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Quantitative Techniques for Accounting and Finance (ACFI815)

Individual Project: Formative

EViews Part

Background

The purpose of this project is to analyze the relationship between some international financial market stock indices during the last two decades. The project would be easier to handle in EViews, as it involves importing and manipulating the data. You will need to estimate and interpret the models, tests the main assumptions and propose strategies to address any arising statistical issue.

Excel spreadsheet "Market_Indices_ALL.xlsx" contains the data needed for this task. The dataset contains the time-series of the selected indices which are i) the US S&P 500 Index (SPX), ii) the Chinese Shangai Composite Index (SHCOMP), iii) the UK FTSE 100 Index (UKX), iv) the Eurozone EUROSTOXX 50 Index (SX5E), v) the Japanese Nikkei 225 Index (NKY), and vi) the Indian Nifty Index (NIFTY). The time period is from January 2000 to December 2020, at a daily frequency. Because the opening days of the markets are not the same, the data are aligned based on the US market timeline and closures. Hint: all the stock market indices are downloaded from Bloomberg where you can also find information, news, and relevant events about them.

1. Plot the time series of the six stock market indices (in level).

a) Comment on the main feature(s) of these time series.

b) What are the main events driving the trends of the market indices?

c) What do we observe during the most recent Covid-19 pandemic?

2. Now study the features of the log returns of the stock market indices.

a) Compute the log-returns of the stock market indices (in percentage) and denote them with their ticker plus adding the word "ret" (e.g. SPXret, NKYret).

b) Compute the descriptive statistics of the six time-series. Discuss the findings.

c) Compute the correlation matrix among the six time-series. What do you conclude?

3. Given your dataset and the evidence gathered so far, your manager is asking you to write down a model in which you select one of the indices as the dependent variables and the other three as independent variables. How would you perform this task? Which model would you build and why? Explain.

4. We now select the Chinese Shangai (SHCOMP) log-returns as our dependent variable and the US S&P 500 Index (SPX) as regressor. Formally test the null hypothesis that the average log-returns of the US S&P 500 Index (SPX) is equal to 0.

• Explain how you would carry out the test.

• Discuss the test statistic and the critical value (provide an example).

• Explain the economic importance of testing this null hypothesis. In other words, why is this an interesting hypothesis and what do we learn from this test?

5. Now analyze the information content of the European stock market indices log-returns to predict the S&P 500 market log-returns. Specifically, estimate the regression model below:

SPXret_t₊₁ = α + β_UKX UKXret_t + β_SX₅_ESX5Eret_t + ϵ_t₊₁ (1)

a) Comment on the results of the model in terms of the significance of the predictors.

b) Comment on the results of the model in terms of the predictors’ coefficients.

6. Now analyze the information content of the Asian stock market indices log-returns to predict the S&P 500 market log-returns. Specifically, estimate the regression model below:

SPXret_t₊₁ = α + β_SHCOMP SHCOMPret_t + β_NKY NKY ret_t + β_NIF _T _Y NIFTY ret_t + ϵ_t₊₁ (2)

a) Comment on the results of the model in terms of the significance of the predictors.

b) Comment on the results of the model in terms of the predictors’ coefficients.

c) What would you conclude about the European (model 1) and Asian markets (model 2) to predict the US market index returns?

7. Now run models 1 and 2 again excluding i) the global financial crisis, ii) the Covid-19 pandemic crisis, and iii) both crises. To check reliable dates for these recession periods, please look at https:

//www.nber.org/research/data/us-business-cycle-expansions-and-contractions. What do you observe?

8. Consider the alternative model:

INDEXret_t₊₁ = α + β_SP _X SPXret_t + ϵ_t₊₁ (3)

where INDEXret is the log-returns of one of the other five stock market indices, namely UKX, SX5E, SHCOMP, NKY, or NIFTY, whereas SPXret is the independent predictive variable.

a) Compare the performance of the five possible models in equation 3.

b) What do you observe? What index log-returns can be predicted better by the US SPX? Discuss.

c) Now run the same model(s) in equation 3 to predict your dependent variable one month ahead. What do you observe?

Numerical and Theory Part

Exercise 1

You estimate a regression of the type

y_t = α + βx_t + ϵ_t

The sample size is made up of 17 observations. Suppose you want to test the null hypothesis that the slope parameter is equal to 0 against a 1-sided alternative at the 5% significance level. What is the relevant critical value of the test statistic? The t-table is at the end of the assignment paper.

Exercise 2

Using daily data from 2014 to today, you estimate the regression of

ttOLD_t = α + β × X_t + ϵ_t

where ttOLD is the time-series of gold futures prices, and X could be either the country’s stock market price (STOCK) or the current inflation level (INFL). The picture shows the parameter estimate for each regression, i.e. the intercept α and the slope associated with the explanatory variables. In parenthesis, we show the t-ratio associated with the parameters of interest.

(−3.976)

(−2.025)

(2.353)

• What can you comment about the regressors’ coefficients?

• What are the standard errors of both estimates in the first regression?

• What is the relevant null hypothesis to test in the first regression to check whether the stock market contains any relevant information to predict ttOLD_t?

• Which variable could we conclude to be more informative for ttOLD_t?

• Which variables would you include to improve the explanatory power or the predictive ability of your model for ttOLD_t (please use academic references to support this point)?

Exercise 3

Which of these is NOT a reason for adding a disturbance term to a regression model?

• (a) Some determinants of the effect variable may be omitted from the model

• (b) Some determinants of the effect variable may be unobservable

• (c) Some determinants of the independent variable may be omitted from the model

• (d) There may be errors in the way that the dependent variable is measured which cannot be modelled.

Exercise 4

The estimated alpha (αˆ) and beta (βˆ) of an investment fund, Fund DEF, are 2.3 and 3.1, respectively. If the expected market risk premium is 12%, what would we expect the excess return of Fund DEF to be?

• 39.5%

• 30.7%

• 5.4%

• 64.8%

Practical Details

Guidelines

Do not write more than 750 words in total, excluding figures, tables, references, equations, and appendices. I strongly recommend that you use a proper Equation editor to type up your formulas. The final report must be submitted as a Word document. First Part: Please provide EViews screenshots for plots, tables, and regressions/test outputs in your report. Discuss your findings and carefully read the instructions and the questions related to your task. Second Part: follow and read (carefully) the instructions at the be- ginning of every exercise. Be concise in your answer. The t-table is provided at the end of the assignment paper.

The assignment is formative and counts for 0% of your total mark in the module. The report should be submitted within 1 Week. The deadline on Canvas is the 16th November 2022. Before submitting the report, include information about the total word count at the bottom of the cover page. Please provide a reference list at the end, should you use any academic citation/articles. The University’s penalty structure for late work will apply to any project submitted after this deadline. Extensions to the deadline will only be given under very exceptional circumstances. For further information, please go to the following page: https://www.liverpool.ac.uk/student-administration/examinations-assessments-and-results/ug-and- pgt/extenuating-circumstances/

Assessment Criteria

The written assignment is to be completed in accordance with University of Liverpool guidelines for academic writing (plagiarism, referencing, etc.). The project will be assessed using the following criteria:

1. Understanding of different theories and concepts (20%).

2. Implementation of the statistical tests (20%).

3. Evaluation of initial results including reflection on potential improvements or ways to address the statistical issues (20%).

4. Interpretation of the results (20%).

5. Communication of results - Is the project well-structured, clearly organised and with good flow? Does the project use clear English with no spelling, grammatical or typographical mistakes, and are the graphs and tables easily comprehensible? (20%).

Figure 1: T-table