Referencing Styles : Harvard It has been over a month since you started working for the small asset management company (see Part I) and in that time your boss agreed to implement the portfolio you constructed on your very ﬁrst day on the job (after some more minor ‘tweeks’). You have now just returned from the break and your boss has set you on your next project! The company is thinking of adding an index tracking fund to their investment oﬀerings and your boss wants you to investigate the diﬀerent methods of constructing such a tracking portfolio. To do this you should perform the following preliminary analysis: 1. (a) Transform the stock prices and index values into continuously compounded returns (you do not need to report these in your submission). (b) Using the resulting returns data, estimate (and report) the vector of expected returns for the six stocks, as well as the variance-covariance matrix of these returns. These expected returns etc. should be annualized (i.e., in annual units). (c) Using the All Ordinaries index as a proxy for the market portfolio (MP), estimate and report the betas of the six stocks. (d) Decompose the total risk (variance) of each asset into its systematic and unsystematic components, i.e., report all three values (variance, systematic risk, unsystematic risk) along with the diversiﬁcation ratio (R2) for each stock and the index. (e) Assuming risk-free borrowing and lending at rF = 2% per annum, plot the capital market line (CML), and indicate the positions of the six stocks as well as the MP. (f) Plot the security market line (SML), and indicate the positions of the six stocks as well as that of the MP. Based on this graph, discuss which stocks look over-valued, and which stocks look under-valued? Since the All Ordinaries index is not traded, you wish to construct a portfolio out of the six 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 (Hint—you will need to use Solver): 2. (a) Report the weights (in the six stocks) of the portfolio whose variance is minimised but whose exposure to the index is exactly one, i.e., that has βP = 1. You should describe in words what you have done in Excel and report the value of your portfolio’s (minimised) variance. (b) Report the weights (in the six stocks) of the portfolio that minimises the variance of the diﬀerence in weekly returns between the portfolio and the AORD index. More speciﬁcally, let r1,..., rT be the vector-valued sample returns of the six 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 2 solves the following minimisation problem: min x Varx⊤rt − rI,t. Again you should describe in words what you have done in Excel as well as report the minimum value achieved for the variance of the diﬀerences. (c) Report the expected return, variance, beta and R2 for your two tracker portfolios constructed above. Which method do you recommend to your boss and why? You present this evidence to your boss, who, after careful consideration, asks you to construct and implement a completely diﬀerent method of her own! Oh well, at least you learnt something. Since the tracking portfolio is a passive strategy, there is not much work to do on it once it has been constructed. The next morning, when your boss realises this she decides to loan you to one of the other partners who specialises in the company’s ﬁxed-income oﬀerings. Within ﬁve minutes of arriving at his desk you are asked to help with an urgent bond portfolio immunization in which you need to perform the following tasks and have the results on your new supervisor’s desk in two hours: 3. A ﬁrm has a liability, L, which requires a payment of $25,000 per year (paid annually at the end of the year), for 15 years, plus a ﬁnal payment of $1,000,000 at the end of the 15th year. The following semi-annual coupon-bearing bonds, with a face-value of $1,000, are available for investment: Bond Maturity (Years) Coupon 1 20 6% 2 15 7% 3 5 8% Assume that the market YTM is a ﬂat 7% per annum, with semi-annual compounding. (a) Construct an immunizing portfolio for L with 50% invested in Bond 1 and 50% invested in Bonds 2 and 3 combined. Report the portfolio weights and show your workings. (b) Assess the eﬀectiveness of your immunizing portfolio if the market YTM increases by 0.5%. (c) What would the coupon rate need to be on Bond 1 for the immunization to be done by simply investing 100% in this (20 year) bond? With more than an hour to spare, you ﬁnish the last calculation and hand the results to your new supervisor. He’s impressed. So much so that he oﬀers to take you for lunch on expenses. As you tuck into your rib eye at Rockpool you start to realise that maybe all your hard work in 25503 Investment Analysis was worth it after all! The End. 3