"Portfolio Optimization and Risk-Return Analysis Using Two Risky Assets and a Risk-Free Asset" FIN302

Perform the following tasks. Write no more than 4 pages in total for this question.

a) You want to build the risky portfolio frontier that can be constructed from investing in stocks A and B only. To do so, follow the instructions below to compute the characteristics of some frontier portfolios. Then plot the frontier by connecting the points representing the frontier portfolios and describe its key features. Explain why the frontier has the shape that you see in your plot, referring to the computations you undertook in answering question 1. [To build the frontier, start with a portfolio that is wholly invested in stock A and compute its mean return and return standard deviation. Then increase the weight on B by 0.1 and reduce that on A by the same amount and re-compute the mean and standard deviation. Continue this process until the portfolio is wholly invested in B.] [15 marks]

b) Using the frontier that you have computed, identify the portfolio that one would select if one wanted to maximise the Sharpe ratio. Explain intuitively, and show graphically, how this portfolio can (or cannot) be used to create a position that dominates either investing only in A or B. [10 marks]

c) Client Z wants a portfolio containing the maximal Sharpe ratio portfolio and the risk-free asset that has a monthly return standard deviation of exactly 5%. Derive the appropriate weights and interpret them. What is the mean return of this portfolio? [5 marks]

d) Client Y wants a portfolio containing only A and B that has minimal risk. Which portfolio of those that you have computed would you recommend? Could this client use the risk-free asset as well to achieve a very similar risk level to that which your recommendation delivers, but with higher mean return? If so, explain how this could be done and describe the alternative approach to the client. [5 marks]