FINC3023 Behavioural Finance
Assignment, 2023 (Semester 1)
In this assignment you are tasked with investigating the value of trading based on a ‘factor’ or
‘anomaly.’ As an investment analyst, you are tasked with assessing the trading potential of a
strategy. You will then be asked to critically evaluate the potential of the trading strategy for
investment purposes.
Ken French’s website contains data on a number of different portfolios, where portfolios are formed
on the basis of proposed mispricing factors. The data has conveniently been arranged for you, with
portfolios formed into quintiles or deciles.
https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
In this assignment, the aim is to determine how these portfolio formation factors have returned over
time, and understand the rationale behind why these factors might work as investment strategies.
Consider the audience of your report to be potential clients of your investment fund. They are
interested in knowing whether a strategy would be feasible or not.
Task.
Choose one of the factors beneath the following headings.
Sorts involving Accruals, Market Beta, Net Share Issues, Daily
Variance, and Daily Residual Variance
1. [6 marks]
Explanation of the theory of the trading strategy.
a. What is the logic behind the portfolio formation strategy? Present some academic /
practitioner evidence towards the performance of the strategy. (Note: if the strategy had
not been proposed elsewhere it is unlikely to appear on the site).
b. Does there appear to be some ‘behavioural’ driver of this portfolio formation strategy? Or
is the strategy purely framed as a risk-based pricing factor?
2. [6 marks]
Univariate portfolio performance evaluation.
Using monthly value-weighted returns, examine the portfolio performance across deciles.
a. What is the average return to each of the deciles? Present a graph of the
performance of the top and bottom deiciles on the same set of axes over the period
196307 (or whenever the first month of available data appears) until 202302.
b. What is the standard deviation of performance across the deciles? Do the observed
return differences seem to be reflected in differences in standard deviation?
c. Construct a portfolio that “goes long” in the higher performing of decile 1 / decile 10
and short in the other portfolio (based on average returns). Examine some of the
characteristics of the portfolio’s returns.
i. Is the portfolio performance positive and significant? Perform an
appropriate statistical test?
ii. Is the distribution of portfolio returns normally distributed (or
approximately normally distributed)? Use a histogram and/or test of
normality (e.g. Jarque-Bera) to demonstrate.
iii. What proportion of the returns are positive / negative? What is the average
return conditional on the return being positive / negative? Is there any
indication of downside (skewness) risk?
iv. How does the performance of the portfolio compare over two periods: From
the start of the data until Dec. 1992, vs. January 1993 until the most recent
data point (Feb 2023)? Does the performance of the strategy appear to have
been reduced over time?
v. Are there any seasonalities? For example, are the returns to the portfolio
higher in a specific calendar month (e.g. January) than other months?
3. [6 marks]
Combine your portfolio with data on the factors from Ken French’s website (Use data under the
heading Fama/French 3 Factors). Link up the monthly factors (plus risk-free rate) from 196307
(or the first month of your data) until the most recent month (Feb 2023)
a. Make sure that the Analysis Toolpak is added to Excel. You should see it under the
‘Data’ Tab at the far-right (with Solver if you aren’t sure of its location). If it is not
there, please add it in, using File -> Options -> Add-ins -> Analysis Toolpak. Note – if
you don’t see it, and it is enabled, disable Analysis Toolpak and then re-enable it.
b. Construct the ‘excess’ returns to your long-short anomaly strategy (i.e. strategy
return less the risk-free rate)
c. Build a one factor (CAPM) model to explain your anomaly’s returns. Is the anomaly
return (alpha) significant after controlling for risk in this model? What stocks appear
to be riskier by CAPM-beta, if beta is significant (i.e., does the long or short
component of the portfolio appears riskier).
d. Now, build a Fama-French three-factor model to explain your anomaly portfolio’s
returns. Compared with the results from part 3c, does the model’s explanatory
power increase substantially (use an appropriate R2 measure to explain)? What
factors are significant (if any) in explaining the anomaly portfolio’s returns? Based on
the result of this regression, does it appear that the anomaly can be reasonably
explained by ‘risk.’
e. Take the next row of data below your original portfolio. For instance, if you selected
“Portfolios Formed on Accruals,” select “25 Portfolios Formed on Size and Accruals.”
Now, use this data to explore further the interaction between size and your anomaly
portfolio’s return. Does taking a portfolio that is long “Small stocks with positive
anomaly characteristic” (e.g. small stocks with low accruals) and short “Big stocks
with negative anomaly characteristic” appear to provide superior performance?
What about the other ‘extreme corner’ of the portfolio (small stocks with high
accruals vs big stocks with low accruals)?
4. [12 marks]
Finding a useful time-series predictor / market state variable.
Next, find one (or more) time-series variables that could be useful for forecasting the
portfolio returns (going back to the original 10 portfolios sorted on the anomaly factor). This
could be considered a ‘leading indicator’ for the purposes of forecasting stock market
returns / economic activity. There are several on the FRED website
(https://fred.stlouisfed.org/), but other data sources can be readily used. For example, you
can find a lot of information on the performance of other anomalies on Ken French’s
website, or the ‘Global Factor Replication’ website (https://jkpfactors.com/?country=usa).
For example, this could be:
• Inflation (consumer price index, producer price index),
• credit spreads (average yield on BAA bonds less AAA bonds, or yield on BAA
bonds minus 10-year Treasury Bonds)
• yield curve slope (yield on 10-year bonds less yield on short-term rates (e.g. T-
bills)),
• economic policy uncertainty,
• industrial production,
• consumption-wealth ratio (CAY)
• non-farm employees or payroll,
• a measure of investor sentiment (using the Michigan sentiment Index or the
Sentiment index from Jeff Wurgler’s website),
• return dispersion,
• or other variables that could potentially be useful in forecasting market or
particular portfolio returns. Select a sensible variable if not listed here – and not
one that is essentially the same as the anomaly portfolio (that is, do not use a
variable such as volatility to predict returns to a volatility-based portfolio).
Note: it may be the case that your variable is not available for the full length of the data
set. Use a variable with availability for at least 10 years, and available at least monthly.
You could find some data available only quarterly, but would need a longer series to
compensate (and to measure returns accordingly.)
a. Justify your choice of time-series predictive variable. What is this variable supposed
to be useful for predicting, and why? Does it indicate the state of the business cycle
or investor’s intentions? Has this been shown to be a useful predictive indicator of
stock returns, or even your anomaly portfolio’s returns in the past? Present some
evidence (from academic literature if possible).
b. If your time-series variable is stationary, examine your portfolio returns in periods of
‘high’ values of your predictor, and low values of your predictor. If it is not stationary
(such as an index that has increased substantially over time) then take the change in
the value of your predictor (such as change in nonfarm payroll) as your variable of
interest.
You will need to explain a suitable choice for ‘high’ and ‘low’ values. Possible
candidates include ‘above/below median’ or ‘top/bottom quartile’ or
‘positive/negative’. Ideally, you would want to have 20% or more of the
observations in each of the high/low groups.
Is there significant difference in the returns to your portfolio in periods of high/low
values of your predictor? If so, what does this suggest about the role of risk in the
portfolio? If not, why might the variable not appear to play a role in the prediction of
your portfolio’s returns? Note – use the original portfolio, not the size interacted
portfolio to perform this task.
c. Take the lagged value of your time-series predictor, and use it to forecast portfolio
returns. For example, for your portfolio return in February 2023, use the predictor
variable’s value in January 2023 (or an indicator variable constructed from its value).
Does the predictor help forecast the return to your portfolio? For example, you may
want to use an indicator variable similar to “Sentiment in the previous month 1SD
below average” as in the notes.
d. Use the lagged value of your predictor from part c as an additional variable in the
Fama-French 3-factor model. Write out the regression model that you have
performed, including the additional predictor. Does the macroeconomic variable
provide incremental explanatory power in the regression? If you conditioned your
portfolio on the information provided by the macroeconomic variable, could you
generate higher returns?
e. Based on the analysis you have performed, would you recommend this portfolio as
an appropriate trading strategy, for say, a hedge fund or sophisticated investor? Do
you have any recommendations for improving the portfolio trading strategy? If you
have found anything else useful for predicting the returns on the portfolio, this could
also be discussed in this section. (In this part, critique the performance based on the
insights of your report).
Notes:
The assignment is to be completed by groups of 1-4 students. You can team up with anyone
in the class.
Write out your report in 10 pages or less, including any appendix or references that you use.
Do not include any unnecessary information such as your data set. Include a coversheet with
the student ID of all group members included.
Please make sure to clearly spell out the four sperate parts (1-4) but within these you can
address the questions however you see fit. You can use the letters a, b, c, as a direction if
you are unsure.
If you are in doubt of what to do, use your judgement. Often, there is not a particular ‘right’
or ‘wrong’ way to do things (such as choosing a predictor variable). Think about what makes
a sensible trading strategy, based on the information that someone would have had at the
time. This is similar to the type of report an analyst / consultant might write.
You could combine regression results, or use pictures to make points more succinct. Ensure
that anyone reading your report would be able to understand what you did – imagine they
would try to replicate your study following the report. Think of the audience as an intelligent
investor interested in new opportunities.
Provide a clear, and concise explanation of your points, where needed. It will be more
interesting if you are able to provide insights that are supported by your data.
Present legible and clear tables and figures. Label each of the tables using a caption. Use
page numbers. Marks will be deducted for poor or unclear presentation.
The assignment is due on Friday 19th May (Week 12) at 12:00 pm. Please use the submission
link on Canvas.