run the solver

Target cell: RMSE to minimise

Variable cells: portfolio weights

Constraints: sum of portfolio weights = 1

- You are also interested in knowing if all 10 stocks are required for your tracker portfolioin (b). To investigate this, report the value of the minimised RMSE achieved if the topfive capitalised stocks were used to construct the tracker portfolio (instead of the top10). Comment briefly on your results

Minimum value of the RMSE achieved is 0.00839731

Fromquestion(b) and (c) we can see thatRMSE of 5 stocks (0.00839731) is higher than 10 stocks (0.00546416). This indicates that 10 stocks portfolio has arelativelyaccurate measurement.

- Report the expected return, variance, beta and R
^{2}for your three tracker portfolios constructed above. Which method do you recommend to your boss and why?

Recommendation:

I would recommend my boss to tracker 1 or 3. Tracker 1 has higher return and low risk compared with tracker 2 due to higher expected return, low variance and beta. Furthermore, tracker 3 has higher return andrisk than tracker 1 due to higher expected return, variance and beta. So, if our boss is risk-taking, I would recommend him to tracker 3, and if he is risk-averse, I would recommend him tracker 1.