Econ634 econometrics and business statistics - conduct a

Question

Instructions

- This is a group assignment; groups may consist of up to 4 students.

- Part A is to be conducted jointly by the whole group (submit only one - group - version in the assignment)

- Part B is to be conducted individually by each group member
(submit 4 versions in the assignment - one for each group member clearly marking which version belongs to which member)

- Your final mark will be the sum of Part A (group) and Part B (individual)

- The assignment should be typed, with the main tables, charts and results presented throughout the assignment to highlight your responses to the questions

- Use the equation editor, e.g. write x_t^² instead of x^² (hint: google MS equation editorshortcuts for keyboard shortcuts)

- 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
- When conducting hypothesis tests, outline all steps in your answer
- Pages should be numbered
- Be as concise as you can, while clearly addressing each question

Data Description:

The excel file "assignment_data.xlsx" located under "Assignment" heading on iLearn contains six series for the period 03 January 2000 - 30 June 2016 totalling 4150 observations. The following variables are included

1. Returns on two portfolio:
- 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.
- BIG_LoBM - a portfolio consisting of all NYSE, AMEX, and NASDAQ stocks which are characterized as large companies with low book-to-market equity ratios.

2. Returns on three pricing factors from Fama and French (1996)

- mkt_rf (Market Risk Premium)
- hml (High minus Low)
- smb (Small minus Big)

3. risk_free (the US risk free rate)

Part A

1. How are the pricing factors computed and what do they represent? (hint: read the Fama and French (1996) paper - its on iLearn). Provide graphs and descriptive statistics for the SMALL_HiBM and BIG_LoBM portfolios and comment on their main characteristics.

2. Consider the following two models:

(SMALL_HiBM_t - risk_free_t) =  β₀ +  β₁mkt_rf_t + β₂hml_t + β₃smb_t + ε_t

(BIG_LoBM_t - risk_free_t) =  β₀ +  β₁mkt_rf_t + β₂hml_t + β₃smb_t + ε_t

What signs (positive or negative) would you expect to estimate for each of the factors in equations (1) and (2)? Explain the reasoning behind your answers?

3. Estimate both models given in question 2, and present the fitted equations. Interpret the fitted coefficients. Which parameters are statistically significant at the 5% level? Are the estimated parameters of the same sign as what you expected in Question 2?

Part B

4. Conduct a test for the validity of the CAPM relative to the three-factor model. What do you find?

5. Conduct the basic diagnostic tests on both estimated models (equations (1) and (2)) including

a. autocorrelation (use 4 lags of residuals),

b. heteroskedasticity (no cross product),

c. non-normality,

d. misspecification of functional form (only quadratic term).

e. Comment on all of your results and carry out remedies for problems you encounter. Do the results change after you have applied remedies?