Due to the reputation of UTS for producing work-ready graduates, you are head-hunted by a small asset management company to work part-time as a portfolio manager whilst you complete your degree. After learning all about mean-variance analysis and efficient asset allocation in 25503 Investment Analysis you are keen to use some of the tools you have learned in constructing your very first portfolio.

It is your first day on the job and your boss is keen to discover how much you really know. She provides you with a list of seven securities, namely BHP, CBA, APA, JHX, CWN, RIO, and AZJ, and asks that you and your team investigate the efficient asset allocation between these stocks. Moreover, you are asked to satisfy an 11% expected return target on the portfolio you build. To get started you collect historical performance data for six years in order to estimate the expected return and variance-covariance matrix of the stocks (the data is in the EXCEL file).

To perform the asset allocation you decide to construct a minimum variance portfolio according to the theory you learned in 25503 Investment Analysis. You recall the 11% expected return target imposed by your boss and note that there was no mention of shortselling constraints. In order to construct this portfolio you will need to perform the following tasks/answer the following questions:

1. (a) Transform the stock prices into simple weekly returns.

(b) Using the returns data, estimate (and report) the vector of expected returns for the seven stocks, as well as the variance-covariance matrix of these returns. This information should be annualised.

(c) Which stocks are dominated by others? Explain.

(d) Compute and report the parameters A, B, C and ∆.

(e) Construct and plot the MVS (with short sales allowed) for expected (annual) returns ranging between -10% and 30%. Your figure should also indicate the positions of the seven stocks.

(f) Identify the global minimum variance portfolio (MVP). That is, report the portfolio weights (in the seven stocks), expected return, and standard deviation of the MVP.

(g) Determine and report the portfolio weights for the efficient portfolio with an 11% expected return.

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