Data Used For Regression Analysis Finance Essay - Free Essay Example

This part of the study will deal with the results obtained from the regression analysis. It will also include a second part which will focus on discussion and interpretation of the results which have been obtained following the regression analysis. 4.1 DATA USED FOR REGRESSION ANALYSIS For the regression analysis time series data has been used for the variables, both dependent and independent. The data used ranges from 2000 Q1 to 2012 Q2. The independent variables used are namely GDP growth, short terms interest rate, change in inflation rate and corporate indebtedness. The graphs below show the data which have been used for all the independent variables. From the figure below, it can be observed that GDP growth had always been a positive figure before the crisis. However, during and after the crisis this situation has changed to a worsening one whereby instead of having growth in the value of the gross domestic product, the country was experiencing a decline in GDP. Figure 1: GDP Growth from 2000 Q1 to 2012 Q2 Looking at Figure 2 below, it can be found that interest rates during the crisis were at a really high value. After this period of 2007/2008, however the interest rate figure has declined. Figure 2 : Short Term Interest Rates from 2000 Q1 to 2012 Q2 From the graph below, which shows the non performing ratio against time, it can be seen that the NPL ratio has had an abrupt increase during the Global Financial Crisis. The situation is now changing and last year has experienced a small but significant decrease in the value of the NPL ratio. This is surely an indication that the situation is getting better and that the credit risk faced by banks has started to decrease. Figure 3: Non Performing Loans From the above figure, it can be seen that corporate indebtedness has increased during the Global Financial Crisis perhaps mainly due to the fact that firms were facing hard times and that they had to borrow more money to inject in the businesses in order to survive. The value of corporate indebtedness has started to go down and we can only hope that this situation will continue. Inflation has also increased during the peak of the Global Financial crisis but since 2010 has started to decline as well. This can certainly be interpreted as good news for the economy in general and also for banks. A low inflation rate is a sign that the economy is in good health. 4.2 REGRESSION ANALYSIS The multiple regression analysis was carried out by regressing Non Performing Loans Ratio of UK banks on Gross Domestic Product (GDP) growth rate, short term interest rate, inflation growth rate and corporate indebtedness for the United Kingdom. The data can be termed as time series data and the method used is multiple regression analysis which involves the use of ordinary least square method. The regression was run using the Microsoft Office tool, Microsoft Excel 2007. The results which were then analysed and interpreted for the purpose of the study are namely: the coefficients, the t-ratios, the probability values obtained for each and every independent variable of the regression analysis. The R-squared and the adjusted R-squared values were also interpreted as well as the f-statistics and the Durbin-Watson statistic. The results of the regression can be seen in Appendix II. 4.2.1 P-Values of the independent variables. In statistics and economics, the p-value is defined as the probability of obtaining a test statistic which is at least as extreme as the one that was actually observed, under the assumption that the null hypothesis is not false. A low p-value usually implies that the result has lower chances of actually happening if the null hypothesis is true. Therefore, the result is believed to be more significant if the p-value is low in terms of statistical significance. Generally, the null hypothesis is accepted and the alternative is rejected and the alternative one accepted if the p-value is less than 0.01 or 0.05 which corresponds to a 1% or 5% chance of rejecting the null hypothesis. The p-values of the independent variable will usually provide an indication as to whether those variables are statistically significant or not. P-values for the different variables are shown in the table below: Independent variables P-values GDP growth rate 0.000356979 Short term Interest rate 1.64154E20 Inflation growth rate 0.350536289 Corporate indebtedness 7.51904E10 From the above table, it can be seen that the p-value for the independent variable GDP growth rate which is 0.000356 is far less than 0.01. thus, it can be implied that this variable is statistically significant at 1%, 5% and 10%. The above conclusion is also true for short term interest rate and corporate indebtedness which demonstrate really low p-values, found below 0.01. However, inflation growth rate has a high p-value and it would therefore be reasonable to conclude that its p-value show that it is statistically insignificant at 1%, 5% and 10%. 4.2.2 T-Ratios T-Ratio is often used in statistics and econometrics to measure whether an independent variable is statistically significant in explaining the dependent variable. It is normally calculated by dividing the estimated regression coefficient by its standard error. Thus, the t-statistic, as it is also called, is a tool for measuring the number of standard errors from which the coefficient is away from zero. T-Ratio values are generally accepted if they are found to be greater than +2 or less than -2. The various T-statistic values for the independent variables used in the regression are listed in the table below: Independent variables T-statistics GDP growth rate -3.862330603 Short term Interest rate -16.30973301 Inflation growth rate 0.943356008 Corporate indebtedness 7.767907625 From the regression results, it can be observed that the second variable which is short term interest rate has a very high negative t-ratio of -16.30973301. This implies that the short term interest rate independent variable is statistically significant and that it greatly contributes in predicting the value of the dependent variable which is the non performing loans ratio. An interpolation could be made and it could even be even said that the short term interest rate charged by banks is one of the main aspect which would help in determining the non performing loans ration of banks. The next variable investigated which is inflation growth rate has a t-ratio of a value of 0.943356008. This implies that the inflation growth rate is statistically insignificant as it has a value of less than 2. Thus the Non performing loans ratio of banks is not really dependent on the inflation growth rate. It might have an indirect effect on the balance sheet of banks but according to the regression analysis performed in this study it does not have any direct relationship. The third independent variable which is the Gross Domestic Product growth rate has a t-ratio of -3.862330603 according to the results of the regression. This can be interpreted as being statistically significant as the value is less than -2. Therefore it can be said that the GDP growth rate has an impact on the NPL ratio value of banks in general. It could be concluded that if the value of GDP growth rate is high the NPL ratio value will on its part undergo a decrease. The last independent variable which has been investigated is corporate indebtedness. The results of the regression show that its t-statistics has a value of 7.767907625 which makes it statistically significant as its value is greater than 2. Therefore it can be said that corporate indebtedness definitely has an impact on the non performing loans ratio of banks and the positive sign of it shows that if the amount of debt taken by companies increases, so will the non performing loans ratio of banks. It would be quite logical to come to such a conclusion as if the number of loans increase the probability of default will also go up and therefore the credit risk faced by banks will also be larger. 4.2.3 Values of the coefficients of the independent variables The degree to which the independent variables are associated with the dependent variable can be often identified by analysing the coefficients of the independent variables after the regression is run. In this particular study, it will indicate to what extent the independent variables GDP growth rate, Short term interest rates, inflation and corporate indebtedness will affect the dependent variable which is the non performing loans ratio of UK banks. For the first independent variable which is the Gross Domestic Product Growth rate, its coefficient after running the regression is found to be -0.330019012. The coefficient being negative, it could be argued that GDP growth rate has a negative relationship with the dependent variable (NPL ratio). Also, considering the results of the p-value and t-statistics for the same variable it can further be said that GDP growth rate has a negative and statistically significant relationship with non performing loans ratio. Thus it can be assumed that if GDP growth decreases non ÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã… ¡Ãƒâ€šÃ‚ ¬performing loan ratio will increase. The next variable investigated is short term interest rates charged by banks which has a positive coefficient of 0.516833108. This implies that short term interest rates has a positive relationship with non performing loans ratio and that it could well be that it could have an impact on the dependent variable. This is accentuated by the fact that both the p-value and the t-statistics are statistically significant. So, it could be concluded that that short term interest rates can have a significant impact on the credit risk faced by banks. The higher the interest rate charged the greater are the chances of having a higher probability of default rate. The third variable which is inflation is statistically insignificant when looking at its p-value and t-ratio. However the fact that its coefficient is positive shows that non performing loans ratio will tend to rise with an increase in inflation. With a high inflation rate, domestic banks may face a higher level of credit risk as with a general increase in the price level, companies and even individuals may find it hard to pay back their loans. Corporate indebtedness also has a positive coefficient which would normally lead to the conclusion that the non performing loans ratio will undergo an increase if debt from the private sector goes up. It is quite logical to come to such a conclusion as the greater the amount of loans given by banks to companies and firms, the greater will be the probability of default. Credit risk faced by banks normally depend also a lot on the types of loans given to firms and also on the collateral which has been given as guarantee. So, the level of debt of companies plays a major role in the estimation of a default rate for banks. 4.2.4 R-Squared values R-squared, also termed as the coefficient of determination is the most commonly used measure of the goodness of fit of a regression line. R squared measures the proportion or percentage of the total variation in the dependent variable explained by the regression model. R squared is normally non negative and values are found to be between zero and one. A value of 1 usually means a perfect fit while a value of zero would normally mean that there is no relationship between the dependent variable and the independent variables. R square also provides a measure of how well future values are likely to be estimated by the system of equations and the regression analysis. R squared is calculated as follows: R2 = 1 SSE / SST For the model used in this present study, it can be observed that the R-squared value is quite high. It is equal to 0.8 and is close to 1.0. Thus it can be deduced that the dependent variables are highly correlated with the dependent variable. The dependent variable which is the non performing loans ratio can therefore be said to be highly related to the dependent variables which are the gross domestic product (GDP) growth rate, short term interest rates, inflation rate and corporate indebtedness. Consequently, it can be said that about 85% of the variation in the dependent variable which is the non performing loans ratio is explained by the independent variables found in the equation while the remaining 15% is explained by the error tem. The error term will usually capture the factors which have not been mentioned in the set of independent variables. The error term will represent the effect of those variables which have not been included in the regression. 4.2.5DurbinÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã… ¡Ãƒâ€šÃ‚ ¬Watson statistic The Durbin-Watson statistic is a test which is used in statistics and econometrics to allow the detection of autocorrelation in the residuals which have been obtained after the regression has been run. If et is the residual associated with the observation at time t, then the test statistic is d = {sum_{t=2}^T (e_t e_{t-1})^2 over {sum_{t=1}^T e_t^2}}. In simpler terms it can be said that d is approximately equal to 2(1-r) where r is the sample auto correlation of the residuals obtained after the regression has been run. The value of this statistical value normally lies in the range of zero to four. A value of d being equal to 2 suggests that there is no presence of autocorrelation while small values of d are usually a sign that successive error term are positively correlated. A value which is inferior to one is also seen as being a bad sign. A level of more than 2 would mean negative autocorrelation and this would imply underestimating the level of significance. Here, it can be seen from the regression results that it has a value which is positive and quite strong of 1.7953 and therefore we can deduce that there is no misspecifications of errors. It can therefore be deduced that there is evidence of positive serial correlation. 4.2.6 Correlation between the variables    GDP IR INFLATION DEBT NPL GDP 1 IR 0.19246 1 INFLATION -0.14265 -0.1936 1 DEBT -0.46554 -0.37221 0.485733 1 NPL -0.1691 -0.81042 0.003032 -0.07156 1 Correlation analysis has as main objective to measure the strength or degree to which the variables in an econometric model are associated. The correlation coefficient will normally measure the strength of this relationship. While doing correlation analysis, the average value of one variable based on the fixed value of one other variable is attempted to be estimated or predicted. In correlation analysis the variable are treated symmetrically, that is, there is no distinction between the dependent and independent variables. Also, both variables are considered to be random. The correlation coefficient is normally situated between -1 and +1, whereby -1 value indicates perfect negative correlation while a value of +1 indicates positive correlation. A value of zero is seen as the variables not having any relationship between them. From the above results its can be seen that the correlation between non performing loans ratio and the GDP growth rate is negative which therefore leads to the conclusion that they are negatively correlated. Thus when the GDP growth rate will go down, the NPL ratio will go up and vice versa. The rest of the independent variables which are namely inflation growth rate, short term interest rate and corporate indebtedness all have positive correlation values which suggest that if their values would be on an increasing rend so will the value of the nonperforming loans ratio. This is certainly in line with the results of the regression analysis performed whereby it was found that an increase in GDP growth would mean a decrease in the probability of default while an increase in corporate indebtedness, short term interest rates or inflation would mean a rise in the value of the non performing loans ratio. 4.2.7 F-test An F-test is a test widely used in statistics and econometrics in which the test statistic has an F-distribution under the null hypothesis. The f-test is most widely used when comparing statistical models that have been fit to a data set, in order to identify the model that best fits the population from which the data were sampled. Exact F-tests mainly arise when the models have been fit to the data using least squares. The overall F-test is also significant according to the regression results having a value of F-stat. F( 3, 16) 2927.1[.000] We can thus deduce that we can reject the null hypothesis that all slope coefficients are simultaneously zero and accept the alternative hypothesis that the coefficients are not equal to zero. 4.3 Stress testing with the model To be able to stress test the equation which has been modeled in the previous chapter, an artificial shock can be introduced in the multiple regression analysis. The elements of the independent variables are replaced by the various which have been assumed. The shocks are introduced at the start of the multiple regression analysis. The non performing loans ratios for the assumed stress test scenarios are then calculated. In the following sections, three examples of macro stress testing will be considered. First, the impact of a temporary negative gross domestic product growth rate shock similar to that faced during the Global Financial Crisis will be analysed. Next, the impact of an increase in the short term interest rate will be examined. Lastly, a stress test is performed by applying combined GDP and short term interest rate shocks resembling the situation faced during the Global Financial Crisis 2007-2008.