ECMT6006 2021S1 Assignment 1
Due: 23:59 Thursday 15 April 2021
Please compile your solutions in ONE file (not including the program code
which you can submit separately) and submit it via Turnitin in Canvas. You
can either handwrite or type your answers. For the empirical questions, please
present the figures and provide your analyses/interpretations properly. If you
use MATLAB, you can present your answers using livescript exported in a doc-
ument format. Except for special circumstances, I DO NOT accept late sub-
mission.
Note: Patton (2019) refers to the reference textbook by Andrew Patton.
Question 1. Question 1 in Section 1.10.2 on Page 44 in Patton (2019).
Question 2. Question 2 in Section 1.10.2 on Page 44 in Patton (2019).
Question 3. Question 3 in Section 1.10.2 on Page 45 in Patton (2019).
Question 4. In this question, you will use time series of daily prices on two
financial assets: the S&P500 index1 and the USD/Euro exchange rate2. Use at
least two years of data to answer the following.
(i) Convert the 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.
(ii) Denote the returns of S&P500 index as Y and the returns of USD/Euro
exchange rates as X. Answer questions (a)–(e) of Question 2 in Section
1.10.3 on Page 47–48 in the textbook.
Question 5. 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.
1The S&P500 index daily prices are provided in the data file SP500 YahooFinance.csv
downloaded from Yahoo Finance. When constructing the daily returns, you can use either
open price or adjusted close price as the index price on that day. Or alternatively, you may
construct the daily index return using the adjusted close (end of the day) and open (beginning
of the day) prices on the same day. Just keep a note on what you do.
2Bank of England provide a wide range of historical macroeconomic and financial data at
https://www.bankofengland.co.uk/statistics. You may download the exchange rate data
from there.
3I provide both CSV and XLSX format files for your convenience. “d-msft8617” and “m-
msft8617” contain the daily prices and monthly prices, respectively, of Microsoft stock from
1986 to 2017.
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(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
statistics including maximum, minimum, median, mean, standard devia-
tion, skewness, excess kurtosis. Brieftly describe the empirical character-
istics 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 conclu-
sion.
(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.
Question 6. Question 1 in Section 4.8.2 on Page 134 in Patton (2019).
Question 7. Question 3 in Section 4.8.2 on Page 136 in Patton (2019).
Question 8. Consider the below three asset return time series:
• daily log returns of Microsoft Corp stock used in Problem 5;
• daily log returns of S&P500 index used in Problem 4;
• daily log returns of USD/Euro exchange rate used in Problem 4.
Complete the following:
(i) Generate the sample autocorrelation functions (up to 20 lags) for these
returns and plot them.
(ii) Generate the sample autocorrelation functions (up to 20 lags) for these
returns squared and plot them.
(iii) For each return and squared return series, conduct a Ljung-Box test for
L = 5, 10, 20 where L is the number of lags considered in the joint test.
(iv) For each return and squared return series, conduct a robust joint test for
the serial correlation based on a linear regression with White and Newey-
West standard errors. Again, consider L = 5, 10, 20 where L is the number
of lags considered in the joint test.
(v) What do you learn from (i)–(iv)?
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Question 9. Consider the following ARMA(1,1)-GARCH(1,1) process
Yt = φYt−1 + εt + θεt−1
εt|Ft−1 ∼ N(0, σ2t )
σ2t = ω + βσ
2
t−1 + αε
2
t−1
where |φ| < 1 and α + β < 1. Assume {Yt} is weakly stationary. Answer the
following.
(i) Find Et(Yt+1)
(ii) Find E(Yt)
(iii) Find Vart(Yt+1)
(iv) Find Var(Yt+1)
(v) Find Et(Y
2
t+1)
(vi) Find E(σ2t ).
Question 10. Question 2 in Section 5.10.2 on Page 185 in Patton (2019).
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