IB9Y8 Asset Pricing 2019/20 Group Project Assignment
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IB9Y8 Asset Pricing
2019/20 Group Project
This project asks students to estimate and test standard asset pricing models as
discussed in the course, and to provide a qualitative evaluation of the results of this
exercise in the context of the relevant theoretical framework. The objective is to
allow students to demonstrate their conceptual understanding of the theory, as
well as their ability to apply this knowledge to a concrete empirical investigation.
The main focus is on time-series and cross-sectional tests of arbitrage pricing theory
within a cryptocurrency context. Although the key research questions are the same
for all groups, each group is given a different data set and will hence obtain
different results. Your mark for this project will be based primarily on the
competence with which the empirical analysis is implemented and, most
importantly, the quality of the discussion. Note that the empirical exercise that is
outlined below has (as of yet) not been fully researched within a cryptocurrency
asset pricing context. As such, we re-emphasize that the motivation and discussion
component of your final hand-in is of utmost importance.
READ THIS FIRST!
Why oh Why? … you may ask. Why are we practising implementing empirical tests of models?
Surely other people have done this before and we could just base our decisions on
their findings? A short answer is given by the motto of the Royal Society1
: “Nullius
in Verba” (loosely translated as “take no-one’s word for it”). In a situation where
(in your future career, for instance) your bonus, your reputation, or even your job is
on the line, would you really want to trust someone else’s judgement to choose the
model, methodology, or theory that you base your company’s (or indeed your own,
personal) million-dollar business decisions on?
If you are content to be the kind of person who simply does, without
questioning, what others tell you when making life or business decisions, then
you’re in the wrong place (you should not be doing a Masters degree!) By
pursuing a higher degree at “Master of Science” level, you are clearly stating
(“revealed preferences”, economists would say) your intent to be the kind of
person who makes their own, independent choices. Be a “decision-maker” rather
than a “decision-taker”!
So … We need to learn how to assess, objectively and independently, the tools at our
disposal for validity and suitability so that we can, with confidence, choose the
“right one” to apply to the problem we wish to solve. More importantly, we must
learn how to identify the shortcomings of existing tools or methods, so that we
know how to tweak existing ones, or even build our own from scratch, to be sure
we’re using the “best possible tool for the job at hand.”
This is what the project is all about.
1
www.royalsociety.org
IB9Y8 Asset Pricing 2019/20 Group Project Assignment
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Data:
An Excel workbook named “IB9Y8 (2019) Group Project (DATA).xlsx”) will be posted
on my.wbs alongside these instructions. The file contains monthly log return data
on 61 cryptocurrencies denominated in U.S Dollars (USD) Specifically:
Sheet “Cryptocurrency Returns”:
The “Crypto Returns” sheet contains daily log returns on 61 cryptocurrencies
downloaded2
from the CryptoCompare API. The sample covers the period from 5th
October 2017 to 7th November 2019 (794 observations). The reported figures are
“raw” daily log returns (not annualised). For example, the entry “7.4%” for ANT for
the day of the 5th October 2017 means that the price of Aragon at the end of the
5
th October 2017 had increased by 7.4% with respect to the U.S Dollar (USD). A day
is defined as a 24-hour period with a sampling time of 00:00:00 GMT. In other
words, relative to the USD which is used as the quote currency, Aragon (ANT) has
increased in value. A lengthy filtering process is undertaken to filter out illiquid
cryptocurrency pairs and pairs which exhibit very low trading volume. The initial
sample included over 3000 pairs which were sequentially screened using raw
exchange volumes, the Amihud liquidity ratio and the Abdi-Ranaldo low-frequency
bid-ask spread measure. A further restriction is that every pair in the sample must
have traded on or before the 1st October 2017.
Sheet “Cryptocurrency Factors”:
This sheet contains daily data (covering the same sample period from October 2017
to 7th November 2019) for five “cryptocurrency” based factors which are derived
from common risk factors identified in generic currency (FX) and equity markets:
DOL - Equal-Weighted: Introduced by Lustig et al. (2011) as a “dollar risk factor”
in currency markets. Constructed as the average return to holding the entire
basket of cryptocurrencies in the sample at each time t. In other words, this
“risk factor” is simply the equally-weighted market return across all
cryptocurrencies quoted in USD for each time t. This factor could be
considered analogous to the “market risk factor” in stock markets except
that the returns are equal weighted as opposed to market-cap weighted.
DOL - Volume-Weighted: As opposed to using equal-weights, trading volume (in
USD) is used to weight the return of each cryptocurrency.
REV: The “Short-Term Reversal” risk factor is a long-short portfolio which initiates
a long position in cryptocurrencies which had poor returns in the previous
day and a short position in stocks that had higher returns. This risk factor is
most similar to a short-term reversal portfolio first identified in equity
markets by Jegadeesh (1990). This factor is not given to you; constructing it
forms part of the empirical exercise.
2
See https://min-api.cryptocompare.com/documentation?key=Historical&cat=dataHistoday for a detailed
description of the data. Log returns are computed from exchange aggregated pricing data to ensure that
outliers and spurious data points are excluded.
IB9Y8 Asset Pricing 2019/20 Group Project Assignment
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Cryptocurrency Factors (cont’d):
LIQ: The “Liquidity” risk-factor is a non-tradable factor that is estimated via PCA
following the methodology of Korajczyk et al. (2008). First, an estimate of
bid-ask spreads is derived using the methodology of Abdi and Ranaldo
(2017) for each cryptocurrency in the sample for each time t. Thereafter,
the LIQ factor is obtained by extracting the first principle component from
the matrix of bid-ask spreads. In this case, an increase in this factor
represents a decrease in liquidity – i.e. the factor is a measure of market
illiquidity. This type of factor is known as a “statistical factor” as opposed to
the tradable factors discussed above.
VOL: The “Volatility” risk factor is a measure of market-wide volatility in the
cryptocurrency markets. This factor is very similar to the FX VOL factor
which was first constructed by Menkhoff et al. (2012b). The factor is a
statistical factor that proxies for volatility risk in cryptocurrency markets.
Sheet “Cryptocurrency Group Selection”:
This sheet contains a “matrix”, with one row for each project group, which contains
a random sample of 40 cryptocurrencies from the original 61. Each group will work
with their randomly generated sub-sample of 40 out of the original 61
cryptocurrencies listed in the “Cryptocurrency Returns” sheet. The idea is this:
1. Locate the row in the “Selection” sheet that corresponds to your group.
2. From the “Returns” sheet, extract those columns of data for which your
sample number matches. i.e. Group 1 will extract the first 9 cryptocurrencies and
then the 11th cryptocurrency and so on until they have extracted their randomly
sampled 40 pairs.
Please contact Alex Dickerson at phd18ad@mail.wbs.ac.uk if the sample extraction
procedure is unclear. Each group should end up with 794 time-series observations
for a set of 40 individual crypto pairs.
IB9Y8 Asset Pricing 2019/20 Group Project Assignment
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Assignment:
The task is to empirically examine the given data in the context of various aspects
of Asset Pricing theory. The following questions are for guidance only; you are
encouraged to “go beyond” these guidelines and explore/investigate whatever
model or hypothesis you deem appropriate. In particular, the structure of your
report should not simply follow the questions below; you should decide upon your
own structure, designed to optimally present the results of your study.
However, all tests should follow a two-stage (first time-series, then cross-section)
rolling-window Fama-Macbeth procedure.
You can use a 36-day window to estimate betas for the time-series regressions,
with 1-day “rolling steps”. However, you have flexibility in the rolling-window; if
36-days is too short a window, extend it.
Guidance Questions:
1) Does the DOL Equal-Weighted risk factor (one-factor) “work” in pricing the crosssection
of cryptocurrency returns? Does the DOL Volume-Weighted risk factor do
a better job? Argue which factor should “work” better from a theoretical
perspective. Is the predictive ability of either of the DOL risk factors “timedependent”,
i.e. is there variation in the average beta coefficient between the
cross-section of returns and either of the DOL factors? Finally, contrast the DOL
Volume-Weighted factor to the market risk factor used by the “CAPM”. Is it
wise/informed to apply CAPM based theory to price cryptocurrencies?
2) Do the additional factors (LIQ and VOL) provide additional power in explaining the
cross-section of expected cryptocurrency returns?
You may notice that the REV factor is not provided. Construct your own “reversal”
factor REV using only the cryptocurrencies allocated to your group:
1. For each day sort the cryptocurrencies in your sample by their lagged returns
(at t-1) into quintiles from low to high.
2. Compute out-of-sample returns (at time t) of each quintile
3. Create a long-short, zero-cost portfolio which is long the lowest quintile (1)
and short the highest quintile (5) to create the REV portfolio.
Include LIQ, VOL and the newly computed REV factor and one of the DOL risk
factors in a multivariate regression setting. Does this “four-factor” model achieve
better results than the one-factor model used in Question (1)? Do the risk-premia
of the factors have the “correct” sign, i.e. do the factors lead to risk premia or not?
If nothing is “statistically significant” at the conventional level (normally 5%), give
some intuition/reasoning as to why?
(Continued on Following Page …)
IB9Y8 Asset Pricing 2019/20 Group Project Assignment
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Assignment (cont’d …):
3) Summarise and discuss your findings (we are looking for a qualitative analysis, not
just a repetition of your results). Does your evidence identify an asset pricing model
that “works”? Or does it suggest that that “something is missing” (and if so, what is
it?). In other words: based on your results (evidence-based reasoning, not generic
opinion!), if you had to build your own asset pricing model to make investment
decisions within a cryptocurrency context, what would you do?
Note that it is very important not to try and “force” the factors to price the crosssection
/ find that some factors are “statistically significant”. It may very well be
that none of the factors provided are able to price the cross-section of
cryptocurrency returns at all. This is a finding in itself and is not to be dismissed.
We are primarily looking for a full understanding of core asset pricing theory in an
arbitrage pricing theory context applied to a cross-section of cryptocurrencies. If
nothing “works” in pricing the cross-section of returns, what do you think is behind
this? Your answer should include factors relating to your statistical work as well as
broader market themes which dominate cryptocurrency markets.
IB9Y8 Asset Pricing 2019/20 Group Project Assignment
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References:
General: The following are in general about factor models and tests thereof:
Fama, E.F., and K. French (2004): “The Capital Asset Pricing Model: Theory and
Evidence”. Journal of Economic Perspectives 18(3), 25–46.
Fama, E.F., and K. French (1992): “The Cross-Section of Expected Stock Returns”.
Journal of Finance 47(2), 427–465.
Fama, E.F., and K. French (1995): “Size and Book-to-Market Factors in Earnings and
Returns”. Journal of Finance 50(1), 131–155.
Carhart, M. M. (1997): "On Persistence in Mutual Fund Performance". Journal of
Finance 52(1), 57–82.
Wooldridge, J.M (2008): “Introductory Econometrics: A Modern Approach”, 4th
edition, South Western College.
Specific: Literature on Cryptocurrency Risk Factors:
Lustig, H., Roussanov, N. and Verdelhan, A., 2011. Common risk factors in
currency markets. The Review of Financial Studies, 24(11), pp.3731-3777 [ DOL
Risk Factor ]
Jegadeesh, N., 1990. Evidence of predictable behaviour of security returns. The
Journal of finance, 45(3), pp.881-898. [ REV Risk Factor ]
Korajczyk, R.A. and Sadka, R., 2008. Pricing the commonality across alternative
measures of liquidity. Journal of Financial Economics, 87(1), pp.45-72. [ LIQ Risk
Factor ]
Abdi, F. and Ranaldo, A., 2017. A simple estimation of bid-ask spreads from daily
close, high, and low prices. The Review of Financial Studies, 30(12), pp.4437-
4480. [ LIQ Risk Factor ]
Menkhoff, Lukas, Lucio Sarno, Maik Schmeling, and Andreas Schrimpf. "Carry
trades and global foreign exchange volatility." The Journal of Finance 67, no. 2
(2012): 681-718. [ VOL Risk Factor ]
Specific: Literature on Cryptocurrency Factor Structure / Empirical Asset Pricing:
Liu, Y. and Tsyvinski, A., 2018. Risks and returns of cryptocurrency (No.
w24877). National Bureau of Economic Research.
Liu, Y., Tsyvinski, A. and Wu, X., 2019. Common Risk Factors in
Cryptocurrency (No. w25882). National Bureau of Economic Research.
Bianchi, D. and Dickerson, A., 2019. Trading volume in cryptocurrency
markets. Available at SSRN
Makarov, I. and Schoar, A., 2019. Trading and arbitrage in cryptocurrency
markets. Journal of Financial Economics.
Griffin, J.M. and Shams, A., 2019. Is bitcoin really un-tethered?. Available at
SSRN
Foley, S., Karlsen, J.R. and Putniņš, T.J., 2019. Sex, drugs, and bitcoin: How
much illegal activity is financed through cryptocurrencies?. The Review of Financial
Studies, 32(5), pp.1798-1853.
IB9Y8 Asset Pricing 2019/20 Group Project Assignment
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General Guidelines / Instructions:
Each group should elect a “liaison officer” to communicate with the module leader
(if required), but also (most importantly) to manage the submission!
Submission: Each group should compose a report summarising the research question and their
empirical findings. Your report should not exceed 2,000 words.
Deadline: Submit your report via my.wbs no later than:
12:00 (noon) on Monday, 16 December 2019.
Group Work: All members of the group are expected to contribute equally to the project, but it
is your responsibility to “manage the group”. Your initial meeting should make sure
that you have processes in place for …
Allocation of work load
Assignment of specific tasks
Decision-making
Conflict-resolution
Peer Review: Next to the Group Project item itself, you will find on my.wbs a link labelled “Peer
Assessment of Group Work”. At the time when your report is submitted, all group
members are also required to evaluate their own and their peers’ performance
in a range of behavioural categories. The outcome of this exercise will have a
material effect on each group member’s individual mark for the project. A
briefing document explaining the details of this process will be posted separately.
Support: Feel free to use our office hours if you have specific questions about process or
details of the assignment that you are unclear about. Note however that we will
give advice only, the ultimate decision (e.g. choice of methodology) lies with you!
If you do make an appointment, it would help if you could send your queries in
advance so that we have a chance to think about how best to deal with them.
Marking: The project is designed to assess students’ conceptual understanding of the
theoretical framework, as well as their ability to apply this knowledge to a concrete
empirical investigation. Your final mark is based on …
1. Clarity of the exposition
2. Evidence of understanding of the relevant theoretical framework
3. Competence of implementation of the empirical analysis
4. Clarity and coherence in reporting results
5. Quality of discussion in the context of existing literature
IB9Y8 Asset Pricing 2019/20 Group Project Assignment
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Summary Table:
Each group should include the summary of the main results of the statistical tests
on the third page of the submission document (after the cover sheet and title page,
before the main text body). You should use (or replicate) the template below (a copy
of this table will be posted in Word format alongside the assignment so you can
copy and paste). This table is not included in the word count, however you should
keep it short (it should fit on one page). You should only provide the numerical
results of your tests. When asked, provide a very brief conclusion of less than 100
words about your tests results.
Summary of Results
Testing the Equal & Volume-Weighted DOL Factor:
Average coefficients and t-statistics
for cross-sectional regression
(DOL Equal-Weighted)
Average coefficients and t-statistics
for cross-sectional regression
(DOL Volume-Weighted)
Any additional tests
(time variation in the betas)
Main conclusion for this section
(less than 100 words)
Reversal (REV) Factor Construction:
Summary statistics of the factor
(mean, standard deviation etc.)
Testing the 4 Factor Model:
Average coefficients and t-statistics
for cross-sectional regression
Any additional tests
(if any, give details)
Main conclusion of the tests
(less than 100 words)
Other Tests:
Any other tests not specified above
(if applicable)
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Sample Outline:
Cover Sheet (automatically generated by my.wbs on submission)
1. Title
2. The summary table (as outlined above)
3. Introduction
Clear description of the research question
Brief summary of your methodology
Brief summary of your main results
Relation to extant literature (theory, methodology, results)
4. Methodology
Brief description, and motivation for choice of, methods employed
5. Data and Empirical Results
Data description
Preliminary data analysis and summary statistics
Description and discussion of results
Tables (with clear captions in appendix)
6. Conclusions (relating to initially specified research questions)