FR2209 Coursework instructions: 2023/24
Below are the instructions for the coursework.
Output: create a 10-page report, containing the tables, statistics, plots and explanations requested below.
NOTE: doing the coursework exercises in Python and submitting your code is worth 15% of your group mark. You can use any other software you like, but you will lose this 15% mark.
Deadline: noon, London time, on Friday 12th April 2024.
You will need to use the data contained in this file: FR2209_assessment_data.xlsx.The data you have been given is monthly and contains (adjusted) USD prices of 1000 major global stocks listed in developed countries for the last 10 years. Where required, assume that the risk-free rate is 0.1% per month.
Perform. the following statistical tasks:
1) Select, at random, 6 (NOT more or less) individual stocks from the set you have been given. Briefly describe the industries these companies operate in.
NOTE: groups should clearly state their selected 6 stocks by their ticker/identifier as in column 1 of FR2209_assessment_data (NOT company names) on the frontpage of their report. Note also that you probably don’t want to choose any stock with a negative mean return over the 10-year period.
2) Create monthly returns for each stock and compute and tabulate mean returns, return standard deviations and a Sharpe ratio for each stock. Comment on these numbers, comparing them across stocks.
3) Create and tabulate the covariance matrix of returns for your stocks. Comment on the sign and size of the covariances. [Before commenting on the size of the covariances, one might want to convert them into correlations.]
Now perform. the following portfolio selection exercise:
4) Create (in Python, Excel or other statistical packages) a set of long only portfolio weight vectors, where the weight on each stock ranges between 0 and 1.00, where weights always sum to 1.0 and where weights cover, in a systematic fashion, all possible and permissible weight combinations. [For example, you might choose to consider portfolios where weights are multiplies of 0.10 e.g., the vector (0.1, 0.6, 0.0, 0.3).] Describe how you have done this step in your report.
5) For each portfolio, compute the expected portfolio return, the standard deviation of the portfolio returns and the portfolio’s Sharpe ratio, under the assumptions that the historical mean returns and return covariance matrix adequately represent what one might expect in the future. Plot the expected return and standard deviation combinations on a graph to show the feasible set of portfolios. Describe the features of the plot and relate to the statistics on the individual stock returns.
6) From your set of portfolios, recommend a portfolio containing only stock to each of the following investors. In each case describe the portfolio weights and the resulting portfolio return statistics and give some intuition as to why the weights take the values that they do. Also mark the location of the portfolio on the plot you created above.
o An investor who simply wants to minimise risk. Call her portfolio M.
o An investor who wants to maximise Sharpe ratio. Call her portfolio S.
7) A third investor wants to hit an expected return target of 1% per month. Tell her how to optimally select a stock portfolio (from the set you constructed earlier) and how to mix that portfolio with the risk-free asset so as to hit the return target. Show her that this strategy is superior to a strategy where she only holds stock.
8) Using the matrix results in the lecture materials, derive and present the equation that generates the weights of the portfolios on the portfolio frontier. Superimpose a plot of the frontier on the picture that you created in your answer to question (5).
9) Perform. the following performance measurement tasks.
a. Consider the portfolio from (6) that maximises the Sharpe ratio. Compute the returns on this portfolio in each month of the sample. Plot them and describe the statistical features of the return series.
b. A data spreadsheet (i.e., FR2209_assessment_data_factors.xlsx) has been uploaded to Moodle that contains monthly percentage point returns for a set of five international risk factors for developed markets for our sample period. These are the excess return on the market (XSMKT),asize factor (SMB), avalue factor (HML), profitability (RMW) and an investment factor (CMA). Plot the returns on the factors and describe any interesting features.
c. Run a multivariate regression of your portfolio returns (from part (a)) on the factor returns (from part (b)). Present the results, interpret them statistically and then describe the implications of the regression for the risks that an investor in this portfolio faces.
Excel hints
The following functions might be useful in computing basic statistics plus portfolio risk and return if you want to do it in a reasonably efficient fashion in Excel :
• AVERAGE
• STDEV.S
• COVARIANCE.S
• TRANSPOSE
• MMULT
Doing regression in Excel is fairly straightforward. There are many resources available on the web to describe how to run a multivariate regression in Excel.