IB9Y60: Empirical Finance Group Project
Ganesh Viswanath Natraj Andrea De Polis∗ University of Warwick, Warwick Business School
Guidelines
All questions can be solved using any language of your choice. It is recommended you stick to Matlab given the seminar material, however the questions can also be done via Python or R if that is your preferred language. Soft copies of your written answers and code must be submitted via myWBS by 12pm March 19th. Code should be commented and be able to execute to generate the results. The Group Project is worth a total of 20 marks. Each question is worth 5 marks.
The main dataset you will be using for this project is ”crypto.xlsx”. The data is a balanced panel from August 2017 to February 2020. Variable definitions with ticker labels are provided in the table below.
Ticker
Description
Source
BTC
Bitcoin price ($)
Cryptocompare
ETH
Ethereum price ($)
Cryptocompare
XRP
Ripple price ($)
Cryptocompare
BCH
Bitcoin Cash price ($)
Cryptocompare
LTC
Litecoin price ($)
Cryptocompare
USDT
Tether price ($)
Cryptocompare
BTC N
Number of unique addresses of BTC
Coinmetrics
BTC H
Hash Rate of BTC
Coinmetrics
∗ganesh.viswanath-natraj@wbs.ac.uk and phd17ad@mail.wbs.ac.uk respectively.
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Cointegration Pairs Trading
Load ”crypto.xlsx” and plot the time series of Bitcoin and Ethereum from 2017 to 2019.
Conduct a Dickey Fuller (constant, no trend) test on the log(price) of both BTC and ETH. Are they stationary series?
Conduct the first step of the Engle-Granger procedure, by regressing the log price of Bitcoin xbtc on the log price of Ethereum xeth.
xbtc,t = α0 + α1xeth,t + zt
Plot the residuals zˆ of this regression. Using the Dickey-Fuller (constant, no trend)
test, are the residuals stationary?
Estimate the VECM equation for the price of bitcoin pbtc below,
∆xbtc,t = β11∆xbtc,t−1 + β12∆xeth,t−1 + δ1z1,t−1 + ε1,t
Interpret the coefficient δ in the above regression. How can you construct a prof-
itable trading strategy based on your result?
Fundamentals- BTC Network and Hash Rate
Plot the time series of BTC, the BTC hashrate and the network metric (number of addresses) over time.1
Conduct a Dickey Fuller (constant, no trend) test on the hash rate and the network indices. Are they stationary series?
Conduct the first step of the Engle-Granger procedure, by regressing the log price of Bitcoin x on the log of the hashrate and network indices. Plot the residuals zˆ of
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btc t
this regression. Using the Dickey-Fuller (constant, no trend) test, are the residuals stationary?
1These factors are used by Bhambwani, Delikouras and Korniotis (2019) which examines two cryp- tocurrency fundamentals, computing power (hashrate) and the network (number of users).
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xbtc,t = α0 + α1xh,t + α2xn,t + zt
Estimate the VECM equation for the price of bitcoin pbtc, using both fundamentals,
as well as each fundamental separately.
∆xbtc,t = β0 + β11∆xbtc,t−1 + β12∆xh,t−1 + β13∆xn,t−1 + δ1z1,t−1 + ε1,t ∆xbtc,t = β0 + β11∆xbtc,t−1 + β12∆xh,t−1 + δ1z1,t−1 + ε1,t
∆xbtc,t = β0 + β11∆xbtc,t−1 + β13∆xn,t−1 + δ1z1,t−1 + ε1,t
Interpret your results. Is there an error correction in the price of bitcoin? How do the fundamentals drive bitcoin prices?
Volatility Modeling
Load ”crypto.xlsx” and estimate an AR(1) model on BTC returns Rbtc,t as Rbtc,t = φ0 + φ1Rbtc,t1 + εt
Take the residuals and estimate an ARCH(1) model defined as σ t2 = α 0 + α 1 ε 2t − 1
Using the AR(1) model from before, take the residuals and estimate a GARCH(1,1) model defined as:
σ2 = α + α ε2 + βσ2
t 0 1t−1 t−1
Now take the residuals from the AR(1), and estimate a GJR GARCH(1,1), defined by the following equation:
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σ2 = α + α ε2 + βσ2 + γε2 I
t 0 1 t−1 t−1
t−1 t−1
It−1 = 1,if
εt−1 < 0 0, otherwise
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What is the estimate of γ? Is there a statistically significant leverage effect in Bitcoin returns?
Compareandcontrastthethreemodels,ARCH(1),GARCH(1,1)andGJR-GARCH. Which model do you prefer and why?
Now, re-estimate the models using data until December 2019 and forecast 1-step ahead volatility within an expanding window scheme. Compare the predictions using the mean square error (MSE) and the mean absolute error (MAE). Which model do you prefer? Why? Is it the same model that best fit the data?
PCA Analysis
Load ”crypto.xlsx” and conduct a PCA analysis on the daily returns of 6 major crypto currencies, BTC,ETH,XRP,BCH,LTC,USDT.
Document the variance decomposition of the PCA. What per cent of variation in asset returns is explained by the first factor?
Plot the first PCA factor and the ETH returns. Do the series move together? What does this tell you about what the first PCA factor is capturing?
Tabulate the correlation of the first factor with the returns of each currency. What do you observe? (Hint: USDT is a stable coin, see https://www.torca.io/blog/what- is-a-stablecoin for more details)
Load ”bidask.xlsx” and conduct a PCA analysis of the bid-ask spreads of the set of currencies.2
Document the variance decomposition of the PCA. What per cent of variation in bid-ask spreads is explained by the first factor? Plot the first PCA factor.
2I thank Alex Dickerson for providing access to the bid-ask spreads. This is computed using informa- tion on open, high, low and close prices obtained from cryptocompare, and follows the methodology in Abidi and Ranaldo, 2017.
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4 Research Proposal
Write a research proposal on a topic in empirical finance. Where possible, use methods discussed in class. The proposal is to be two pages maximum (excluding references). Here are some tips on how to frame the proposal.
Introduction and Motivation
(1-2 paragraphs)
• What is the question you are answering? Why is it important? Were there any particular economic circumstances leading to the emergence of your topic?
• Is your question filling a gap in a particular line of research? Where does it fit in the literature?
• Is there a potential policy decision that may be informed by your research?3 Con- vince the reader that your question matters
Research Hypothesis
(1-2 paragraphs)
• Clearly state your specific, empirically answerable research question. If possible, state it in a way that can be empirically tested using the framework for hypothesis testing.
• Yourresearchhypothesisshouldbeaclearoutcomeofyourmotivation/introduction.
• What is it you want to find out and using what measurable variables?
Data and Methodology
(2-4 paragraphs)
• What data will you use? What are the independent and dependent variables you need to collect? What is the appropriate temporal and geographic unit for each variable? It will be a great bonus if you can show us that you already have access to the data, for instance by providing a link to your source.
3Not all questions can be motivated by a policy. However, relating your question to the real world and how it enhances understanding of financial markets is important
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• What econometric techniques will you use to analyze your data? For example, are you using a VECM, a GARCH, or PCA analysis? You are open to use other methods if they are more relevant in your context, however we recommend using one of the methods discussed in class.
• Wherepossible,stateclearlytheequationsoftheregressionspecification/methodology. Relate the steps of the method to the research hypothesis.
Hypothesized results
(1-2 paragraphs)
• What results of interest do you expect your analysis to give? Do you think they would have external validity i.e. would they hold up in other geographic, temporal, etc. conditions?
• What are some proposed modifications to your hypothesis and/or methods to better answer the question?
• How broadly applicable do you expect your results to be?
• If you do have results, then you are welcome to briefly state them. However, addi- tional material (Tables/Figures) may be relegated to an appendix after references. This is NOT required for the project and you will be graded on the 2 page research proposal.
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