Semester 2, 2019
ECMT 2130 Financial Econometrics
Instructor: Dr. Yunjong Eo
• Due Date: November 8, Friday, 5:00 pm
• You need to (i) submit your answers to Section 2 Proposal only to [Final Project (Proposal)]
into Canvas1 and (ii) upload your data file (excel file) and other excel files used for estimation
to [Final project (Excel zip file)] into Canvas2
(zip all the files and upload the zip file only).
• Write the proposal concisely (no more than 10 pages).
• You are NOT allowed to discuss this assignment with your classmates. You are not allowed
to copy a classmate’s assignment (or to borrow the bulk of the material from a classmate’s
assignment). You are required to perform the full assignment on your own and hand in
For this project, you will analyze the behaviour of 10 stocks listed on the Australia stock market
to make calculations and answer questions. The project has two stages. The first stage is a data
work, for which you will choose the stocks and make basic return calculations. In the second stage,
you calculate summary statistics, and write up a short discussion about your data. You will make
formal portfolio theory calculations and run regressions for some tests. Your answers should be
1 Preliminary Data Work
1. [Downloading Data]
We collect price data for 10 stocks listed on the Australian stock market over the period from
December 2008 to December 2018. You will also collect price data for a broad market index
(e.g., the ASX 200) and yield data for a government bond.
(a) Go to the Yahoo Finance link https://au.finance.yahoo.com.
(b) You need to have 10 risky stocks with 9 stocks from (a) common companies and one stock
from (b) individual company in Table 1. The last digit of your SID number determines
the 10th stock from (b) individual company in Table 1. For example, if you SID is
47033566, you select Insurance Australia (IAG.AX) in number 6.
(c) In the Enter Symbol box at the top, type the symbol of the stock for which you want
data. For example, the symbol for Commonwealth Bank in CBA.
(d) Record the current market capitalization (“Market Cap”).
(e) On the left, under Quotes, click on Historical Prices.
1Go to Canvas → Modules → Final Project and then click Final project (proposal) for uploading your file.
2Go to Canvas → Modules → Final Project and then click Final project (excel zip file) for uploading your file.
Table 1: List of stocks
(a) common companies
CBA.AX Commonwealth Bank
CSL.AX CSL Limited
BHP.AX BHP Group Limited
WBC.AX Westpac Banking Corp
NAB.AX National Aust. Bank
ANZ.AX ANZ Banking Group Limited
WOW.AX Woolworths Group Limited
TLS.AX Telstra Corporation
WES.AX Wesfarmers Limited
(b) individual company
Number Code Company
0 MQG.AX Macquarie Group Limited
1 RIO.AX RIO Tinto Limited
2 WPL.AX Woodside Petroleum
3 NCM.AX Newcrest Mining
4 FMG.AX Fortescue Metals Group
5 ALL.AX Aristocrat Leisure
6 IAG.AX Insurance Australia
7 STO.AX Santos Limited
8 BXB.AX Brambles Limited
9 SUN.AX Suncorp Group Limited
(f) In the SET DATE RANGE box, select monthly and change the start date to December
31, 2008 and the end date to December 31, 2018. Click Get Prices.
(g) This will bring up the table with price data for the selected time period. Make sure that
the data are available at the beginning of the sample period.
(h) At the bottom of the screen, select Download to Spreadsheet. Change the name of the
file to the symbol name (e.g., cba.csv). (Note: csv stands for comma separated value
file, which is easily read by Excel.)
(i) Open the Excel file. The file will have the price data in descending order (most recent
data is at the top). You will want the data in ascending order. To do this, highlight all
of the data (including column headers). Then, select Data/Sort, which brings up the
Sort dialogue box. The default should have sort by date with ascending order selected.
If so, click OK. Otherwise, select those options and then click OK.
(j) Save the file. Note that the data you will use in the project are the Adj. Close data.
(k) When you have done this for 10 stocks, do the same for the market index. The symbol
for the ASX 200 is “AXJO”. Name the file “axjo.csv”. You can also find it by selecting ˆ
the Indices link from the initial Yahoo! Financial Quotes page. (As with individual
stocks, make sure to use adjusted price measure that includes dividends.)
(l) Finally, you will need data for the risk-free asset. Again, you can get data from the FRED
https://fred.stlouisfed.org/series/IR3TBB01AUM156N. You want yield data for
the 3-month bill yield. For this series, you only need data from January 2009 to December, 2018. Name the file “tbill.csv”.
2. [Return Calculations]
The next thing to do is to calculate continuously compounded returns for the ten stocks, the
market index, and the risk-free rate. For the price data, the procedure is standard. Compute
the continuously compounded monthly returns ln(Pt/Pt−1). (Note: you will not have a return
for Dec. 2008. The first return will be for Jan. 2009.)
For the risk-free rate, the given data is not price data, but annualized percentage yields. To
convert to a continuously compounded return, you need to first divide by 100 to get the
yield as a decimal. Then, take the natural log of (1+yield). Finally, you can convert to
a monthly continuously compounded return by dividing by 12. Also, construct an equalweighted portfolio for your 10 stocks (i.e., construct a return series that is an equal-weighted
average of the returns for the 10 stocks) and a value-weighted portfolio for your 10 stocks (i.e.,
construct a return series that is a weighted average of the returns for the 10 stocks, where the
weights are proportional to the current Market Cap for each firm). For the value-weighted
portfolio, a specific firm’s implicit weight is its market cap divided by the sum of the market
caps for all ten firms (collect all ten market caps on the same day).
1. [Summary Statistics]
(a) Compute time plots of each of the 12 return series (the 10 individual stock returns and
the equal-weighted and value-weighted returns). When reporting plots for each return,
report along with ASX200 return and risk-free return on each graph. Also, report the
Market Cap numbers for each firm and the corresponding weights used in constructing
the value-weighted return series. Provide time plots of the data but try to convey this
information in an efficient way by having multiple panels in a given figure. If there are
large outliers for any of the series, try to determine what happened at the time. Please
include this material in your final project too.
(b) Compute histograms for each of the 14 series (the 10 individual stock returns, the equaland value-weighted returns, the ASX 200 return, and the risk-free return). Do they look
Normal? Provide histograms. Make the presentation of graphs as concise as possible
(i.e., use multiple panels per page).
(c) Compute mean, variance, standard deviation, skewness, and kurtosis for each of the
14 series. Report kurtosis (not excess kurtosis). (Note: Usually, we think of a normal
distribution as having a kurtosis of 3. For reporting purposes use the standard definition
of kurtosis. )
If the mean is negative for any of the series, compute the median. Is the median positive?
If so, why do you think there is a difference between the mean and median? Also,
compare the standard standard deviations of the other 13 series to the standard deviation
of the ASX 200 return series. Provide tables reporting the summary statistics.
(d) Compute the (10×10) sample covariance matrix for 10 return series for the individual
(e) Compute the Sharpe Ratio for the 10 return series for the individual stocks and for
the ASX 200. You can use the average t-bill yield to proxy for the risk-free rate in
these calculations. This is equivalent to using the mean excess return for each stock to
estimate its risk premium. For the mean returns, use the median estimate if the excess
mean based on the sample average is negative. If it is still negative for the median
estimate, set the excess mean to zero.
2. [Test for Random-walk]
For individual stocks, i = 1, . . . , 10, you want to test H0 : φi = 1 for
ln(Pi,t) = αi + βi × t + φi
ln(Pi,t−1) + ei,t, ei,t ∼ iid(0, σ2
∆ ln(Pi,t) = αi + βi × t + γi
ln(Pi,t−1) + ei,t, ei,t ∼ iid(0, σ2
Construct t-statistics for H0 : φi = 1( or γi = 0). To do this, you will need to calculate the
OLS standard error. Show the t-statistic for each stock. Would you reject the null hypothesis
using a 5% critical value for a one tailed test? Note that the distribution for this test statistic
is different from Student-t distribution and use the critical value for the 5% test of -3.41.3
3. [Portfolio Theory Calculations]
(a) Using the estimated means and the sample covariance matrix, compute the global minimum variance portfolio for the 10 risky assets.
(b) Using the highest historical mean among 10 stocks as a target, compute a second efficient
(c) Using the two efficient portfolios computed in a. and b., compute the Markowitz bullet
(portfolio frontier for 10 risky assets).
(d) Using the mean monthly risk-free return, compute the tangency portfolio and the efficient
set for the 10 risky assets and a risk-free asset.
(e) Compare weights to the weights for the value-weighted portfolio based on current market capitalization. Discuss why you might expect the weights to be related and why
you might expect the weights to be different. (Hint: think about when the market
capitalization is measured.)
4. [CAPM Estimations]
(a) Using the risk-free rate data, calculate excess returns. Run the CAPM regression for
(b) For each stock, test the hypothesis that the intercept term αi = 0 versus the alternative
that it does not. Again, use a 5% test. Also, calculate the 95% confidence intervals for
If your regression equation does not have an intercept, yt = ρyt−1 + t, the 5% critical value is -1.94.
If it has an intercept yt = c + ρyt−1 + t, then the 5% critical value is -2.86.
(c) Test the CAPM by running a CAPM regression with the excess return on your tangency
portfolio as the dependent variable (instead of the return on a given asset, as in part
b.). Is α = 0?