COMP0040 – Assignment 1
Probability and Statistics
This assignment is focused on: Empirical Probability distributions; Fat tails; Quantile estimation; VaR; CVaR and quantiﬁcation of statistical robustness of the various measures. It is part of feedback for the preparation of ﬁnal report.
Each group is associated with one of the main currencies: Bitcoin (BTC), Bitcoin Cash (BCH), Ethereum (ETH), Litecoin (LTC) and Ripple (XTC) and then other 8 chosen at random. The data set reports hourly prices of cryptocurrency assets (the hour is described as unix time stamp), and their textual sentiments (e.g. from Twitter, online news). Student should look at the list of student number (see ’Groups’ and ’ListData’ ﬁle on Moodle) and analyze the data series corresponding to their number. You can also include other currencies and other market signals to enrich your analysis.
From the lecture notes of Part I, you have learned about some statistical properties of ﬁnancial market data set. Investigate whether this cryptocurrency asset has empirical properties similar to them.
You have to estimate the risk associated to this cryptocurrency asset. You must characterize/describe the data series statistically estimating the kind of probability distribution and the associated parameters; estimate risk measures such as VaR, CVaR associated with your portfolio at diﬀerent time horizons in both parametric and non-parametric approaches; estimating extreme event tail properties of the distribution.
Discuss statistical signiﬁcance and robustness of these estimations. The approach and the choice of measures are left to students but must be well justiﬁed in the report. [Hints: Follow the lecture notes of Part I and consider which method, which technique and which test can be used and why. Consider whether the analysis should be done on the prices or on the relative returns or the log-returns. Consider the range of dates that is most appropriate to analyze and why. Consider if you must look at all hourly prices or longer intervals (i.e. daily or weekly prices). Describe and justify every assumption or choice. To perform your analyses upload the data on a system such as Matlab, R, Excel, etc.]
4 Written report
A brief written report (about 5 pages including Figures and Tables; — do NOT submit your codes) containing the justiﬁcation of the approach, the presentation of the results, the discussion of the results and conclusions should be submitted to Moodle before the deadline of Sunday, 17/02/2019 at 23:55. Cleary write your student number on the heading of ﬁrst page. File name format must be: StudentNumber.pdf.
The report must be brought in the class at the lecture on Monday (18/02/2019) with all sheet stapled together and with the ﬁrst page reporting the self marking sheet ﬁlled with all information. This report should be identical with the one you uploaded to Moodle. Assignment not delivered in time and not delivered in the right format will be marked with a zero mark.
You can discuss the work within a group, but you need to produce and submit an individual report.
5 Class discussion and oral presentation
Your work will be discussed in class in groups of students on Monday 18/02/2019.
You will be marked based on the individual report you submitted. This assignment is worth 8% of the total exam mark. The marking will be based on the following criteria:
- Justiﬁcation of the choice of measures, assumptions and approaches;
- Clarity of presentations and explanations;
- Validity of the results;
- Consistency of language and mathematical notation;
- Scientiﬁc soundness;