Quantitative Finance and Methods

Part A: Analysing Computer Output

Q1.    In the evaluation of corporate liquidations, a logistic regression is used. Based on historical data, a firm is assigned a value one if it goes into liquidation the following year, and zero if it does not. Computer output shows:

Logistic regression results                              Coefficient     Probability
Constant                                     €“ 1. 0           not given
Return on capital employed                                 €“ 0. 4             0.04
Gearing                                                                 +0. 1             0.40
Turnover ratio                                                     + 0.3           0.70
Current ratio                                                                        €“ 0.2           0.01
Retained earnings/total assets                                  €“ 0. 6          0.52

The above probabilities are derived from likelihood ratio tests.
Firm X, which is not in the original sample, has values of:

Return on capital employed                                  €“ 0.1
Gearing                                                              + 0.6
Turnover ratio                                                   + 1.5
Current ratio                                                           €“ 0.1
Retained earnings/total assets                             €“ 0.4

Required

(a)    State whether gearing is a dependent variable or an independent variable
of the logistic regression.                                                                (1 mark)

(b)    According to the logistic regression, determine the probability that Firm X
is likely to go into liquidation in the following year.                      (10 marks)

(c)    From a table (not shown) representing a correlation matrix, you find that
return on capital employed and retained earnings/total assets have a correlation coefficient of 0.6, compared with other coefficients which are all less than 0.4 in absolute terms. Bearing in mind the correlation matrix and the likelihood ratio tests, which one variable might you consider removing and why?                                                                                      (8 marks)

(d)    A table of residuals shows two entries:

Row 46 indicates a Pearson’s residual is 3.2.
Row 104 indicates a Pearson residual of 9.5.

Which of these two outliers creates more of a problem for the fitted model?
(1 mark)

(e)    From the coefficients of the original logistic regression, and ignoring the likelihood ratio tests, is it generally true that firms with a higher current ratio are more likely to go into liquidation? Explain.                               (6 marks)

(f)    Taking into account the likelihood ratio tests, is your conclusion from
part (e) statistically significant at the 95% confidence level or not?
(3 marks)

(g)    Bearing in mind both the logistic regression coefficients and the likelihood ratio tests, state:

(1)    whether a firm with a lower, but positive, return on capital employed is more likely to go into liquidation,                                               (3 marks)

(2)    whether a firm with a lower, but negative, return on capital employed is more likely to go into liquidation,  and                                       (3 marks)

(3)    whether the above two results are statistically significant, at the 95% level of confidence.                                                                   (2 marks)
Q2.   In evaluating the default risk of bank customers, two approaches are used, namely, multiple discriminant analysis and conventional methods. From a sample of 460 customers, observed results and predicted results of good and bad loans are summarised below.

MDA
Predicted
1= good        0 = bad

Observed
1 = good                                         300                  20
0 = bad                                             40                100

Conventional

Predicted
1= good        0 = bad

Observed
1= good                                                 270             50
0 = bad                                                   20            120

Required: Compare and contrast the classification rates for the two approaches.
(Total 13 marks)

Part B: Research Design

Q3. You are working on a research project on capital structure. You are surprised to find that for your sample of firms a sizeable proportion use all-equity finance, although the majority do not. Nevertheless, you are interested in pursuing the phenomenon, and decide to use logistic regression. For this aspect of the project involving logistic regression:

(a)    State what the object of the study would be.                                      (4 marks)
(b)    Define the dependent (zero-one variable).                                         (6 marks)
(c)    Define three suitable independent variables.                                   (12 marks)
(d)    Explain why the particular independent variables have been chosen
(9 marks)
(e)    Explain whether they are hypothesised as being positively or negatively associated with the dependent variable, and                                   (12 marks)
(f)    Choosing any two of your independent variables give one financial reason as to why there may be a multicollinearity issue.                                   (7 marks)