Business School
QBUS6830
Financial Time Series and Forecasting Semester 1, 2019
Group Assignment
The Group Assignment will contribute 40% towards your final grade and is to be completed in groups of 4 students. The due date is Monday 27th May, by 4pm via online Turnitin submission and in Canvas.
The assignment will be graded out of 100 marks and is divided into two parts: part A (25 marks) and part B (55 marks). Overall presentation will be worth 10 marks of your final grade. In part A you are required to demonstrate an ability to build, assess and interpret factor models using both the principle components technique and factor analysis. In part B you will compare a range of models/methods for forecasting, in the context of a dynamic portfolio allocation problem, regarding investment performance. The dynamic allocation problem will involve obtaining forecasts from different methods/models to dynamically set optimal asset portfolios, using different rules. The aim is to assess and compare these competing models and methods for investment purposes, including for risk management. Please see the Guidelines document in addition to the following minimum requirements.
Minimum Requirements
Historical Daily Index Prices for the S&P/ASX200 Index as well as for the 11 GICS Industry sectors for the period 6th April 2014 to 6th April 2019 (source: https://au.finance.yahoo.com) are provided in the file “Index_Values.xlsx” which is provided in the Group Assignment folder on Canvas. The first row of the file has variable names representing the various indices (actually their ASX codes) which are defined in the Table 1 below:
Table 1: Variables and Series Numbers
Series Number
Variable
Description
Date
Dates of observed index values
1
XPJ
S&P/ASX 200 A-REIT
2
XDJ
S&P/ASX 200 Consumer Discretionary
3
XSJ
S&P/ASX 200 Consumer Staples
4
XEJ
S&P/ASX 200 Energy
5
XXJ
S&P/ASX 200 Financials excluding A-REITs
6
XHJ
S&P/ASX 200 Health Care
7
XNJ
S&P/ASX 200 Industrials
8
XIJ
S&P/ASX 200 Information Technology
9
XMJ
S&P/ASX 200 Materials
10
XTJ
S&P/ASX 200 Telecommunication Services
11
XUJ
S&P/ASX 200 Utilities
12
XJO
S&P/ASX 200
Part A – Factor modelling (25 marks)
1. (5marks)Calculatethedailypercentagereturnsforeachofthe11GICSsectorseries for the entire data period 6th April 2014 to 6th April 2019 and perform a Principle Components Analysis on the returns data. Present the results of your analysis with a discussion of how many principle components would be adequate to explain the index return series.
2. (10 marks) PCA analysis is often used as an exploratory tool to find the various underlying drivers of asset returns. Provide an investigative analysis of the PCA results to help develop an intuitive understanding of the key drivers of sector returns. You should attempt to explain what the drivers are, how they affect the sectors differently, and, where possible, provide an explanation of why.
Restricting your analysis to the first 4 Principle components found, initially describe these components. After your initial description, you should conduct some research in an attempt to find relevant interpretations for each of these 4 components. Suggestions from previous research may help you here. You should consider examining each components relationships with other potentially relevant data series over the same period such as index returns (e.g. for provided XJO index), key macroeconomic variables (interest rates, exchange rates, unemployment rates, etc.), industry specific variables (e.g. accounting ratios such as P/E, B/M) or anything else you think may be relevant. Provide evidence that helps justify any conclusions.
3. (5 marks) Conduct factor analyses on the 11 GICS industry returns series using method 1 from lectures: the maximum likelihood estimation method (see pages 53- 55 of Lecture_3_M1.pdf)). Use the estimation output and calculate any relevant statistics or tests to provide an informed discussion of how many factors should be used. Present your final chosen model and discuss the model fit.
4. (5 marks) Reestimate a factor model, now using method 2 from lectures, exploiting the PCA analysis from Q2 above (see pages 55-56 of Lecture_3_M1.pdf). For this purpose, you should include the same number of principle components here, as the number of factors used in the final model chosen in Q3. Present the model, discuss the model fit and compare with the factor model from Q3 in terms of model fit, adequacy and usefulness.
Part B – Dynamic portfolio optimisation (55 marks)
Data Selection for Part B
In part B you are required to analyse 3 of the industry returns series described in Table 1 above. The 3 series your group must select are based on the 3-digits in your group number and the Series Numbers provided in the first column of Table 1. You must select the 3 series that correspond to the 3 digits in your group number, with the following 2 caveats:
I. If your group number contains the digit ‘0’, select series number 10 for this digit, and
II. If you group number has repeated digits select series 11 for the first repeated digit
and series 12 for any second repeated digit.
For example, if your group number were 345 you should select series numbers 3 (XSJ), 4(XEJ), and 5(XXJ) for analysis. For the group number 201 you would choose series
QBUS6830, Financial Time Series and Forecasting
numbers 2(XDJ) 10(XTJ) and 1(XPJ). For the group number 333, you would require series numbers 3 (XSJ), 11(XUJ), and 12(XJO).
Use the 3 series for your group, in a dynamic portfolio allocation problem, by completing the tasks below.
5. (10marks)Convertthe3seriesofindexvaluestopercentagelogreturnsdata.Next, split your returns series into two sub-parts by time. For the first sub-sample, the in- sample or learning period, use all observations up to and including 6th April 2018. The remaining data for the period 7th April 2018 to 6th April 2019 is the second sub-sample, and shall be used as the forecast sample.
Provide a thorough statistical analysis of the percentage log returns data in your learning sample for each of your 3 series. Your analysis should help inform the building of time-series forecasting models for portfolio construction as laid out in the steps that follow and should consider any model assumptions or possible distributions for your data.
Clearly present, interpret, and discuss the relevance of any output you present.
6. (15marks)Motivateanddiscussquantitativemodelsyouwillemployforforecasting the 3 asset returns series. You should choose at least 4 different models/methods here for forecasting each asset’s return and volatility. At least 2 of these must be GARCH-type parametric models, while the others can be naive, ad hoc, non- parametric, etc.
Estimate your models using only the ‘learning sample’ period. For one of your series only, you should fully describe the process you followed to choose or adapt/refine these models including any tests and any diagnostics you applied along the way. For the remaining two asset series, you may present your final models only, along with all relevant diagnostics and tests in a table, and provide a thorough discussion of these.
7. (10marks)Generatemovingoriginhorizononeforecastsofbothreturnandvolatility for each observation in your forecast sample for the models in Q6. Clearly explain and justify how your forecasts will be calculated for any ad-hoc or non-parametric models. Assess the forecast accuracy of these models for forecasting both the returns and volatilities of each of your 3 series.
8. (10 marks) Asset portfolio returns are given by the weighted sum of the individual asset returns. Motivate, then clearly present at least three (3) different rules or methods for choosing ’optimal’ portfolio weights for use in your study. At least one of these methods must involve the concept of risk management, using a quantitative risk measure appropriate for these asset portfolios to choose portfolio weights. You can be creative with your choices, but you must clearly define and justify each weighting method and properly explain how your forecasts enter the weight calculations.
9. (10 marks) For each weighting strategy in Q8 use your forecast models to dynamically assign optimal portfolio weights during the forecast sample period (i.e. do this for each combination of strategy and model). Present and discuss the optimal portfolio weights. You should also justify your frequency of optimally choosing portfolio weights; use at least two different frequencies of changing weights (e.g. every period, every 5th period). Under each choice you must ‘update’ the portfolio
QBUS6830, Financial Time Series and Forecasting
weights at least 5 times in the forecast sample. Also justify how often model parameters are re-estimated (a separate decision).
10.(5 marks) Assess and compare the returns and risk measures from all combinations of portfolio strategies and model types. These must be fully and properly discussed, presented, evaluated, compared and interpreted in detail.
11.(5 marks) Include a final discussion that compares the competing models and methods for portfolio allocation on investment and accuracy criteria. Was all this quantitative effort worth it in this case? Discuss.
Overall Presentation (10 marks)
In addition to a Written Report (30 page limit), you will be required to submit the Matlab code used for all of the calculations/output in the assignment, peer assessment documents and group meeting minutes. Detailed submission instructions will be provided closer to the due date of the group assignment. Note that your assignment shall be processed by the anti- plagiarism software Turnitin.
QBUS6830, Financial Time Series and Forecasting
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