SMM466 Applied Empirical Accounting 2020
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MSc International Accounting & Finance
SMM466
Applied Empirical Accounting
2020
Section A
(50 marks total – Answer all questions)
Question A.1
A researcher is interested in assessing the driving factors of the returns on BP. She has collected a sample of monthly data on the returns on BP (BP) and of monthly factors covering the same time period: the MARKET(MARKET) is the excess return on the FTSE100; the size factor (SIZE) is the return on a portfolio of small stocks less the return on a portfolio of large stocks. The researcher estimates a multiple linear regression model using OLS and obtains the following estimation output.
Dependent Variable: BP
Method: Least Squares
Sample: 1980M10 2000M09
Included observations: 240
Variable Coefficient Std. Error t-Statistic Prob. |
|||
C 0.008951 0.002103 4.255616 0.0000 |
|||
MARKET |
0.701381 |
0.044070 15.91511 |
0.0000 |
SIZE |
1.003009 |
0.069573 14.41661 |
|
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) |
0.636695
0.245402 485.7144 207.6726 0.000000 |
Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat |
0.014684 0.053162 -4.022620 -3.979112 -4.005089 1.343742 |
a. Write down the model being estimated and the fitted model.
Define and compute the adjusted R- square of the model. What does this tell you? Define and compute the standard error of the regression.
(7 marks)
b. Is the regression significant overall? Justify your answer. Interpret all the coefficients that the researcher has obtained and run the hypothesis tests that you feel are appropriate for understanding the determinants of the returns on BP.
(10 marks)
c. Can you conclude from the regression output above that the impact of SIZE on BP is bigger than 1? Justify your conclusion.
(5 marks)
d. The researcher wants to find out if the model in a) is an improvement with respect to full four factor model, thus she runs the regression adding two more variables: VALUE, the value factor defined as the return on a portfolio of high value stocks less the return on a portfolio of low value stocks (where value is measured using the book-to-market ratio), and the momentum (MOMENTUM) which is the return on stocks that have performed strongly over the last year less the return on a portfolio of stocks that have performed poorly. She obtains the following regression output
Dependent Variable: BP
Method: Least Squares
Sample: 1980M10 2000M09
Included observations: 240
Variable Coefficient Std. Error t-Statistic Prob.
C |
0.006812 |
0.002148 |
3.171613 |
0.0017 |
MARKET |
0.708147 |
0.042934 |
16.49390 |
0.0000 |
SIZE |
1.028737 |
0.069503 |
14.80127 |
0.0000 |
VALUE |
0.299247 |
0.075743 |
3.950830 |
0.0001 |
MOMENTUM |
0.202169 |
0.075786 |
2.667638 |
0.0082 |
R-squared |
0.659428 |
Mean dependent var |
0.014684 |
Adjusted R-squared |
|
S.D. dependent var |
0.053162 |
S.E. of regression |
0.031288 |
Akaike info criterion |
-4.070567 |
Sum squared resid |
0.230047 |
Schwarz criterion |
-3.998053 |
Log likelihood |
493.4680 |
Hannan-Quinn criter. |
-4.041349 |
F-statistic |
113.7537 |
Durbin-Watson stat |
1.490006 |
Prob(F-statistic) |
0.000000 |
|
|
Comment on the change in explanatory power of the model and test if the specification proposed in a) is an improvement relative to this simple linear specification.
(6 marks)
e. The researcher suspects that the regression errors of the model in d) might exhibit serial correlation and she runs the test displayed below. Explain which test for serial correlation is reported, clearly stating the null and the alternative hypotheses, the auxiliary regression, the test statistics, and its distribution under the null. Comment on the p-values and draw conclusions. How can the serial correlation be remedied?
(7 marks)
Serial Correlation LM Test:
F-statistic Obs*R-squared |
2.169032 Prob. F(12,223) 25.08474 Prob. Chi-Square(12) |
0.0141 0.0144 |
f. The researcher wants to test for the presence of a structural break in January
1993. Describe the Chow break test, stating very clearly the null and alternative hypotheses of the test, the restricted and unrestricted model, the test statistics and its distribution under the null hypothesis.
(5 marks)
Question A.2
Write down the Gauss-Markov assumptions for the following simple linear regression model
yi = Fxi + ei
Define and derive the OLS estimator of F .
(5 marks)
Question A.3
Consider the following multiple linear regression model:
y= βX+ u
Write down the formula of the OLS estimator of β . Find the variance of the estimator assuming that all the classical linear regression assumptions are satisfied and that the estimator is unbiased.
(5 marks)
Section B
(50 marks total - choose TWO of the following THREE questions)
Question B.1
a. A researcher is interested in identifying day of the week effects in the returns on Jo Malone London, a luxury candles company. Note that stocks are traded only five days a week. She collects a sample of returns on Jo Malone, and a sample of returns on the FTSE100 index for the same time period. Then she creates five dummy variables, D1,t , D2,t , D3,t , D4,t , D5,t , one for each day of the week . D1,t takes value one on Monday and zero on any other day of the week and the other dummies are defined similarly for the other days of the week. Explain why the model
rt =α +β rtM + γ1D1t + γ 2D2t + γ3D3t + γ4D4t + γ5D5t + ut
suffers from perfect multicollinearity. Write down two different specifications of the model that allow for seasonality effects without causing perfect multicollinearity. Interpret the parameters of the dummy variables in both models.
(10 marks)
b. Discuss the problem of heteroskedasticity in the multiple linear regression model. Which are its consequences on the OLS estimator? Can the estimator still be used? How can such a problem be remedied?
(7 marks)
c. In a multiple regression model
y = Xβ + u
define the consistency of an estimator. Discuss two possible situations that cause inconsistency in the OLS estimator in the model above.
(8 marks)
Question B.2
A researcher collects data on the daily returns on LVMH and runs a simple linear regression model of LVMH returns on S&P500 returns. Note that returns are defined as log returns. The features of her data are the following:
N 22
Xt(2)
Xtyt
t(2)
0.134
5.227
675
15.04
0.011
a. Using the data above, compute the intercept and slope coefficients from a regression of investment rates on interest rates. Give an economic interpretation of your results.
(5 marks)
b. Write down the formulae for the standard errors of the OLS estimator of the slope and the intercept coefficients. Discuss how the sample size, the error variance and the sample variance of x influence the precision of the estimators. Compute the standard errors of the estimates and comment upon the estimates’ precision. Test the null hypothesis that the slope equals zero against the one-sided alternative that is less than zero. Interpret your results.
(10 marks)
c. Write down the Gauss-Markov assumptions for the following multiple linear regression model
y = βX+ u
Discuss the properties of the OLS estimator under these assumptions. How are these properties affected if the regression errors display heteroskedasticity? Are the OLS estimation results still valid in presence of heteroskedasticity?
(10 marks)
Question B.3
In the multiple linear regression model
y = Xβ + u
a. Derive the variance of the OLS estimator of the parameters under serial correlation. Will it be bigger or smaller than under no serial correlation? Discuss.
(10 marks)
b. Discuss the problem of misspecification of the linear regression model and explain its consequences on the OLS estimator. Make sure to discuss both cases of misspecification.
(10 marks)
c. Show that the OLS estimator of β the model is unbiased even if the homoscedasticity assumption is violated.
(5 marks)
2022-08-02