# Discuss in your report diversification referring to the efficient frontier and comparing the expected return and standard deviation of the optimal risky portfolio to the minimum-variance portfolio in your answer. (6 marks)

Assessment 2 aims to provide students with an opportunity to analyse various investment alternatives based on the respective risk and return so as to choose the most appropriate investment opportunity. You are expected to read beyond textbooks and able to apply the knowledge gain from real life examples either from your working environment or/and case studies read, and are able to demonstrate your competence in the areas indicated in the questions. You are encouraged to provide specific in-depth comments instead of general comments.
Instructions to students:
a. Download stock prices for any two different companies – 5 years of monthly closing prices for each company. You can use any database to obtain the prices e.g. datastream, yahoo finance (click the Investing tab followed by the Historical Prices tab) etc. Use data from December 2008 to December 2013 to generate average monthly returns. Calculate the annualised mean return, standard deviation and correlation of the stocks.
(5 marks)
b. Use investment proportions for the two stocks ranging from 0% to 100% using intervals of 5%. Tabulate the investment opportunity set of the two stocks. Plot the investment opportunity set of the two stocks.
(3 marks)
c. Calculate the weights on the optimal risky portfolio consisting of the two stocks, which we denote by stock 1 and stock 2, using the following formulae:
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[E(r)?r]x?2?[E(r)?r]x? ??
w1? 1f22f1212 ,
E(r)?r ]x?2 ?E(r )?r ]x?2 ?[E(r)?r ?E(r )?r ]? ? ? 1 f 2 2 f 1 1 f 2 f1212
w2 ?1?w1.
(3 marks)
d. Calculate the expected return and standard deviation of this optimal risky portfolio. Plot the optimal risky portfolio on the diagram determined in (b) above.
(5 marks)
e. Calculate the weights on the minimum variance portfolio consisting of the two stocks, which we denote by stock 1 and stock 2, using the following formulae:
?w1 ? ?2 ??12?1?2 , ?12 ??2 ?2?12?1?2
w2 ?1?w1.
?f. Calculate the expected return and standard deviation of this minimum variance portfolio (MVP). Plot the minimum variance portfolio on the same graph in (b) above. Identify the MVP and efficient frontier consisting of the portfolios made up of these two assets. Label them clearly on the graph.
(5 marks)
e. Discuss in your report diversification referring to the efficient frontier and comparing the expected return and standard deviation of the optimal risky portfolio to the minimum-variance portfolio in your answer.
(6 marks)