• Form a group of 5-7 members. Group members receive the same grade for the project. Working in your group, your specific assignment is to develop complete and well-supported answers to the following questions.

• Prepare a short presentation (limit to 4 slides, 5 minutes) during Session 6 or 7. The slot will be allocated by TA. You can selectively present/discuss some questions (presented by one or some group members). Or, you can present something you find interesting during the exercises, which may not be directly from the questions. The key elements for the project are (1) how to formulate a question; (2) how to solve a question in a reasonable way; (3) how to interpret and think beyond the data and questions presented upon you.

• Each group needs to submit only ONE project report electronically through Canvas (Canvas > FINA5210 > Assignments) on the last lecture day (Session 7) with names and student ID of the participants clearly printed on the front page. Your final report should include: (1) A complete set of numerical, written, and graphical answers to the assigned questions. (2) Data files (e.g., Excel sheets) containing all of your supporting calculations.

Background: Portfolio optimization through mean-variance analysis proposed by Markowitz (1952) has been an important step in the mathematical modeling of portfolio choices. In this project, you will investigate the optimal portfolio choices and factor investing, and examine some

pricing factors in a practical way, using data from US markets. For example, you will explore the impacts of short-selling and transaction costs on investment performances, apply factor investing and build a market neutral strategy.

 Data:

(1) Spreadsheet “PortfoliosFormedBySize”, the monthly returns of 10 portfolios formed by firm size.

(2) Spreadsheet “PortfoliosFormedByBEME”, the monthly returns of 10 portfolios formed by BEME.

(3) Spreadsheet “PortfoliosFormedByProfitability”, the monthly returns of 10 portfolios formed by operating profitability.

(4) Spreadsheet “PortfoliosFormedByInvestment”, the monthly returns of 10 portfolios formed by corporate investment.

(5) Spreadsheet “PortfoliosFormedByMomentum”, the monthly returns of 10 portfolios formed by momentum.

(6) Spreadsheet “FamaFrenchFactors”, the monthly factor returns, including the excess market return (MKT-Rf), the size factor (SMB), the value factor (HML), the investment factor (CMA), the profitability factor (RMW), the momentum factor (Mom), and the risk-free rate (Rf).

Additional instructions: Please watch the videos for step-by-step instructions of performing optimization or running regressions in Excel, if necessary. See the “Excel Shortcut functions for regressions.docx” for some Excel shortcut functions regarding regressions, which can be very handy in some cases. Of course, feel free to use other software like Matlab, Mathematica, R, Python, or Julia if you want.

(3) One concern with the mean-variance analysis is the significant portfolio rebalancing over time which leads to large transaction costs. Factor ETFs usually have low transaction costs. Suppose you pay transaction fees of 0.2% for the total dollar

amount traded. What’s the Sharpe ratio of portfolio Q (which is rebalanced from P), after paying for the transaction costs of rebalancing? Compare it with the case without rebalancing your portfolio (that is, the Sharpe ratio of portfolio P computed in part

(2). In this case, you hold portfolio P into July 2022 which is not a tangent portfolio at

the end of July 2022).

(4) Now, consider a simple factor investing strategy based on the 6 Fama-French factors: using the market factor (MKTRf), the size factor (SMB), the value factor (HML), the profitability factor (RMW), the investment (CMA), and the momentum factor (MOM) to construct the portfolio frontier and the tangent portfolio. Assume that you can’t short sell these factors. Compare the results in Part (1) and (4).

 Part IV: Pricing factors

8. CAPM

One-factor model:

fi,t = αi + βi[rm,t - rf,t] + εi,t,

where f_i,t , r_f,t , and r_m,t are the test asset i’s return, the risk-free rate, and the market portfolio return at time t, respectively.

Run the above regression for each factor (SMB, HML, CMA, RMW, MOM). That is, treat each factor as the test asset. Compute the alpha, beta, and idiosyncratic risk for these factors from the one-factor model, using the whole sample period.

Can CAPM explain these factors? Interpret the results of each regression analysis.

9. Market neutral strategy

Using the 10 BEME-sorted portfolios.

(1) Using a subsample of 196307-202106 to estimate market beta of each portfolio. That is, running the one-factor model as in Question 8.

(2) Now, suppose you want to take advantage of the value effect, i.e., you wish to long the highest BEME portfolio and short the lowest BEME portfolio. Compute the returns of this long-short portfolio (e.g., long $1 in the highest BEME portfolio and short $1 in the lowest BEME portfolio, so the long-short portfolio has zero costs) and estimate its

market beta over a subsample of 196307-202106. What is the average return of this long-short portfolio over a subsample of 202107 - 202207.

(3) The above long-short portfolio in Part (2) might not have a zero market beta over a

subsample of 196307-202106. Suppose you wish to construct a long-short portfolio which has a zero market beta. Describe the positions of such a portfolio (which might not have zero costs), using the highest BEME portfolio and the lowest BEME portfolio.

Compute the average return and market beta of this market neutral portfolio over a subsample of 202107 - 202207. Is its market beta close to 0 over 202107 - 202207? Compare the average returns of long-short portfolios in Parts (2) and (3).