Subject of Accounting and Finance

Degree of MSc International Financial Analysis, MSc International Corporate

Finance and Banking

Degree Exam

Financial Econometrics, ACCFIN5217

Friday, 13 December 2019, 09:30-11:30

Question 1

An empirical regression model is specified to estimate the relation between the return ri,t of a stock i in day t and trading volume Vi,t- 1  in the previous day t- 1. The model also includes a short-sale variable Si,t- 1 , which measures the percentage of shares being sold short to the total number of shares outstanding. A regression equation, as shown below, is from the results of ordinary least squares (OLS) estimation based on time-series daily data from January 1975 to December 2018 as:

ri,t = 0.411 + 1.04Vt- 1  + 0.72 Si,t- 1               R2 = 0.31

(0.18)   (0.35)     (0.66)

The Newey-West (1987) standard errors are in parentheses below a coefficient estimate.

You are required to answer the following:

1.1    Set up the null and alternative hypotheses for a two-sided test for the relation between the return and trading volume of a stock, and compute the t-statistic for your test using a significance level of 5%. Your answer should include the economic meaning of the test result of the slope coefficient. (20%)

1.2    Construct a 95% confidence interval for the regression slope coefficient on trading volume, and use the 95% conference interval to justify whether you should or should not reject the null hypothesis in Question (1.1). (15%)

1.3    Suppose  that  the  correlation  coefficient  between trading volume  and short-sale  is  0.8. Critically discuss how this correlation may have affected the slope coefficient estimate and the standard error on trading volume, and the consequences to the test statistic. (15%)

(TOTAL 50%)

Question 2

An entrepreneur is interested in understanding what factors may contribute to the probability of successfully  creating  a  business.  To  this  end,  the  entrepreneur  collected  a  sample  of  100 business start-ups for the following regression analysis:

2.1  Run a Probit regression model to analyze whether the number of years of prior experience the entrepreneur has in the industry may affect the probability of success. The estimation results (standard errors in parentheses below coefficient estimates) are as the equation below:

Pr (Si,t  = 1| Exi) = 。(-2.19 + 2.97Exi,t)

(0.16)   (0.47)

where Si,t (success) is equal to 1 if the business of the entrepreneur i is profitable at time t, and is zero otherwise, Exi (experience) is the number of years of prior experience the entrepreneur i has in the industry when setting up the business.

From the above estimation results, explain whether the coefficient on Ex is statistically significant at the 5% level. Calculate the predicted probability of success S when the Ex is 0.3. What is the effect on the probability of Success of an increase in the Ex from 0.3 to 0.4? (15%)

2.2    It  has been  suggested  that  a  sole  ownership may  increase  the probability  of  getting  a successful business. Thus, you add a dummy variable, Sole, into the regression model. The results (standard errors in parentheses below coefficient estimates) are:

Pr (Si,t  = 1| Exi, Solei) = 。(-2.26 + 2.74Exi  + 0.71Solei)

(0.17)   (0.44)       (0.08)

where Solei  is a dummy variable = 1 if the person i has a sole ownership, and 0 otherwise.

From the above estimation results, explain whether the coefficient on Sole is statistically significant at the 5% level. When Ex is 0.3, what is the difference in the probability of Success between a sole ownership and not having a a sole ownership? (15%)

2.3    It has further been suggested that the equity ratio of equity to the total assets may influence the effect of a sole ownership on the probability of getting a successful business. Thus, you add an interaction term between Sole and a variable, Equity, into the regression model. The results (standard errors in parentheses below coefficient estimates) are:

Pr (Si,t  = 1| Exi, Solei, Equityi) = 。(-1.29 + 1.97Exi + 0.65Solei + 0.55Solei × Equityi)

(0.16)   (0.39)       (0.07)                (0.18)

where Equityi  is the ratio of equity to the total assets of business i when it is set up.

From the above estimation results, test whether the coefficient on interaction term Solei × Equityi  is statistically significant at the 5% level. Discuss what effect the equity ratio has on the probability of getting a successful business. (20%) (TOTAL 50%)