FINC3017

Investments and Portfolio Management

S1-2024

Assignment 2

Due date: 8th May 2024

Background

You and your team are analysts working for a large fund manager. Your clients have expressed interest in investments that can replicate the returns earned for bearing systematic risk.  They are aware of academic research that has developed various risk factors and wish to have access to portfolios that reproduce the returns earned for bearing specific sources of systematic risks.

Your team has hence been tasked with developing an investment methodology to build an exchange traded fund (ETF) that represents exposure to a specifictype of systematic risk through portfolio tracking methods. You are hence asked to determine the feasibility of producing portfolios that mimic systematic risk factors that have been developed in academia. However, your clients wish to ensure their investments are liquid and hence also require you to restrict your attention to the largest 100 stocks in the US. The factor your ETF will need to track is one of:

● Value (HML)

● Earnings Quality (RMW)

● Investment Performance (CMA)

● Momentum (MOM)

and will be emailed to the group.  You will not investigate the size factor due to the restricted investment universe.

Data Analysis

Estimating and Testing Risk Premiums

Before you outline your investment philosophy, you will first investigate the risk premia associated with systematic risk factors.  For this, you are to perform a Fama-MacBeth regression using the 25 Portfolios Formed on Size and Book-to-Market as your test assets (the dependent variable in the regression) and the Fama-French five-factor model + momentum as the explanatory variables. The time-series model you are to estimate is:

Ri,t  = αi + βMKTRM,t + βSMBSMBt + βHM L HMLt + βRM WRMWt + βCMA CMAt

+ βMOM MOMt + ∈i,t                                                                       (1)

You are to use monthly return data ranging from (in YYYYMM format) 198001 to 202312.  Your factors should cover the same period. This data can all be sourced from the Ken French Data Library. To account for time variation in factor betas, you are to use a rolling regression that uses 5 years (60 months) of data to compute betas.  For example, to compute the regression coefficients on 198412, you would use the 60 data points from 198001-198412. Using the factor betas obtained from the time-series regression, conduct a Fama-MacBeth test to see which, if any, factors carry a risk premium. Ensure that you conduct all appro- priate statistical tests.

ETF Construction

You are examine some approaches to factor tracking that form. form. the basis of your ETF. For this purpose you have been provided with daily return data on the 100 largest stocks in the US from (in YYYYMMDD format) 20190102 to 20231229. You have also been provided the returns on the S&P 500 index which will serve as a proxy for a market tracking ETF available for investment. You are to use the data from 2019-2022 to compute all required statistical estimates and build the ETF and the remaining data in 2023 will be used to examine the performance of your ETF. You will explore several methods for constructing your ETF. Specifically:

1. Build a fully invested portfolio that minimises tracking error variance that contains:

● Long the 30 stocks that have the highest beta with respect to your allocated factor

● Short the 30 stocks that have the lowest beta with respect to your allocated factor

● Any position (long/short or zero) in the risk-free asset.

2. Build a fully invested portfolio that minimises tracking error variance that contains:

● Long the 30 stocks that have the highest beta with respect to your allocated factor.

● Any position in a market tracking ETF.

● Any position in the risk-free asset.

3. Build a fully invested portfolio that minimises the tracking error variance between your portfolio and your allocated factor that contains:

● Any positions in all 100 of the stocks. No allocation may be larger than 20% in absolute value.

● Any position in the risk-free asset.

4. Build a fully invested portfolio that minimises the tracking error variance between your portfolio and your allocated factor that contains:

● A long or zero position in all 100 of the stocks.

● Any position in a market tracking ETF.

● Any position in the risk-free asset.

Following the construction of your portfolios, you are to compute their returns over 2023 assuming that you construct your portfolio at the beginning of the first trading day in January and you rebalance the portfolio back to target weights at the beginning of April, July and October.

Client Report

You are to write a report for your client that outlines the analysis you have done and provides a recommen- dation on the feasibility of tracking their desired risk factor with the portfolios you have studied. You report should be clear, concise and professional in presentation. It should include an executive summary, an analysis of your investigation into risk premia, including your results and the associated background literature, and the analysis of the four tracking portfolios and their ability to replicate your allocated factor.  You should also include a brief discussion of any potentially competing products in the market and a recommendation of which, if any, of your methods is well suited to provide the ETF construction methodology. Your report should be sufficiently detailed that another financial analyst could replicate it. You are advised to examine the academic literature for examples of how to write such a report.  Results should be presented in tables and figures where appropriate and these should be captioned and referenced in the text. Your report should be between 5 and 6 pages in total, including references, tables and figures.  Appendices may be included but will not be looked at closely. Text should be single spaced and no smaller than 11 point font. Margins should be standard (1 inch).