Instructions
– This is an individual assignment. It should reflect your individual effort.
– The assignment should be typed, with the main tables, charts and results presented throughout the assignment to highlight your responses to the questions.
– There should be no appendices (appendices will not be marked).
– Marks will be awarded for neatness, conciseness and clarity of answers.
– Where answers call for explanation, a simple reporting of numerically correct results will yield few (if any) marks.
– Maximum number of pages allowed: 15 (additional pages will not be marked).
– Pages should be numbered.
– Be as concise as you can, while clearly addressing each question.
– Use a 5% significance level for all statistical tests unless otherwise instructed.
– Total marks: 50
Submission instructions
– You are required to submit the assignment in both print and electronic copies.
– Electronic submission is via a submission link on iLearn.
– Print copy (with a signed assignment coversheet) must be submitted at BESS (E4B).
– A link to the FBE cover sheet is provided under the “Assignment” heading on iLearn Fill in the details of the cover sheet and staple it to the front of your assignment.
Part A
Total number of marks: 25
The excel file “assignment_data.xlsx” located under “Assignment” heading on iLearn contains five series for the period 3 January 2000 – 29 December 2017 totalling 4528 observations. The following variables are included:-
1. Daily returns on two portfolios of stocks: • SMALL_HiBM – a portfolio consisting of all NYSE, AMEX, and NASDAQ stocks which are characterized as small companies with high book-to-market equity ratios. • market – a weighted portfolio of all the stocks in the market
2. Daily returns on two pricing factors from Fama and French (1996)
• ℎ?? (High minus Low)
• ??? (Small minus Big)
3. Daily returns on a risk free asset (US 4-week T-bill). The returns are only updated on the first day of the month in this data set but that is not important for this assignment.
• rf
Note: all of the returns are expressed in percent, e.g. 3.45% is represented by 3.45, not by 0.0345.
Answer the following questions:
Question 1.
What are the pricing factors smb and hml and how have they been computed? (hint: read the Fama and French (1996) paper – its on iLearn) (2 marks)
Question 2.
Open the excel data file in EViews (File/Open/Foreign data as workfile).
a) Create a new variable (mkt_rf) for excess returns of the market over risk free, also known as daily market risk premium, i.e. mkt_rf = market – rf. (hint: If you do this correctly the first value of mkt_rf will be -0.710.) Next, create a new variable for excess returns on the SMALL_HiBM portfolio, i.e. SH_rf = SMALL_HiBM – rf. (hint: if you do this correctly the first value of SH_rf will be -0.531.) (1 mark)
b) Provide a graph of rf and comment on its behaviour before and after the global financial crisis in 2008. (1 mark)
Question 3.
Provide a graph and descriptive statistics for both the SH_rf and mkt_rf returns, and compare them. Highlight any important differences between them. (3 marks)
Question 4.
Repeat the exercise from Question 3 for a different sample period: 3 January 2000 – 31 December
2007. You do not need to repeat the preliminary steps. Use the “sample” tab in Eviews to set the
new sample period. Comment on the performance of the SMALL_HiBM portfolio relative to the
market portfolio during this period. (2 marks)
For the following questions restore the sample period to the full period in EViews for the
remainder of the assignment, unless a question specifically asks you to do otherwise.
Question 5.
Estimate the following model for the full sample period:
0 1 2 3 _ _ t t t t t SH rf = + mkt rf + smb + hml + (1)
Present the fitted equation showing coefficient estimates, standard errors and t-statistics (type
the results in your assignment, do not simply copy and paste the EViews output). (4 marks)
Question 6.
Is the estimate of 0 significant at the 5% level? Explain your finding, do not just answer yes or
no. How do you interpret this result? (2 marks)
Question 7.
a) Explain whether we should expect the estimates of 1 2 , and 3 to be positive or
negative. (2 marks)
b) Are the signs of your actual estimates the same as what you expected? If not, how do they
differ? (1 mark)
Question 8.
a) Conduct a hypothesis test to determine whether ?0, ?2 and ?3 are jointly significantly
different to zero, i.e. test the following null hypothesis ?0: ?0 = 0 and ?2 = 0 and ?3 =
0. Set out all of the steps for a formal hypothesis test and state the conclusion. Use a 5%
significance level. (hint: in Eviews click View Coefficient diagnostics/Wald test) (2 marks)
b) What does your test result imply in relation to the validity of the CAPM? Why? (1 mark)
Question 9.
Conduct the basic diagnostic tests on the estimated model, i.e. autocorrelation (use 5 lags of
residuals), heteroskedasticity (White’s test with no cross product), non-normality,
misspecification of functional form (only one fitted term, quadratic). You do not need to write out
all of the steps of the hypothesis tests and you may copy the EViews output of the tests into your
assignment. However you must clearly write out the null and alternative hypotheses in each case, and clearly state the conclusion of each test. Use a 5% significance level. (4 marks)
Part B
Total number of marks: 25
Question 1.
Conduct ADF and KPSS unit-root tests on the market series for the full sample period (conduct the tests in levels, not differences, with an intercept and no time trend, and use default values for the remaining settings). Be careful to properly state the null and alternative hypotheses for the two tests. You may copy in the relevant parts of the EViews output. Comment on your findings. (4 marks)
Question 2.
Plot the ACF and PACF functions for market (include 12 lags). Comment on the magnitude and significance of the correlations. What optimal ARMA(p,q) model would you choose based on these graphs? Why? (4 marks)
Question 3.
Select an optimal ARMA(p,q) model for the returns based on an information criterion (see below). Select from the set of models up to and including the largest model of ARMA(3,3). You may use the automatic procedure (set no transformation, max.-difference=0 and max SAR=0) or you may undertake this task manually. (hint: Refer to examples in the Week 7 tutorial)
a) Present a single table of the criterion values for AIC, SBIC and HQ over all combinations of p and q. What is the preferred model on the basis of the AIC criterion? (2 marks)
b) What is the preferred model on the basis of SBIC? (1 mark)
c) Do both information criteria select the same model? Explain why the two criteria may select different models. (1 mark)
Question 4.
a) Estimate the ARMA(1,1) model for the market series. Report the fitted equation and comment on the significance of the parameter estimates. (3 marks).
b) Present the ACF and PACF graphs and statistics for the residuals (use 12 lags) and comment on them. (2 marks)
Question 5.
a) Perform a test for fifth order ARCH effects in the estimated residuals of the model in Question 4. (hint: After you estimate the model for Question 4, click on View from the
Equation Window and select Residual Diagnostics and then Heteroscesdasticity tests. In the ‘Test type’ box, choose ARCH and the number of lags to include is 5). Write out the null and alternative hypotheses for the test. Explain your conclusion from the test. (3 marks)
b) Estimate the ARMA(1,1)‐ARCH(5) model for the market series (hint: select Quick, Estimate Equation, under method select ARCH. In the mean equation box type market c ar(1) ma(1) and in the variance part, specify the order of ARCH as 5 and the order of GARCH as 0). Report the fitted equation. Do all of the parameter estimates satisfy the ARCH restrictions? (2 marks)
c) Graph the conditional variance from part (b) and comment on its behaviour. Explain why a GARCH(1,1) specification might be more effective for modelling persistent volatility clustering than the ARCH(5) specification (you are not required to estimate the GARCH model). (3 marks)
References
Brooks, C. (2014) Introductory Econometrics for Finance, 3rd edition, Cambridge University Press.
Econ334 Lecture Notes and Tutorial Questions and Solutions.
Fama, E. F., & French, K. R. (1996). Multifactor explanations of asset pricing anomalies. The Journal of Finance, 51(1), 55-84.
