Reference no: EM133662930

Homework: Financial Risk Analysis

Portfolio Choice and Performance Attribution

I. Familiarize yourself with the content of the data library on Professor Kenneth French's webpage by reading the online legends and help.

II. Then, select data from January 1963 to December 2023 on the 17 industry portfolios (value-weighted) and carry out the following analysis:

1. Sketch the monthly MV efficient frontier of these portfolios using first the sample estimates of the required means and variance-covariance matrix.

2. On the frontiers you constructed, highlight the points corresponding to the global minimum variance portfolio and to the tangency portfolio, assuming a risk-free rate equal to its average over the sample period. For these portfolios, also compute and report the mean excess-return, volatility and Sharpe ratio.

3. Compare and contrast the frontiers you constructed. How would you explain their differences?

III. Next, choose one stock from each of the 17 industries and repeat the analysis above. Compare and contrast the two pairs of MV efficient frontiers you constructed. How would you explain their differences?

IV. Select data for the appropriate sample period on the risk-free rate (included among the so- called "Fama and French factors", and available for download from the same data library) and sketch the monthly MV efficient frontier for the 17 industry portfolios and the risk- free asset, using sample estimates of the required means and variance-covariance matrix. Compare and contrast this frontier to the ones previously constructed, after having explained the sample period for which you obtained data on the risk-free rate.

V. Repeat the analysis required in the item just above (i.e., in question 4) using the Fama and French factor-mimicking portfolios, also available from the webpage of Prof Kenneth French, in place of the industry portfolios. Do so first using the so called "Fama/French 3 Factors" and then the "Fama/French 5 Factors (2x3)" mimicking portfolios (See Fama and French, 1993, "Common Risk Factors in the Returns on Stocks and Bonds," Journal of Financial Economics, and Fama and French, 2014, "A Five-Factor Asset Pricing Model" for a complete description of the factor returns). Compare the resulting efficient frontiers to the ones previously obtained. How would you explain their differences?

VI. Repeat the above analysis (as specified in the item just above, namely question 5) using suitable "practical proxies" for the Fama and French factor-mimicking portfolios in place of the Fama and French factor-mimicking portfolios themselves. These practical proxies should be highly investable, keeping transaction and execution costs in mind. That is, they should be investable by the average portfolio manager, not necessarily the highly sophisticated portfolio manager capable of replicating the actual factor-mimicking portfolios. You may look for such proxy portfolios by checking out the websites of the main futures exchanges (e.g., look for futures on small caps, such as the Russell 2000 Index mini futures, and value/growth stocks) or even look for suitably focused ETFs (exchange traded funds).1 In particular, try and find ways to work around the difficulty of short-selling or minimize the associated costs.

Do so at least for "practical proxies" for the "Fama/French 3 Factors" and, ideally, also for the "Fama/French 5 Factors (2x3)" mimicking portfolios, for as long a sample period for which you can find data, making sure that the last observation is for December 2019 or later (i.e., do not work with ‘dead' series). To work around the lack of long time series on suitable "practical proxies" (e.g., the Russell 2000 Index mini futures), you may use the time series on a closely correlated asset or portfolio (e.g., the stock index underlying the Russell 2000 Index mini futures, available since 1978), possibly after showing some evidence on the strength of the correlation.

Compare and contrast the resulting efficient frontiers for the "practical proxies" to the ones for the corresponding factor mimicking portfolios (make sure both frontiers are estimated using the same sample period), explaining and/or commenting as appropriate.

VII. Re-estimate the monthly frontiers for the 17 industry portfolios and for the "Fama/French 5 Factors (2x3)" mimicking portfolios over two contiguous time periods of equal length, one ending in December 1993 and the other one ending in December 2023, including the risk-free asset in the investment opportunity set. Pick at least one portfolio from each of the frontiers estimated in the first period and, for the portfolios thus selected, compare the performance during this period to the performance during the second period. Do these portfolios remain on the efficient frontier out-of-sample?

VIII. Then, for at least some of the assets previously considered, repeat the above analysis subject to any constraint and/or by applying any method, approach or technique (e.g., adding assets to better exploit the benefits of diversification, relying on the global minimum variance portfolio, resampling, etc.) that you believe might be of interest and might offer valuable insight from an investment management point of view.

IX. Use the market portfolio, the practical proxies and the tangency portfolios (as appropriate) on the various efficient frontiers you constructed above to assess the performance of three mutual funds of your choice, commenting on the results. A good source of data on mutual funds is Yahoo Finance. See the Appendix for help on how to access data on Yahoo Finance.