You endorse the role of a portfolio manager. You have a client who is an individual investor with preferences characterised by a simple mean and variance utility function. This 25-year-old individual lives in the US and has a steady annual income. Your client wishes to invest in a portfolio of assets to provide funds for retirement. The investor has no dependents. Your role is to find the optimal risky portfolio and the optimal complete portfolio using portfolio optimisation, while assuming different levels of risk aversion for this individual. The investor is considering an investment in either a) a group of individual stocks listed on the New York Stock Exchange (NYSE), b) a group of US portfolio funds or c) country portfolios. You will also need to discover portfolio weights in different scenarios using expected returns based on historical means and expected returns from different asset pricing models. This is unconstrained optimisation where short selling is allowed, and borrowing can take place at the risk free rate.
You will be provided with a data set which consists of observations from January 2008 to December 2017 (information on the sources for the data will be provided in your data set). These are:
- Monthly returns for six stocks listed on the New York Stock Exchange (NYSE). These are high volume stocks from different sectors listed on the NYSE quoted in US dollars.
- Monthly returns for six country portfolios. These track the results of an investment composed of the individual countries equities and quoted in US dollars.
- Monthly returns for six US portfolio funds that characterise different styles.
- Monthly interest rates on the 4-week Treasury Bill.
- Expected returns for the static capital asset pricing model, the Fama-French 3 factor model, and a macro 3 factor model.
You need to replace the data in the Excel file you constructed from the sample Excel sheet provided by Craig Holden available from excelmodeling.com.
On page 7.2 of the Excel sheet, you should be able to observe the mean returns from the historical data, the standard deviations, correlations and the covariances. Undertake the following:
- Using the historical mean as the expected return, use the portfolio optimisation procedure in the Excel sheet to determine the portfolio weights of the optimal risky portfolio and the optimal complete portfolio. Select your own estimate of risk aversion for the individual stating what would happen if risk aversion changes (either up or down) from your own initial estimate. (You are given the chance to select a level of risk aversion, in part, to ensure you have flexibility over the diagram demonstrating the optimal complete portfolio and optimal risky portfolio.)
- Imagine you are doing security analysis on some of the stocks, what happens when you change the expected return? Select a security (or securities) of your choice and analyse the results.
- Compare the portfolio weights for both the optimal risky portfolio and the optimal complete portfolio using the portfolio optimisation procedure in the Excel sheet for the three methods to forecast expected returns, a), historical, b) static CAPM, and c) Fama-French 3 factor. Offer an interpretation of your findings.
When your analysis is complete write up your results as if you were presenting them to your client. Use graphs and tables. (You do not need to present all the results. Just select the ones that seem the most important to you and justify the reasons why you have chosen those particular results.) Make clear the weaknesses and strengths (referring to academic and professional papers where appropriate) of your analysis and recommend a course of action for your client.
Key Specifications and Requirements
You may refer to any of the materials and tools introduced on the course but must include:
- Presentation of data in a clear and precise manner
- Your work should be set out as an essay; including an abstract and a well structured conclusion.
- Label any diagrams used (eg. Figure One), give the diagram a title and credit the source.
- You should make use of graphs and charts to support your analysis.
- Use Harvard referencing appropriately and accurately.
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