ECON1195 Financial Econometrics
Assignment 1
March 2021
This is an individual assignment comprises 25% of the overall assessment.
It consists of Three questions. You need to attempt All three Questions.
This assignment is based on the relevant course materials (lectures, practice
exercises, R exercises, etc). It covers the lecture materials between week 1 and
week 5. Use 5% level of significance in all hypothesis test questions.
This assignment is due for submission on Canvas by Sunday, 11th April
2021. Answers can be typed or handwritten and scanned. You also need submit
your R script on Canvas.
Academic Integrity/plagiarism: You can achieve academic integrity by
honestly submitting work that is your own. Presenting work that fails to ac-
knowledge other people’s work within yours can compromise academic integrity.
Submission guidelines: All work for Assessable Tasks is required to be
submitted on the due date and time as outlined in the Assessment Briefs. The
exception to this is where an approved ELS plan, an application for Special
Consideration or an approved Extension of Time is in place, submitted before
the task’s due date with appropriate documentation.
Re-submission: can only be authorised in specific circumstances by formal
RMIT committees. Please visit the RMIT appeals site,
https://www.rmit.edu.au/students/student-essentials/rights-and-responsibilities/appeals,
for information for appealing a grade. Please visit the RMIT website,
https://www.rmit.edu.au/students/student-essentials/assessment-and-results, for
all information regarding adjustments to assessable work.
Late Submission: Work submitted within 7 calendar days of a due (or an
approved amended due) date may be accepted in exceptional circumstances but
will only be assessed as Pass (50%) or Fail. Work submitted beyond 7 calendar
days of a due date will be assessed as 0%.
1
Question 1
The dataset assignment capm.csv contains daily returns, it includes the fol-
lowing variables:
Mkt RF: excess return on a market portfolio (return on market portfolio minus
the risk-free rate);
SMB: measures the “size” factor;
HML: measures the “value” factor;
RF: risk-free rate as the U.S. Treasury Bill rate;
IBM: Continuously compounded returns on IBM stock (tech company);
Coca cola: Continuously compounded returns on Coca-Cola (retail company);
NRG: Continuously compounded returns on NRG (energy company);
(a) If we wish to invest in one stock, which one of these three stocks will you
suggest? Give your reasoning (model estimation and R codes are not required
in this question).
(b) Estimate the basic CAPM model (only consider the market portfolio in
the model) for each stock and write down the estimated models.
(c) Interpret the αˆ and βˆ in the CAPM for IBM.
(d) Is IBM an aggressive or conservative stock? Why?
(e) Compare αˆ from three models. What does it tell you?
(f) If the IBM stock is an independent portfolio (ie. β = 0), do you agree
that the percentage of idiosyncratic risk for this stock is 100%? Explain.
(g) Compare and provide an economic interpretation of these three R2 values
from the three regression models estimated in (b)?
(h) Fit the Fama-French three-factor model to each stock and write down
the estimated models.
(i) Test whether Fama French three-Factor model outperforms the CAPM
model.
(j) Write a summary of the market risks based on the results of the CAPM
models and three-factor models for three stocks.
2
Question 2
This question uses the same data given in Question 1. Suppose stock
A=IBM, stock B=Coca Cola and stock C=NRG. Let rA denotes the return
of IBM stock, rB denotes the return of Coca Cola stock and rC denotes the re-
turn of NRG stock, respectively; σ2A denotes the variance of return of IBM, σ
2
B
denotes the variance of return of Coca Cola stock and σ2C denotes the variance
of return of NRG, respectively.
We consider the following FOUR possible portfolios:
Portfolio 1: 30% stock A and 70% stock B;
Portfolio 2: 50% stock B and 50% stock C;
Portfolio 3: 60% stock A and 40% stock C;
Portfolio 4: 40% stock A and 50% stock B and 10% Treasury Bill (Let assume
Treasury Bill is independent of other three stocks);
(a) Compute the expected value of returns and variances of returns for all
four portfolios. You need to show the workings, for example:
E(portfolio 9) = E(axA + bxB + cxC) = aE(xA) + bE(xB) + cE(xC),
= 0.5× 10% + 0.4× 12% + 0.1× 1.5% = 11.3%
(b) If you were a conservative investor, which portfolio would you invest?
Explain.
(c) If you were aggressive investor, which portfolio would you invest? Ex-
plain.
3
Question 3
(a) Write down an MA(2) model.
(b) Derive the unconditional mean and unconditional variance for the MA(2)
model. You need show all the workings.
(c) The dataset assignment JNJ.csv contains only one variable: JNJ, which
is the daily stock price of the JohnsonJohnson Co. Read the data into R and
obtain the continuously compounded returns (in % by ×100). Construct one
line plot and one histogram with appropriate labels and title. In addition, make
some comments on these two graphs.
(d) Discuss the efficient market hypothesis (EMH) in detail. Is the return
series consistent with the EMH?
(e) Is it reasonable to fit the MA(2) model in (a) to the daily returns of JNJ
stock? Explain why or why not (you are not required to fit the model at this
stage).
(f) Estimate the MA(2) model and report the estimated model, is it reason-
able to fit the MA(2) model? Explain why or why not.
(g) If we wish to improve the model, provide two possible models and give
the reason why you think these two models are reasonable.
(h) Estimate the two models you suggest in (g) and write down the estimated
models.
(i) Compare all three models and select the best model to the data?
4