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Theory and the Efficient Frontier

Question 1: Portfolio Theory and the Efficient Frontier
You work with a group of people in a fund management company. The company
provides portfolio management services to clients all over the world, who are looking
to maximise their wealth. You’ve been allocated a client who is looking for a 5-year
investment in any equity market and would like exposure to a diversified portfolio,
invested in 20 stocks across five sectors.
a) Following a meeting with your colleagues, decide on which market (which
country) you believe you should invest the money for the next five years. State at
least three reasons why you picked a specific market and elaborate each of them
clearly.
b) Now that you’ve decided in which market you wish to invest, you need to select
five sectors and choose four stocks in each sector. Your goal will be to create a
diversified portfolio. State at least three reasons why you picked these sectors
and explain in detail how you selected the stocks.
c) Download 10 years of historical daily data for your selected stocks; you should
also obtain a proxy for the risk-free rate. Justify your choice of the risk-free asset.
Form and plot the efficient frontier and find the “market portfolio” assuming that
no short-selling is allowed.
d) Do you believe that the composition of the “market portfolio” that you have found
is a desirable or practical one as an investment for your client? Explain why or
why not, and what can you do to resolve such issues.
e) Obtain the minimum variance portfolio. Present and explain in words the
compositions of the market portfolio and the minimum variance portfolio, and
contrast them.
f) Repeat steps c), d) and e) above allowing for short selling. [Note: do not select
new stocks to short-sell, use your existing stocks from b)]. Discuss any changes in
your portfolio and what do these imply about your original choice of stocks.
g) Form an equally weighted portfolio of the stocks and a market-capitalisation
weighted portfolio using the sample period, and compare the risk-adjusted
performance of the four portfolios (the market portfolio, the minimum variance
portfolio, the equally weighted portfolio and the market-capitalisation weighted
portfolio). Discuss your findings.
Question 2: Testing the CAPM
a) Obtain 10 years of monthly data for the 20 stocks of Question 1 and a proxy for
the risk-free rate. Implement the Fama-MacBeth 2-step procedure to test whether
the CAPM works. What is your conclusion concerning whether the CAPM is
supported in this case? Explain your answer.
b) Discuss whether your results tie in with those found in empirical studies in the
literature. If you reach different conclusions, can you explain why this might be?
Note that, in order to provide a good response to this question, it will be necessary
to read and briefly summarise some of the literature that tests the CAPM.