23LLP104 Report (100%) - Statistical Methods in Finance Submission deadline: 02/02/2024 23:59 Weighting: 100% of the module assessment Answer all questions. The marks for each question are shown. Question 1

(20%): Suppose that X has the uniform distribution on the interval [a, b]. (a) Prove Var(X)=E(X²)-(E(X))². (3%) (b) Compute the mean of X. (6%) (c) The following is the Law of the Unconscious Statistician theorem: Let X be a random variable, and let r be a real valued If X has a continuous distribution, then: E[r (X)] = [₁ r(x) f(x) dx, Given this theorem, compute E(X2), where X is the uniform distribution in the question. (2%) (d) Using the proof in (a) and theorem in (c) compute the variance of X. (2%) (e) Suppose that the return R (in dollars per share) of a stock has the uniform distribution on the interval [-3, 7]. Suppose also, that each share of the stock costs $1.50. Let Y be the net return (total return minus cost) on an investment of 10 shares of the stock. Compute the expectation of Y. (7%) Your answer should include the following points: The distribution of X and R, the derivation of expectation and variance of X. (Correct answer without the above points will not get full score). Question 2 (30%): Regression Analysis The excel table “Belgium” (under the folder '23LLP104 Report - Belgium Data' on Learn Assessment Section) shows the annual GDP, education investment, unemployment rate, and employment compensation in Belgium from 2000 to 2018. Use this table to complete the following financial analysis: (1) Provide the descriptive statistics (mean, median, mode, variance, trend) of these four economic variables in tables and graphs, and explain these statistics. (10%) (2) Use regression to analyze how the three variables (education investment, unemployment rate, and employment compensation) affect Belgium GDP. The three requirements are as follows: (a) use Excel to conduct regression analysis and provide your results with screenshots or tables. (5%) (b) provide and evaluate your regression model (standard errors of estimates, R2, significance F). (6%) (c) verify the impact of the three variables on GDP via coefficient significance testing at 10% significance level. (9%) Question 3 (50%): Asset Pricing Asset pricing is an essential topic in Finance. One key objective of asset pricing is to explore the factors that determine the prices of and returns on financial and real assets, including stocks, bonds, currencies, and real estate. In terms of stock pricing, Fama and French (1992) propose a well-known model, "Fama and French Three Factor Model", to describe stock returns. Read the paper below from Fama and French (1992) and write a critical review. Paper title: "The Cross-Section of Expected Stock Returns", which is available to download in the Learn assessment section. Your review should summarize the following points in your own words: • What are the motivations and contributions of this paper? • How does this paper achieve claimed contributions? • How does this paper design experiment? • What would you contribute to the Fama-French Three Factor model if you were working on stock pricing? • If you were a professional stock investor, how would you use the stock pricing model to help your investment? (Word limit: 1000 words, excluding graphs, equations, formulas, and references) Submitting your coursework To submit your work on Learn, you will need to submit: your report in PDF version. REMEMBER: You must NOT include your name in your submission title or file, in line with anonymous marking. Grading & Marking: Your grade will be assessed on the overall quality of each part. The following points will be considered while marking your answers: 1: Layout and presentation. including the use of references and citations, Quality, and clarity of written English. 2: Clear calculations and programming codes - Have they provided clear calculation steps and excel regression results? Have they used appropriate methods to work out the questions? Have they shown understanding of the key concepts? Is the excel analysis rational? Have they discussed and interpreted the results correctly? Have they learnt different methods additional knowledge beyond classroom material? 3: Illustration of their understanding of questions after self-study Have they shown their appropriate understanding towards the questions? Have the questions been discussed satisfactorily, illustrating a clear understanding of the statistical methods utilized? Is there adequate evidence of independent learning and experimenting? 4: Critical reflection- Have they clearly communicated their own thoughts, identified issues/challenges faced during the assignment? Have they understood the limitations of the current work? Ideas/thoughts that are rational and realistic, potentially linking them with related literature, instead of vague and superficial, are valued. Are there adequate academic references