Data Analytics Question
ETF3600 – ETF5600 Assignment Due date: Sunday 12 May 11:55 pm Instructions: This is an individual assessment task. You are supposed to prepare your submission without help from or collaboration with anyone else. Part A of the assignment should be completed by all students. Part B must be completed only by ETF 5600 graduate students. You may use generative AI tools (or other language tools) to: (i) correct your typos and grammatical mistakes, and (ii) help you create the R code to run your analysis. Make sure to cite and point out where Generative AI was used and include the prompts used in the appendix. The assignment should be submitted electronically via Moodle. All answers must be typed, including equations. Equations can be handwritten and inserted into your document (e.g. scanned and inserted in the correct spot) if that makes it easier. You may include R (or other statistical software) output to justify your answers in an appendix, but you need to report results appropriately within the text. All numerical results must be rounded to no more than 3 decimal places. Unless otherwise instructed, all hypothesis tests should be conducted at the 5% level of significance. For questions that need programming, please include your R annotated program. In case your answers are incorrect, the marker can try to highlight where a programming error has been made. THE FULL ASSIGNMENT REPORT SHOULD BE UNDER 5 PAGES SINGLE-SPACED, HALF INCH MARGINS, 11pt Size Font. Statistical software code and output that you decide to include should be RELEVANT and placed in an appendix, and do not count towards the page limit. Relevant equations and results of the model should be in the main report. 1 In this assignment, your task is to explore whether the volatility of asset returns can help predict their sign. This exercise will allow you to develop and apply a range of skills related to empirical investigation, including collecting, cleaning, and merging data, as well as modelling and reporting results. Through this assignment, you will gain valuable experience in all aspects of the research process, which cannot be assessed through the final exam. The context: Your boss, while playing with ChatGPT to learn about the VIX index, has come across this: The VIX index, also known as the ”fear index,” is a measure of market volatility based on the prices of options on the S&P 500 index. It is often used as an indicator of the level of fear or uncertainty in the stock market. The relationship between the sign of stock returns and the VIX index is typically inverse. When the stock market experiences positive returns, the VIX index tends to decrease, indicating lower levels of fear and uncertainty. Conversely, when the stock market experiences negative returns, the VIX index tends to increase, indicating higher levels of fear and uncertainty. This inverse relationship between the sign of stock returns and the VIX index can be attributed to the fact that investors tend to become more riskaverse and fearful during times of market downturns, leading to an increase in demand for options contracts as a way to hedge their portfolios against further losses. This increased demand for options drives up the prices of options and, in turn, the VIX index. Overall, the relationship between the sign of stock returns and the VIX index is an important aspect of understanding market dynamics and can be useful for investors in managing their portfolios. Based on that, he has come up with the idea that if he can predict the sign of stock returns using the VIX index, he may be able to develop more effective trading strategies than his current methods. He has asked you to investigate the accuracy of ChatGPT’s information using the S&P 500 returns before proceeding with a study of individual stocks. Additionally, your boss is unsure whether ”returns” refers to raw returns or excess returns (returns above the risk-free rate), and he would like you to investigate whether partitioning positive returns into positive excess returns and positive returns less than the risk-free rate could lead to more accurate predictions. To complete this task, you will need to collect data on the S&P 500 index, a measure of the risk-free interest rate, and the VIX index, merge them, and calculate returns, excess returns, and the sign of returns. Then, you will need to use an appropriate model to answer the research question and report your findings. I provide some additional instructions to ensure that the reports are not too heterogenous and can be easily marked given the class size. PART A (Required for all students) 1. (Fundamental knowledge, integrating the knowledge from our first, second and third-year econometrics units): For data collection, please use FRED (https://fred.stlouisfed.org/) as the data source, and be sure to cite it in your report. Collect data for the S&P 500 Index at a daily frequency, covering all available days from 1/1/2016 to 2 31/12/2019. Also, obtain the daily VIX Index, and for the risk-free rate, use the 3-month Treasury bill rate (3-Month Treasury Bill Secondary Market Rate, Discount Basis). Merge all data by date, and double-check for any mistakes after merging. It is permissible to merge the data on Excel if you prefer. To compute the S&P 500 returns, use the so-called annualised “log-returns” (i.e. 1200 × (log(SP 500t ) − log (SP 500t−1 ))) – do not worry that on Mondays and after public holidays t − 1 refers to the previous working day, rather than the previous day. If there are missing values in your data series and you are using R, be sure to appropriately clean the data for estimation. Construct two separate binary variable that indicate if returns were positive for a given day, one using raw returns and the second using excess-returns. Finally, create a trichotomous variable that takes value -1 for negative returns, 0 for days in which the raw returns were positive but smaller than the risk-free rate, and +1 when excess returns are positive. 2. (Application of knowledge) – We expect to see a comprehensive analysis that utilises your knowledge of econometrics to develop good predictive models for both binary and trichotomous ordered dependent variables. This should involve: exploring the functional form, including considering the use of VIX or an appropriate nonlinear transformation of VIX, considering the use of lags of VIX, including a determination of the optimal number of lags of VIX, proposing one additional explanatory variable (available on FRED) to be included in the model, evaluating the quality of the models explored as far as predictive ability. Additionally, please provide a thorough explanation of how you selected your final model and the rationale behind your decision-making process. 3. (Communication) – We expect to see a clear exposition of what was done, the reasoning behind it and the conclusions. Your report should commence with a concise one-paragraph summary that clearly presents your findings. The remaining sections of the report should focus on your empirical investigation and be organised into headings of ”Data”, ”Modelling”, and ”Conclusion”. Appropriately cite your sources and references. (It is unnecessary to provide citations for lecture notes or econometric textbooks.) As you write, keep in mind that this report could serve as a valuable sample of your econometric analysis for potential employers. Strive to produce a document that you can proudly showcase to highlight your analytical strengths. Each of the above will contribute almost equally (6-7-7 points) to your overall mark. 3 PART B (Required exclusively for ETF 5600 students) You are required to produce an additional report updating the analysis for the period starting in 2020. Organize it in a similar way of the report in Part A. Limit this report to three pages (consider it as an update to the previous one, so no need to repeat things). Download the same data from Part A for the period from 01/01/2020-31/12/2023. Estimate the same final model you used in Part A. Consider which changes might be appropriate for the model, for example, altering the number of VIX lags, or proposing alternative explanatory variable(s) to include in the model. Estimate the altered/updated model and compare its performance for this period/sample with the final model from Part A. Communicate clearly your conclusions. In particular, discuss the changes that might have occurred in the model and consider possible reasons for the changes within the broader context of the period being analysed. 4
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