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IC212 Financial Modelling 2022-23 Project

Portfolio Optimisation/Capital Asset Pricing Model

Data:

I have uploaded the dataset on Blackboard under Assessment where you can access the monthly prices for 30 UK stocks over a sample period of 10 years (December 2007 – December 2017) for each of those 30 stocks. Additionally, you have also been provided with a proxy for the risk-free rate, a proxy for the market return and the market capitalisations for each of the 30 stocks.

Task Description:

1. Allowing for short-selling, form and plot the Mean-Variance Frontier. Plot the 30 stocks on the same graph. Use the sample variance-covariance matrix. Explain your findings.

2. Find the minimum variance portfolio and the market portfolio (tangency portfolio). Plot the Capital Market Line. Present and explain in words the compositions of the minimum variance portfolio and the market portfolio.

3. Do you believe that the composition of the market portfolio that you have found is a desirable or practical one as an investment? Explain why or why not, based on the positions of each of your stocks.

4. Repeat Tasks 1 to 3 above, with short selling not allowed. Are your new conclusions similar to your previous ones? Justify your answers.

5. Assuming that short selling is not allowed and using the first half of the data only (in-sample data), re-estimate the market portfolio and the minimum variance portfolio. Use the second half of the data (out-of-sample data) to determine whether the market portfolio or the minimum variance portfolio performs better on a risk-adjusted basis (using the Sharpe ratio). Discuss your results.

6. Repeat Task 5 (above) with an equally weighted portfolio and a market capitalisation weighted portfolio of the 30 stocks. Compare the risk-adjusted performance of the four portfolios using the Sharpe ratio. Discuss your results. How do your findings regarding the relative performance of these four approaches differ from what you might have expected, and compared with what other studies have found in the empirical literature?

7. Test the CAPM based on the set of companies using the 1^st pass testing and 2^nd pass testing procedures, inspired by Black, Jensen and Scholes.

8. Based on your findings from Task 7 (above), do your results support the CAPM? How do your results compare with earlier findings? Describe the relevant literature and compare/contrast with your results. In your opinion, is the CAPM still relevant for investment purposes?