**Faculty of Business and Law**

**School of Accounting, Economics and Finance**

**Student to complete:**

Family name

Other names

Student number

Table number

ECON339

Applied Financial Modelling

Wollongong

Final Examination Paper

Spring 2020

Exam duration | 3 hours |

Weighting

50 %

Items permitted by examiner

UOW approved calculator

Aids supplied

None

Directions to students

Answer ALL questions in Sections A and B.

This test is graded out of 50:

Section A – 15 marks, Section B: B1 – 20 marks and B2 – 15 marks.

Submit your answer in WORD document through Turnitin on the Moodle page.

**This exam paper must not be removed from the exam venue**

**Section A. Answer all questions. (15 marks, 1 mark each)**

1. Violating which of the classical linear regression model assumption will lead to an inconsistent OLS estimator? [1]

2. State two methods that can be used to estimate simultaneous equation regression models. [2]

3. In a system of equations given below, Y’s are endogenous while X’s are exogenous. Which of the equation is over identified? Explain. [2]

4. State two properties of a good instrument when applying an instrumental variable approach? [2]

5. State one advantage of using a Vector Autoregression (VAR) model. [1]

6. Name the tool used to produce a graph that plots the correlation of each residual with lags of itself and with all other residuals in a VAR model. [1]

7. In the following VAR model, write down the null hypothesis for the Granger causality test of does not Granger cause ? [1]

8. Name the decomposition that identifies the structural shock from the reduced form shock in a VAR model. [1]

9. In a VAR model, name the method of analysing the proportion of the movements in the dependent variables that are due to their “own” shocks, versus shocks to the other variables. [1]

10. The diagram below depicts the plot of a series X. State a property of the series that suggests the series may not be stationary. [1]

11. Suppose stock price *y _{t} *follows the process:

*y*

_{t}=*m*

*+*

*f*

*y*

_{t-}_{1}

*+ u*If f>1, what can be said about the effect of the stock price shock

_{t}.*u*on stock price

_{t}*y*? [1]

_{t}12. A plot of the series X is depicted below. Write down the appropriate regression specification for a unit root test of series X. [1]

**Section B. Answer ALL questions (35 marks)**

**Question B1 (20 marks)**

In the paper on the “Overreaction Hypothesis and the UK Stock Market” by Clare and Thomas (1995), the authors employed monthly UK stock returns from January 1955 to December 1990 on all firms traded on the London Stock exchange to run a regression

(B1-1)

where , denotes the monthly average excess return over the stock market and *t* denotes the 18 independent tracking periods. and are the loser’s and winner’s portfolio returns respectively.

- State the overreaction hypothesis and how can one use regression (B1-1) to test for the overreaction hypothesis? [2]

(b) Suppose the loser stocks are generally more risky, explain the drawback of using regression (B1-1) when testing the overreaction hypothesis. How would you correct for it? [2]

Using the data employed by Clare and Thomas (1995), suppose you are interested in analyzing whether there are quarterly return differences between the loser and winner portfolios. You estimated the following regression by OLS:

(B1-2)

where , *R* denotes monthly excess return over the stock market, is a dummy variable for *i*=1, 2 and 3 such that if return is in the *i*-th quarter and 0 otherwise.

The result is

- What is the difference in the mean return between the first and second quarter? [1]

- Now define a fourth quarter dummy as 1 if return is in the fourth quarter and 0 otherwise. Suppose you drop the first quarter dummy from regression (B1-2) and include the fourth quarter dummy instead such that

. (B1-3)

What will the estimated value of now be? [4]

- Suppose you run an additional regression:

. (B1-4)

For this regression, the RSS=720. The sample consists of 420 observations. Use the critical value for the F-distribution, F(3,416)=2.60. The formula for the F-test is *F=***.**

With this information, formulate and test the hypothesis of no quarterly return differences between the loser and winner portfolio at 5% level of significance. [3]

- Can one run the following regression

(B1-5)

to analyse whether there are quarterly return differences between the loser and winner portfolio? Explain. [2]

(g) Referring to part (b), suppose the differences between the loser and winner portfolio may differ prior to the black Monday crisis on October 19, 1987 when stock markets around the world crash. You plan to run a CAPM regression to test whether there is structural stability in the coefficient estimates of the regression. Explain how you can perform a Chow test to determine the presence of structural stability. [6]

__Question B2 (15 marks)__

The graph below shows the plot of the log prices for SPOT denoted by LSPOT and FUTURES denoted by LFUTURES.

LFUTURES |

LSPOT |

(a) Is the statement “LFUTURES leads LSPOT” true or false? Explain. [1]

(b) A student runs the following regression to determine the relationship between LFUTURES and LSPOT:

Is this the correct regression to run? Explain based on your answer in (a). [2]

The results of the Augmented Dickey Fuller test for both series are shown below.

Exogenous: Constant, Linear Trend |

Lag Length: 1 (Automatic - based on SIC, maxlag=10)

t-Statistic

Prob.*

Augmented Dickey-Fuller test statistic

-4.515486

0.0031

Test critical values:

1% level

-4.107947

5% level

-3.481595

10% level

-3.168695

*MacKinnon (1996) one-sided p-values.

__Unit Root Test for LFUTURES__

Exogenous: Constant, Linear Trend |

Lag Length: 0 (Automatic - based on SIC, maxlag=10)

t-Statistic

Prob.*

Augmented Dickey-Fuller test statistic

-3.284052

0.0780

Test critical values:

1% level

-4.105534

5% level

-3.480463

10% level

-3.168039

*MacKinnon (1996) one-sided p-values.

(c) Explain the difference between the Augmented Dickey Fuller (ADF) test and the Dickey Fuller (DF) test. Why does one perform an ADF test in the presence of autocorrelation? [2]

(d) Stat the null and alternative hypotheses for the ADF test. Using the unit root test results, what do you conclude about the stationarity property of LSPOT and LFUTURES at the 5% significance level. [2, 2]

(e) Provide two different and alternative terminologies for a series that has a unit root. [2]

(f) State and explain two problems associated with using LSPOT and LFUTURES in regression analysis? [2]

The table below shows the results of the Engle and Granger test. The test is performed with LSPOT as the dependent variable followed by LFUTURES as the dependent variable.

Series: LSPOT LFUTURES |

Sample: 2002M02 2007M07

Included observations: 66

Cointegrating equation deterministics: C @TREND

Automatic lags specification based on Schwarz criterion (maxlag=10)

Dependent

tau-statistic

Prob.*

z-statistic

Prob.*

LSPOT

-8.101528

0.0000

-66.98674

0.0000

LFUTURES

-7.928076

0.0000

-65.65357

0.0000

*MacKinnon (1996) p-values.

(g) What can you conclude about the nature of long run relationship (or cointegration) between LSPOT and LFUTURES based on the Engle and Granger test results? Explain. [2]