Quantitative Finance and Methods Analysis - Statistics Project Example

Quantitative Finance and Methods work Report 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) Gearing is an independent variable, because it is expected to influence the probability going or not going into liquidation the following year (b) According to the logistic regression, determine the probability that Firm X is likely to go into liquidation in the following year. (10 marks) Given one independent variable, x: ln[pi/(1 – pi)] = a + bxi, pi/(1 – pi) = exp(a + bxi), – 0.1+ 0.6+ 1.5– 0.1– 0.4= +1.5 pi = exp(– 1. 0+ 1.5xi)/[1 + exp((– 1. 0+ 1.5xi)]. Logistic regression results Coefficient Probability Expected Return on capital employed – 0. 4 0.04 -0.016 Gearing +0. 1 0.40 0.04 Turnover ratio + 0.3 0.70 0.21 current ratio – 0.2 0.01 -0.002 Retained earnings/total assets – 0. 6 0.52 -0.312 0.08 If the accumulated average ratio is 0.08, then: pi = exp(– 1. 0+ 0.12)/[1 + exp((– 1. 0+ 0.12)]. =-0.88/-1.88 =0.468 Therefore, it is 46.8% probable that Firm X is likely to go into liquidation in the following year 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? Considering that return on capital employed and retained earnings/total assets have a very high correlation (0.6), it would be advisable to remove both of them in order to avoid the problem of problem of multicollinearity. Regarding whether to remove either retained earnings/total assets or return on capital employed based on the likelihood ratio tests, it will depend on their respective p-values. The one with its p-value approaching 1 than the other should be removed, as that implies that it is irrelevant. (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) Row 104, which indicates a Pearson residual of 9.5 creates more of a problem for the fitted model, possibly because there was a fault in the computation of data. (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) Firms with a higher current ratio are more likely to go into liquidation. This is because if we were to carry out a comparative analysis between the original logistic regression and Firm X statistics, it is apparent that the lower the returns of a firm, the higher the current ratio. Furthermore, it is a common knowledge that the firms with lower returns are the ones with the highest possibility if of going into liquidation. (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) since we have concluded that firms with a higher current ratio are more likely to go into liquidation, the p-value must be less than 0.05, which shows that the model is statistically significant at the 95% confidence level. (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) Supposing firm x had a coefficient of +2.0, then: pi = exp(+0.5 + 0.12)/[1 + exp((+0.5+ 0.12)]. =0.62/2.62 =0.247< 0.468 This means that a firm with a lower, but positive, return on capital employed is less likely to go into liquidation (2) whether a firm with a lower, but negative, return on capital employed is more likely to go into liquidation, and (3 marks) Following the results in g(1), that a firm with a lower, but positive, return on capital employed is less likely to go into liquidation; clearly the results for this case is vice versa. (3) whether the above two results are statistically significant, at the 95% level of confidence. (2 marks) Whether the above two results are statistically significant, at the 95% level of confidence will depend on the p-value generated from the computer. If p-value is less than 0.05, the two results are statistically significant, at the 95% level of confidence. (Total: 37 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) (Total: 50 marks) Overall Total: 100 marks Read More