ECMT6006 Applied Financial Econometrics Semester 1, 2023 Assignment 1
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ECMT6006 Applied Financial Econometrics
Semester 1, 2023
Assignment 1
Due: 11.59PM Sunday 26 March 2023
Academic Honesty
Academic honesty is a core value of the University, and all students are required to act honestly, ethically and with integrity. The consequences of engaging in plagiarism and academic dishonesty, along with the process by which they are determined and applied, are set out in the Academic Honesty in Coursework Policy 2015. Under the same policy, as the unit coordinator, I must report any suspected plagiarism or academic dishonesty.
Instructions
• This is an individual assignment which accounts for 10% of your final grade. You may discuss with your classmates, but please ensure that the submitted work is independent.
• You can either hand-write or type your answers, but please compile all your answers in one PDF file and submit it via a file upload in Canvas. You can only submit your work once, so please double check before you submit. The page limit of the submission is 30 pages including appendix (penalty will apply if the page limit is exceeded).
• There are 7 questions (with sub-questions) in this assignment, and please attempt all questions. Detailed solution to each question will be provided after the assignment is due.
• I will randomly select 4 questions (same 4 questions for everyone) to grade, and each question is worth 5 points. The total point of this assignment is 20. The grading will be based on the completion and general quality of your submission.
• For the analytical questions, please show your derivations. Answers without interme- diate steps will be considered as incomplete.
• For the empirical question, please feel free to use any statistical software to answer them. Make sure that you present the required results, including figures, and provide your interpretations if asked. If you use MATLAB live script, you can present your answers in a document (exported from the live script) which contains your code, output, and your explanations in texts. If you use separate code, then please attach your code in an appendix at the end of your submitted PDF file.
• Based on the University late policy, a late submission is subject to a penalty of 5% (of the total points) per calendar day; and work submitted more than 10 days after the due date will receive a mark of zero.
• Patton (2019) refers to the reference textbook by Andrew Patton.
Questions
1. Question 1 in Section 1.10.2 of Patton (2019, p. 44). Note that in part (d), “one-month log returns have constant mean µ”means Et(Yt+1,t) = µ for any month t.
2. Question 2 in Section 1.10.2 of Patton (2019, p. 44).
3. Question 3 in Section 1.10.2 of Patton (2019, p. 45).
4. Question 1 and Question 2 in Section 3.11.2 of Patton (2019, p. 89–90).
5. Consider a simple three time period model for returns Rt of an asset where t = 1, 2, 3. Let R0 = 10%, and the returns in later periods follow
Rt = ϕRt − 1 + εt ,
where ϕ = 0.2 and ε 1 ,ε2 ,ε3 are i.i.d. random variables with probability distribution
εt = 
for t = 1, 2, 3. Let Ft be the information set containing all the past returns before time t. Answer the following questions.
(i) What is the probability distribution of R1? (ii) What is the probability distribution of R2?
(iii) Compute E(R2), Var(R2), Skew(R2) and Kurt(R2), the unconditional mean, vari-
ance, skewness and kurtosis of R2 .
(iv) Compute the conditional mean E1(R2) := E(R2|F1) and conditional variance
Var(R2|F1).
(v) Compute the conditional mean E1(R3) := E(R3|F1).
(vi) Verify the law of iterated expectation, E(R2) = E [E1(R2)] and E(R3) = E [E1(R3)],
using the results above.
6. In this question, you will use time series of daily prices on two financial assets: the S&P 500 index1 and the Euro/USD exchange rate2 from 1 April 2016 to 1 March 2019 in data Q6 .csv. Use this dataset to answer the following two questions.
(i) Generate time series plots of these two asset prices. Put a title, x-axis label and y-axis label on your figures.
(ii) Convert these two prices into continuously compounded returns. Generate a plot
of each of these returns. Put a title, x-axis label and y-axis label on the figures.
(iii) Denote the returns of S&P500 index as Y and the returns of Euro/USD exchange
rates as X . Answer questions (a)– (e) of Question 2 in Section 1.10.3 of Patton (2019, p. 47–48).
7. You can find the daily and monthly stock prices of Microsoft Corp. from March 1986 to December 2017 in the attached data files3. Assume there is no dividend payoffs for simplicity. Work on the following questions for both daily and monthly series.
(i) Generate a time series plot of each of the price series. Put a clear title, x-axis label and y-axis label on your figures.
(ii) Compute the arithmetic net returns and log returns. Generate a time series plot
of each of these returns. Put a clear title, x-axis label and y-axis label on your figures.
(iii) For both arithmetic net returns and log returns, compute the summary statis-
tics including maximum, minimum, median, mean, standard deviation, skewness, excess kurtosis. Brieftly describe the empirical characteristics of the returns in words.
(iv) Are the sample means of these return series statistically different from zero? Use
a simple t-test at the 5% significance level to draw your conclusion.
(v) Obtain the histogram of each of the return series, and compare it with the normal distribution that has the same mean and standard deviation.
2023-03-22