Assignment #1: Backtesting an Equity Momentum Strategy 1 This assignment is based on data provided in a spreadsheet posted on Moodle. You can complete the assignment in Excel or use a programming language of your choice. When you are ready, fill in your answers in the Moodle quiz Quiz 1. Note: All questions asking for a rate of return or a standard deviation should be answered as a percentage number with precision 2, without the % sign. For example, a return of 1.45% should be expressed as 1.45. Sharpe ratios and average ranks should be expressed with a precision of 2, e.g. 1.12. In this assignment, you backtest and analyze a simple momentum strategy as explained in class. To complete the assignment, use the data in the Excel spreadsheet posted on Moodle. It shows monthly returns for the 10 ETFs from 2012-2021. Assume the risk-free rate to be zero. 1. For each ETF, calculate the arithmetic average monthly return and standard deviation. (1.a) What is the arithmetic average of monthly returns of VNQ? (1.b) What is the standard deviation of monthly returns of VNQ? (1.c) What is the annualized Sharpe ratio of VOX (using arithmetic averages)? 2. Create a pro-forma market portfolio by averaging the returns over all 10 ETFs for each month from 1/2013 to 12/2021 (i.e. disregard the year 2012). (2.a) What is the arithmetic average of monthly returns of this portfolio? (2.b) What is the geometric average of monthly returns of this portfolio? (2.c) What is the annualized geometric average of monthly returns of this portfolio? (2.d) What is the standard deviation of monthly returns of this portfolio? (2.e) What is the annualized Sharpe ratio of this portfolio (using geometric averages)? (2.f) What is the cumulative total return over the lifetime of this portfolio? 3. For each ETF and for each month from 1/2013 to 12/2021, compute the (arithmetic) average return over the preceding 12 months. Then, for each month, rank the ETFs based on their preceding 12-month average returns. (Hint: use the RANK function in Excel). (1 = lowest preceding 12-month return, etc., 10 = highest return) (3.a) What is the average rank of VCR? (3.b) Which ETF has the lowest average rank? (3.c) Which ETF has the highest average rank? 4. Create a long portfolio by selecting each month the three ETFs with the highest preceding 12-month average returns (i.e. the ranks 8-10). Calculate the pro-forma portfolio return for that month as the average of the returns of the three selected ETFs (i.e. assign them equal weights). (4.a) What is the arithmetic average of monthly returns of this portfolio? (4.b) What is the geometric average of monthly returns of this portfolio? Adapted from an exercise provided by Lasse Pedersen to accompany his book 1 Efficiently Inefficient. (4.c) What is the annualized geometric average of monthly returns of this portfolio? (4.d) What is the standard deviation of monthly returns of this portfolio? (4.e) What is the annualized Sharpe ratio of this portfolio (using geometric averages)? (4.f) What is the cumulative total return over the lifetime of this portfolio? 5. Create a short portfolio by selecting each month the three ETFs with the lowest preceding 12-month average returns (i.e. the ranks 1-3). Calculate the pro-forma portfolio return for that month as the average of the returns of the three selected ETFs (i.e. assign them equal weights). (5.a) What is the arithmetic average of monthly returns of this portfolio? (5.b) What is the geometric average of monthly returns of this portfolio? (5.c) What is the annualized geometric average of monthly returns of this portfolio? (5.d) What is the standard deviation of monthly returns of this portfolio? (5.e) What is the annualized Sharpe ratio of this portfolio (using geometric averages)? (5.f) What is the cumulative total return over the lifetime of this portfolio? 6. Create a long/short portfolio by each month buying 1$ of the long portfolio and selling 1$ of the short portfolio. (6.a) What is the arithmetic average of monthly returns of this portfolio? (6.b) What is the standard deviation of monthly returns of this portfolio? 7. Do a linear regression on the monthly returns of the long/short portfolio (y) against the market portfolio (x). (7.a) What is the alpha (intercept)? (7.b) What is the beta (slope)? (7.c) What is R-squared? (7.d) What is the annualized alpha (multiply monthly alpha by 12)? 8. Create a market + l/s portfolio by adding a long/short overlay to the market portfolio, i.e. adding each month the return of the long/short portfolio to the return of the market portfolio. (8.a) What is the arithmetic average of monthly returns of this portfolio? (8.b) What is the geometric average of monthly returns of this portfolio? (8.c) What is the annualized geometric average of monthly returns of this portfolio? (8.d) What is the standard deviation of monthly returns of this portfolio? (8.e) What is the annualized Sharpe ratio of this portfolio (using geometric averages)? (8.f) What is the cumulative total return over the lifetime of this portfolio?