Discipline of Finance
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 specific type 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:
ˆ Value (HML)
ˆ Earnings Quality (RMW)
ˆ Investment Performance (CMA)
ˆ 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 + βHMLHMLt + βRMWRMWt + βCMACMAt
+ βMOMMOMt + ϵi,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. You are to
use all available observations over the stated period to compute the time-series betas for your 25 portfolios.
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 appropriate statistical tests.
1
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:
ˆ Long the 30 stocks that have the highest beta with respect to your allocated factor
ˆ Short the 30 stocks that have the lowest beta with respect to your allocated factor
ˆ Any position (long/short or zero) in the risk-free asset.
2. Build a fully invested portfolio that minimises tracking error variance that contains:
ˆ Long the 30 stocks that have the highest beta with respect to your allocated factor.
ˆ Any position in a market tracking ETF.
ˆ 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:
ˆ Any positions in all 100 of the stocks. No allocation may be larger than 20% in absolute value.
ˆ 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:
ˆ A long or zero position in all 100 of the stocks.
ˆ Any position in a market tracking ETF.
ˆ 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.1 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).
1Note that this doesn’t mean providing specific the specific functions that you have used and in what language (e.g. I used
mmult in Excel ...). You can assume that the analysts knows how to run a regression and perform all statistical tests but they
would need to know what regression to estimate, what data to use etc. Academic articles are good examples of the kind of
detail required.