Case #2

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New York University *

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3605

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Finance

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Jan 9, 2024

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1 FINC-UB 44 P ORTFOLIO M ANAGEMENT Case #2: ProShares Hedge Fund Replication ETF The assignment consists of two sets of questions: (1) quantitative, Excel-based questions, which should be completed and submitted, and (2) more qualitative questions, which will form the basis for part of our in-class discussion, answers to which you do NOT need to turn in. The spreadsheet is due by the beginning of class (2:00pm). You may collaborate with your classmates in preparing the solutions to both sets of questions, but each student must hand in a separate assignment, and all students are responsible for participating in the discussion. Assignments should be submitted through Brightspace. Assignments that are late but within 24 hours of the deadline, will receive ½ credit. After 24 hours no assignments will be accepted (unless due to documented serious illness or family emergency)! For the quantitative questions, download the Excel spreadsheet “Case #2” from Brightspace. Please put your name and net ID in the blue boxes at the top of the worksheet. This spreadsheet contains monthly returns on the 4 global Fama-French-Carhart factors, and the excess returns on two US fixed income factors (level and slope), the HFR Fund of Funds Composite Index and 2 hedge fund replication ETFs (HDG and QAI, created by ProShares and IndexIQ, respectively). Note that some of the returns do not span the full sample. The worksheet also contains a template for entering your solutions. The cells where results need to be added are highlighted in yellow. Because your solutions will be computer-graded it is very important to follow the instructions: • Please do NOT reformat the file or move the yellow cells. Do NOT add rows or columns to the worksheet. However, you can add additional calculations in non-highlighted cells if you wish. Everything in non-highlighted cells will be ignored for grading purposes. You can either enter the formula to calculate your answer in the yellow cells, or enter these formulas elsewhere and just put references to these answers in the yellow cells. • Please do NOT round your answers or intermediate calculations. Excel will display rounded answers based on the formatting of the cells, but it will retain the unrounded numbers. • Please do NOT add a new worksheet to the file. Do all of your calculations in the “Results” worksheet and submit a file with only a single worksheet. 1. Over the full sample, calculate the annualized mean, standard deviation, and Sharpe ratio plus the skewness and excess kurtosis of the monthly returns on the 4 FFC factors, and the monthly excess returns on the HFR index, and the pairwise correlations between the hedge fund index and these monthly returns. (Do not attempt to annualize skewness or kurtosis.) 2. Over three sample periods—(1) the full sample, (2) Jan. 1991 to Dec. 2010, and (3) Jan. 2011 through the end of the sample—run regressions of the monthly hedge fund index returns on the 4 Fama-French-Carhart factors. Report the annualized intercept (alpha), the associated annualized standard error, the t-statistic, the slope coefficients on the independent variables, the associated standard errors, the t-statistics, and the regression R 2 s. Use the regression package within Analysis ToolPak, putting the output somewhere else in the Results worksheet and formulas that reference the results in the relevant cells.

2 3. Over the period from Aug. 2011 to the end of the sample, calculate the annualized mean, standard deviation, and Sharpe ratio plus the skewness and excess kurtosis of the monthly returns on the 4 FFC factors, the excess returns on the HFR index, the two fixed income factors, and the 2 ETFs (HDG and QAI), and the pairwise correlations between the hedge fund-related returns and these monthly returns. (Do not attempt to annualize skewness or kurtosis.) 4. Over the period Aug. 2011 to the end of the sample, run regressions of the monthly hedge fund index and the 2 ETF excess returns on the 4 Fama-French-Carhart factors and the two fixed income factors. Report the annualized intercept (alpha), the associated annualized standard error, the t-statistics, the slope coefficients on the independent variables, the associated standard errors, the t-statistics, and the regression R 2 s. Use the regression package within Analysis ToolPak, putting the output somewhere else in the Results worksheet and formulas that reference the results in the relevant cells. 5. Finally, over the period Aug. 2011 to the end of the sample, run regressions of the 2 monthly ETF excess returns on the excess return on the hedge fund index. Report the annualized intercept (alpha), the associated annualized standard error, the t-statistics, the slope coefficient on the independent variable, the associated standard errors, the t-statistics, and the regression R 2 s. Use the regression package within Analysis ToolPak, putting the output somewhere else in the Results worksheet and formulas that reference the results in the relevant cells. For class discussion only! (Consider material in the case, including the video available at http://youtu.be/XEUa45fjOD4 , material in the lecture notes, and the HDG fact sheet https://www.proshares.com/globalassets/proshares/fact-sheet/prosharesfactsheethdg.pdf and the QAI fact sheet https://www.newyorklifeinvestments.com/assets/documents/index-iq/qai-iq- hedge-multi-strategy-tracker-etf-fs.pdf ) 6. What is the theoretical/conceptual case for investing in hedge funds? Based on the evidence from questions 1 & 2 above, is this case consistent with the data? What are the average returns, volatilities, Sharpe ratios, correlations, betas and alphas of hedge fund returns over this sample and over the shorter sample that ends in 2010? Are hedge funds market neutral? Are global factors the relevant benchmarks (as opposed to US factors)? What are the potential barriers or problems associated with hedge fund investing? 7. What is hedge fund replication? Why might it work at the index level but not at the individual fund level? Does a factor-based (regression-based) replication of hedge fund returns make sense? Under what circumstances? 8. Who are the natural customers for a hedge fund replication ETF? Why? 9. Are HDG and QAI achieving their stated goals? Based on the results from questions 3, 4 and 5, do their returns (average returns, volatilities, Sharpe ratios, alphas, betas, etc.) resemble those of the fund of funds indexes? Is the fund of funds index the right benchmark? Does this more recent data change your perception of the value of hedge fund replication? How have

3 hedge funds performed in this later sample period? Again, are the global factors the relevant benchmarks? 10. What are the differences between the methodologies underlying HDG and QAI? Do these differences explain the differing performance? Look at the fact sheets. What are the holdings of HDG and QAI? 11. Has this segment of the market gained traction? What are the AUMs of HDG and QAI? 12. Is there a future for these types of products? Do you view these products differently from the QuantShares products we examined in Case #1? If so, why?

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