Your assignment should be prepared, typewritten, of between 2,500 and 3,000 words, divided into sections (say five or six, but you should judge this) including an introduction, a description of relevant models, a critical examination of the theories, the answering part, conclusion and a full bibliography. Make sure that you follow normal citation conventions in preparing your coursework, by citing the ideas or data of others at the point in your coursework where this is included, and set out the full reference of this citation in your bibliography. Any evidence that students have colluded or copied work between groups, or used the work of another source without reference will be investigated and may result in failure.

Your assignment should follow the requirements set out below.

1. Write your results as a typed report with an appropriate title page and section headings. Put trivia (which you think is necessary to be included in the report) in footnotes for the sake of smooth reading. Avoid using appendix.

2. You must provide an introduction to your report. This should introduce the subject, give background information and refer to relevant concepts.

3. You should give a brief description of the models. You should use graph and mathematical equation to help explain the theories. You can choose in the Microsoft Word menu the button ‘insert’, ‘object’, then ‘Microsoft Equation 3.0’ to help you edit equations, if necessary.

5. You must display appropriate procedures with explanations showing how you solve questions before answers are given. The solving process, again, should be helped with numbers, formulas or tables.

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6. Any tables, charts or graphs that you produce must be clearly numbered and labelled. Every table and figure should be fully explained saying what it shows and how this relates to the issues you are examining. They should also be put in the body (not in the appendix) and as closely as possible to the associate explanations.

7. References to sources must be provided in the text of the report and all sources should be fully identified in a bibliography at the end of the report.

8. The recommended word count (excluding tables and figures) is 2500 words for the whole report. You must provide a word count at the end of the report.

9. You should attach the group agreement (see Appendix 1) to your assignment. Any dispute or argument within your group reported to the lecture will be judged, and grade of the individual will be adjusted accordingly.

References

You must provide a list of works that are cited in your coursework at the end, with references presented in the following format:

Brealey, R.A., Stewart S.C. and Allen F. (2008) Principles of corporate finance. 9th editioin. McGraw Hill, New York.

Fama, E. and MacBeth, J. (1973) Risk, Return and Equilibrium: Empirical tests. Journal of Political Economy, 71, 607-36.

Sharpe, W.F. (1964) Capital Asset Prices: a theory of market equilibrium under conditions of risk. Journal of Finance, 19, 425-42.

Appendix 2

Case study: John and Marsha on a Portfolio Selection

John and Marsha hold hands in a cozy French restaurant in downtown Manhattan. Marsha is a futures-market trader. John manages a $125 million common-stock portfolio for a large pension fund. They have just ordered tournedos financiere for the main course and flan financiere for dessert. John reads the financial pages of The Wall Street Journal by candlelight.

John: Wow! Potato futures hit their daily limit. Let¡¦s add an order of gratin Dauphinoise. Did you manage to hedge the forward interest rate on that euro loan?

Marsha: John, please fold up that paper. (He does so reluctantly.) John, I love you. Will you marry me?

John: Oh, Marsha, I love you too, but¡Kthere¡¦s something you must know about me ¡V something I¡¦ve never told anyone.

Marsha(concerned): John, what is it?

John: I think I am a closet indexer.

Marsha: What? Why?

John: My portfolio returns always seem to track the S&P 500 market index. Sometimes I do a little better, occasionally a little worse. But the correlation between my returns and the market returns is over 90%.

Marsha: What¡¦s wrong with that? Your client wants a diversified portfolio of large-cap stocks. Of course your portfolio will follow the market.

John: Why doesn¡¦t my client just buy an index fund? Why are they paying me? Am I really adding value by active management? I try, but I guess I¡¦m just an¡Kindexer.

Marsha: Oh, John, I know you¡¦re adding value. You were a star security analyst.

John: It¡¦s not easy to find stocks that are truly over- or undervalued. I have firm opinions about a few, of course.

Marsha: You were explaining why Pioneer Gypsum is a good buy.

John: Right, Pioneer. (Pulls handwritten notes form his coat pocket.) Stock price $87.50. I estimate the expected return as 10% with an annual standard deviation of 30%.

John: Yes, I¡¦m using a market risk premium of 7% and the risk-free interest rate is about 5%. That gives 12%. But Pioneer¡¦s beta is only 0.3. I was going to buy 30,000 shares this morning, but I lost my nerve. I¡¦ve got to stay diversified.

Marsha: Have you tried modern portfolio theory?

John: MPT? Not practical. Looks great in textbooks, where they show efficient frontiers with 5 or 10 stocks. But I choose from hundreds, maybe thousands, of stocks. Where do I get the inputs for 1,000 stocks? That¡¦s a million variances and covariances!

Marsha: Actually only about 500,000, dear. The covariances above the diagonal are the same as the covariances below. But you¡¦re right, most of the estimates would be out-of-date or just rubbish.

John: To say nothing about the expected returns. Rubbish in, rubbish out.

Marsha: But John, you don¡¦t need to solve for 1,000 portfolio weights. You only need a handful. Here¡¦s the trick: Take you benchmark, the S&P 500, as

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security 1. That¡¦s what you would end up with as an indexer. Then consider a few securities you really know something about. Pioneer could be security 2, for example. And so on. Then you could put your wonderful financial mind to work.

John: I get it: active management means selling off some of the benchmark portfolio and investing the proceeds in specific stocks like Pioneer. But how do I decide whether Pioneer really improves the portfolio? Even if it does, how much should I buy?

Marsha: Just maximise the Sharpe ratio, dear.

John: I¡¦ve got it. The answer is yes!

Marsha: What¡¦s the question?

John: You asked me to marry you. The answer is yes. Where should we go on our honeymoon?

Marsha: How about Australia? I¡¦d love to visit the Melbourne Stock Exchange.

QUESTION

„h Table 1 reproduces John¡¦s notes on Pioneer Gypsum. Calculate the expected return, risk premium, and standard deviation of a portfolio invested partly in the market and partly in Pioneer. (You can calculate the necessary inputs from the betas and standard deviations given in the table.) Does adding Pioneer to the market benchmark improve the Sharpe ratio? How much should John invest in Pioneer and how much in the market? (John neglected to mention the standard deviation of the S&P 500. We will assume 12%. )

1. Using the CAPM to decide whether John should buy or sell Pioneer¡¦s.

2. Given the formulae of Beta, calculate the covariance. Given the formulae of covariance, calculate the correlation.

3. Construct the covariance matrix.

4. Calculate the portfolio return, portfolio standard deviation and the Sharpe ratio for different fractions invested in the market and Pioneer. Start the calculation by supposing the market gets 99% and Pioneer 1%.

5. Repeat the procedure 4 by decreasing the weight of market to 98% and hence increasing the weight of Pioneer¡¦s to 2%. Then try 97% and 3%, ¡K etc.

6. Construct a table showing the relationship between the weights of market and Pioneer, the portfolio return and the portfolio risk, and the Sharpe ratio.

7. From the table, you will find that the Sharpe ratio will increase and then decrease as the weight of market decreases. The highest Sharpe ratio will determine for John how to allocate his fund between the market and Pioneer.

(The calculations can be done by using Excel, which greatly reduce the workload)

Expected return

10.0%

Standard deviation

30%

Beta

0.3

Stock price

$87.50

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