Results at Execution of the Contract

The out-of-time performance measurements at execution of the contract are pre- sented in Table 3.8. The outcomes show that incorporating macroeconomic fac- tors generally improves the LGD estimation for both companies, irrespective of whether the estimates are obtained by the linear regression or the nonlinear re- gression spline model.

Company A Company B

Linear Regression Regression Spline Linear Regression Regression Spline

Year FIRM FIRM+MACRO FIRM FIRM+MACRO Year FIRM FIRM+MACRO FIRM FIRM+MACRO

MAE 2005 0.2939 0.2717 0.2932 0.2698 2005 0.3468 0.3461 0.3457 0.3470 RMSE 0.3555 0.3408 0.3555 0.3408 0.4094 0.4089 0.4085 0.4087 REC Area 0.7080 0.7307 0.7020 0.7324 0.6538 0.6545 0.6549 0.6535 MAE 2006 0.2806 0.2679 0.2806 0.2640 2006 0.3407 0.3362 0.3399 0.3412 RMSE 0.3484 0.3369 0.3484 0.3334 0.4032 0.4005 0.4023 0.4033 REC Area 0.7236 0.7238 0.7236 0.7238 0.6599 0.6644 0.6606 0.6594 MAE 2007-2009 0.5195 0.5048 0.5099 0.4962 2007 0.3095 0.2992 0.3089 0.2989 RMSE 0.5804 0.5638 0.5695 0.5562 0.3689 0.3629 0.3688 0.3627 REC Area 0.4877 0.5022 0.4971 0.5110 0.6911 0.7014 0.6916 0.7016 MAE 2008-2009 0.3126 0.3031 0.3088 0.3008 RMSE 0.3726 0.3663 0.3689 0.3641 REC Area 0.6885 0.6891 0.6921 0.7003

Table 3.8: Out-of-time performance measurements at execution of the contract by com- pany and forecast period. The estimates were carried out each with the nonlinear regression spline model and the linear regression model. FIRM represents that only idiosyncratic factors were used as explanatory variables, FIRM+MACRO implies that additionally macroeconomic factors were included, in each case the better result is un- derlined. REC Area is defined as the area under the regression error characteristic curve, MAE is the mean absolute error, and RMSE is the root mean squared error. For the REC Area higher, for MAE and RMSE lower outcomes are preferable.

Upon closer inspection, the outcomes for company A clearly demonstrate that the respective models using macroeconomic factors yield throughout more accu- rate LGD estimations for all forecast periods. Consequently, at execution of the contract the out-of-time results for company A confirm the in-sample findings, discussed in Section 3.4, that the additional use of macroeconomic factors leads to better estimations of the LGD. In particular considering the poor predictions for the last forecast period, which includes the financial crisis, one may argue that these results are biased due to the low number of observations. However, it should be borne in mind that the respective training sample already includes information about the Dotcom crisis and according to the in-sample results the relationship between the LGD and the economic situation is similar for the Dotcom crisis and the financial crisis. Consequently, although the estimation accuracy is poor for this forecast period, improved predictions by using macroeconomic factor are quite comprehensible. Basically, by assuming an identical relationship between the LGD and the explanatory variables over the entire observation period, com- paratively poor estimates for the final forecast period are indeed surprising, as most training data are available for this period. On the other hand, it should be

considered that the few estimations carried out for this period focus on the year 2007. The observations in 2007 exhibit significantly higher LGDs than those of the previous years which are used for model fitting (see Table 3.2). On average, basically all models underestimate the LGD in particular for the period 2007-2009. However, this underestimation of the LGD is minor if macroeconomic factors are considered.

With regard to the outcomes for company B we recognize that the inclusion of the macroeconomic factors is overall less beneficial than for company A. The linear model achieves a higher estimation accuracy in all forecast periods by in- corporating the macroeconomic factors, however, a distinct advantage over the respective model without macroeconomic factors can only be obtained in the last two periods. In addition, the nonlinear regression spline model only benefits by the inclusion of the macroeconomic factors from the year 2007 onwards. One reason for the use of the macroeconomic factors being clearly beneficial only in the last two forecast periods might be the requirement of more training data for an adequate model fitting, because, as stated in Section 3.4, the models for company B feature a significant lower coefficient of determination than those for company A. Still, altogether the out-of-time results at execution of the contract confirm also for company B largely the in-sample observed benefit of considering macroeconomic factors for estimating the LGD.

Analyzing the performance measurements for both companies, we observe that the LGD estimations for company B are less accurate in the early forecast periods. Nevertheless, in contrast to company A the quality of the estimations remains stable in the later periods. This can be explained, among other reasons, by the fact that for company B the level of the LGD increased only moderately in the last years of the observation period.

Besides, we have seen that the nonlinear regression spline model achieves a higher estimation accuracy than the linear regression in-sample. Out-of-time we

again observe this tendency for company A, however, it is mainly reflected in the models that incorporate macroeconomic factors. Furthermore, for company B, out-of-time a slight advantage of the nonlinear model over the linear model only exists from the forecast period 2007 onwards. One possible explanation might be in turn the rising number of training data over time. As Hartmann-Wendels et al. (2014) have shown, more complex models, as the nonlinear regression spline model, typically yield better results in-sample. However, those complex models might require more training data to achieve an adequate model fitting, which is necessary to perform accurate out-of-time.