Posted: August 24th, 2015

A wealthy German investor (diversified in terms of exposure to different sectors in Germany and Austria, but not diversified in terms of international geographical exposure) is considering the strategic decision of investing in a portfolio of five FTSE100 firms. You are employed by a leading financial institution and have been asked to advise this client. You will prepare an investment report in Microsoft Word for her containing all your work, results and arguments. All the relevant tables and figures should be contained and discussed in the main body of the report, not in some appendix. The report should not exceed 4,000 words in total (without appendices) and should include all of the following five sections. You can also find the suggestions about Tables/Figures you should at least include, and textbook chapters that you could start reading from in each section.

Section 1. Following the scandals and rumours about the LIBOR and FX market in the UK, your client believes that the London Stock Exchange (LSE) may not be perfectly market and is not sure if this is good or bad for her or not as an aspiring passive investor. Discuss your arguments on the validity of her view and the implications of market efficiency for passive investors. Do not perform your own empirical analysis and testing but use the evidence from the literature.

Section 2. Use your sample data to form the following four portfolios: A) equally weighted portfolio; B) value-weighted portfolio; C) global minimum-variance portfolio; and D) optimal risky portfolio. According to the five stocks and risk-free rate, build the optimal capital allocation line, minimum-variance frontier and the efficient frontier, and identify the positions of those five stocks and four portfolios (A, B, C and D) in a scatterplot of standard deviations against returns. Explain and discuss your results.

Tables: Portfolio weights, returns and standard deviations.

Figure: One scatterplot includes the optimal capital allocation line, minimum-variance frontier and efficient frontier.

Section 3. Determine the proportion of the overall complete portfolio in the UK financial market that should be held in the optimal risky portfolio of the five stocks along with the proportion that should be held in the risk-free asset. Assume that your client has the same coefficient of risk aversion as yours and that you should determine this by using the Charles Schwab Investor Profile Questionnaire (you can find the questionnaire from here). Transform the questionnaire risk tolerance scores “x” (0 to 40) into risk aversion coefficients “y” (0 to 2) by using the following transformation: y = 2 – x/20. Thus, a risk tolerance score of 30 becomes a risk aversion parameter of 0.5 (= 2 –30/20). Explain and discuss your results.

Section 4. On the basis of the single-factor market model CAPM, estimate the beta coefficients for each one of the five stocks you have selected. You are free to use whatever method you prefer in estimating the market model parameters (scatterplot trendline, slope function, or regression). Discuss if the beta values you have estimated are sensible given the nature of the business activities of each firm. Discuss the relationship depicted in a scatterplot between average annualised returns and beta coefficients for the five stocks.

Table: Beta coefficients and returns for the five stocks.

Figure: Scatterplot of expected returns against beta coefficients for the five stocks.

Section 5. Evaluate in absolute and relative terms the investment performance of each one of the five portfolios A, B, C and D that created in Section 2 and the UK market portfolio over the five-year sample period:

(i) Compare your portfolio performances in terms of return, standard deviation, beta, Sharpe ratio, Treynor measure, Jensen’s alpha, information ratio, and M2 measure. All metric components (e.g., average return and standard deviation) should be annualised as appropriate.

(ii) Determine which portfolio is more favourable for a risk-averse and for a risk-tolerant investor, respectively. Which portfolio would you advise your client to invest in? Which portfolio do you consider the worst choice? Justify and explain your recommendations.

(iii) Compare the best and worst portfolios graphically by using wealth indices.

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