One of the objectives in our study is to compare the predicted with the observed CDS spreads. This is accomplished by examining the relationship between the theoretical spreads using the CreditGrades model and the empirical spreads as it is depicted in Figure 2 and Figure 3 where they are plotted together. These two figures show the comparison between the average observed CDS spreads and the average predicted spreads. Specifically, Figure 2 presents the whole sample period of our study; from December 2004 until December 2014, while Figure 3 presents the CDS spreads after the financial crisis; from January 2009 to December 2014. Before the financial crisis, the empirically observed CDS spreads appear to be more stable than during the financial crisis of 2008 where the spreads reached new high levels. In the
aftermath of the global financial crisis, the investors’ uncertainty led to bigger fluctuations in the CDS market with a remaining uncertainty.
The uncertainty in the financial markets highlights the importance of the accurate estimate of credit risk (Belke and Gokus, 2011). Financial institutions use different kinds of credit risk models in order to estimate with accuracy the risk. In the credit risk model used in our study, the CreditGrades model, volatility is one of the driving factors. As a result, an accurate prediction of volatility facilitates the estimation of credit risk. In this study the estimation of volatility is conducted by the GARCH model and a Moving Average approach. Observing Figure 2 it can be noticed that during the financial crisis the CreditGrades model with GARCH estimated volatility overestimates the CDS spreads. On the other hand, the CreditGrades model with the volatility being estimated by the MA approach presents more stable CDS spreads. Figure 3 representing the period after the financial crisis has a different outlook where both models on average underestimate the real spreads. Based on the MA approach the volatility is too stable without taking the short-term trends into account in comparison with the GARCH model which takes them into consideration. Moreover, the GARCH model generates more volatile CDS spreads than the observed ones, particularly, during turbulent times.
Figure 2: Average observed and predicted CDS spreads, whole period
The figure shows the estimations of the predicted spreads in the CreditGrades (CG) model as well as the observed spreads expressed in basis points. For the predicted spreads two different methods are used to calculate the volatility; Moving Average (MA) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model.The period examined is from December 2004 to December 2014 which is the whole sample period of our study.
Figure 3: Average observed and predicted CDS spreads, after financial crisis
The figure shows the estimations of the predicted spreads in the CreditGrades (CG) model as well as the observed spreads expressed in basis points. For the predicted spreads two different methods are used to calculate the volatility; Moving Average (MA) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model. The period examined is from January 2009 to December 2014 which is the period after the financial crisis.
0 200 400 600 800 1000 1200 1400 1600 04-1 2-03 05-1 2-03 06-1 2-03 07-1 2-03 08-1 2-03 09-1 2-03 10-1 2-03 11-1 2-03 12-1 2-03 13-1 2-03 14-1 2-03
Average CG MA Average CG GARCH Average Real
0 50 100 150 200 250 300 09-01-01 10-01-01 11-01-01 12-01-01 13-01-01 14-01-01
Regarding the results previously mentioned the model specifications provided by CreditGrades (2002); the expected average recovery rate (𝐿̅) and 𝜆, may not be optimal in our study which focuses on the European CDS market. Thus, the method used at either Byström (2006a) or Avino and Lazar (2012) where they optimize 𝐿̅and 𝜆 could have more preferable results. Figure 2 & 3 could be misleading since they show the average results. In addition, Appendix A shows the spreads for the first eight companies where the MA approach generates stable estimates while in the GARCH model fluctuations are detected especially during the financial crisis.
In order to accomplish our objective of reviewing the relationship of the predicted with the observed spreads a comparison of the two volatility methods is applied. The comparison is implemented based on the average volatility of each method which is presented in Figure 4. In addition, this approach can be an explanation for the performance of the CreditGrades model with these two volatility estimators. The MA approach generates a stable volatility as anticipated by CreditGrades (2002) and the GARCH model exhibits more fluctuations. As a consequence, the volatility estimated by the GARCH approach indicates a faster reacting model that takes the market shocks into account. Reviewing our estimations, we observe that volatility is a driver factor in the CreditGrades model since it is strongly affected by the different estimates. The high peaks of volatility generated by the GARCH estimator could be the reason for the overreactions in the estimated CDS spreads. The MA approach implemented in our study takes approximately four years of data into consideration. In the beginning of our sample can be possibly seen that the volatility is relatively high since this can be explained by the burst of the IT bubble at the turn of the millennium which could still affect our volatility estimate.
Figure 4: Displaying average volatility
The figure displays the average moving average volatility (MA) and the average GARCH estimated volatility.
An essential part of risk management is evaluating the performance of the models. Giving a more objective view, two of the most popular measures used to predict the average error in the models are the Mean Absolute Percentage Error (MAPE) and the Root Mean Square Error (RMSE) (Maris et al., 2004). Table 2 & 3 display the MAPE and the RMSE respectively. Table 2 displays that for the whole period the GARCH produces a mean MAPE of 68.61 % that is slightly lower than the 75.03% given by the MA approach although the difference is not significant. Reviewing the subsamples more carefully reveals that before the financial crisis the GARCH model was a significant estimator. Nevertheless during the financial crisis the MA approach was significantly better than the GARCH model and during the European sovereign debt crisis there was no significant difference between the models. According to Table 3, the MA approach is significantly better than the GARCH model during the whole period.
0 20 40 60 80 100 120 04-1 2-03 05-1 2-03 06-1 2-03 07-1 2-03 08-1 2-03 09-1 2-03 10-1 2-03 11-1 2-03 12-1 2-03 13-1 2-03 14-1 2-03
Table 2: Mean absolute percentage error
MAPE
Mean Upper Lower Min Max
Before Financial crisis. Dec 2004 - Dec 2006
MA 159.80% 191.57% 128.03% 16.92% 496.88%
GARCH 79.76% 90.90% 68.61% 23.98% 244.58%
Financial crisis. Jan 2007- Dec 2008
MA 67.34% 76.96% 57.72% 20.47% 322.88%
GARCH 100.11% 114.51% 85.71% 29.94% 395.21%
European sovereign debt crisis. Jan 2009 - Dec 2014
MA 48.26% 56.15% 40.37% 17.03% 243.91% GARCH 54.20% 57.98% 50.43% 32.03% 93.85% Whole period MA 75.03% 83.14% 66.91% 23.99% 188.45% GARCH 68.61% 73.04% 64.19% 40.38% 127.75%
The table presents the mean absolute percentage error (MAPE) as well as includes 95% confidence intervals. The mean, upper bound, lower bound, min and max values are calculated based on the MAPE of the individual companies. In addition, it covers the whole sample period as well as three sub-periods; before the financial crisis, during the financial crisis and during the European sovereign debt crisis.
Table 3: Root mean squared error
RMSE
Mean Upper Lower Min Max
Before Financial crisis. Dec 2004 - Dec 2006
MA 50.41 63.11 37.71 3.57 282.13
GARCH 33.80 40.30 27.30 7.05 161.31
Financial crisis. Jan 2007- Dec 2008
MA 72.99 93.10 52.89 18.50 632.57
GARCH 194.06 222.34 165.78 20.73 4050.70
European sovereign debt crisis. Jan 2009 - Dec 2014
MA 69.47 85.36 53.57 13.26 423.06 GARCH 78.75 94.37 63.14 23.85 435.78 Whole period MA 72.27 86.98 57.56 18.94 431.71 GARCH 116.32 134.01 98.63 30.41 1810.66
The table presents the root mean squared error (RMSE) as well as includes 95% confidence level. The mean, upper bound, lower bound, min and max values are calculated based on the RMSE of the individual companies. In addition, it covers the whole sample period as well as three sub-periods; before the financial crisis, during the financial crisis and during the European sovereign debt crisis.
In addition to the comparison of the volatility estimates according to MAPE and RMSE on an overall view that was previously implemented, we conduct an assessment on an individual level. This is satisfied by comparing the MAPE and RMSE for the individual companies of our study for each volatility estimator. Hence, the best performing estimates according to MAPE and RMSE respectively are depicted in Table 4 & 5. These tables can be seen as an added dimension in the process of assessing the performance. According to both tables the MA approach has the best performance except the period before the financial crisis. This can be verified by the fact that GARCH is the best performing model at that period. An explanation for the weak performance of the MA model could be the high levels of volatility in the beginning of our sample at that period. The objective comparison of MAPE and RMSE does not give a clear answer about the model that gives the best performance. Nonetheless, the MA approach seems having more satisfactory results.
Table 4: Individual evaluation of MAPE
MAPE Times Percentage of times
MA
Dec 2004 - Dec 2006 (Before Financial crisis) 25 37.31%
Jan 2007- Dec 2008 (Financial crisis) 45 67.16%
Jan 2009 - Dec 2014 (European sovereign debt crisis) 56 83.58%
Dec 2004 - Dec 2014 (Whole period) 35 52.24%
GARCH
Dec 2004 - Dec 2006 (Before Financial crisis) 42 62.69%
Jan 2007- Dec 2008 (Financial crisis) 22 32.84%
Jan 2009 - Dec 2014 (European sovereign debt crisis) 11 16.42%
Dec 2004 - Dec 2014 (Whole period) 32 47.76%
The table presents a comparison between the two different volatility measures and how they have performed on an individual level according to MAPE. In addition, it covers the whole sample period as well as three sub-periods; before the financial crisis, during the financial crisis and during the European Sovereign Debt crisis.
Table 5: Individual evaluaion of RMSE
RMSE Times Percentage of times
MA
Dec 2004 - Dec 2006 (Before Financial crisis) 30 44.78%
Jan 2007- Dec 2008 (Financial crisis) 49 73.13%
Jan 2009 - Dec 2014 (European sovereign debt crisis) 57 85.07%
Dec 2004 - Dec 2014 (Whole period) 51 76.12%
GARCH
Dec 2004 - Dec 2006 (Before Financial crisis) 37 55.22%
Jan 2007- Dec 2008 (Financial crisis) 18 26.87%
Jan 2009 - Dec 2014 (European sovereign debt crisis) 10 14.93%
Dec 2004 - Dec 2014 (Whole period) 16 23.88%
The table presents a comparison between the two different volatility measures and how they have performed on an individual level according to RMSE. In addition, it covers the whole sample period as well as three sub-periods; before the financial crisis, during the financial crisis and during the European Sovereign Debt crisis.
Apart from the models that we used in our study in order to estimate the volatility, we
also implemented trading strategies aiming to give us a wider indication of volatility’s
accuracy. The results from the trading strategies are displayed in Table 6, where the estimates without a threshold suggest the MA being the preferred estimator of volatility. However, the model using GARCH estimated volatility is the one generating the highest returns when the thresholds are introduced. As seen in Appendix A the CreditGrades model using GARCH is more volatile and hence introduces more trading signals in comparison with the MA approach where the volatility could be too stable without giving enough signals.
Another goal of this study is to assess the possibility of finding risk adjusted returns using trading strategies on the CDS market. Appendix B reports the total performance of the examined different trading strategies which can also be seen in Table 6. The highest return is produced by the strategy based on the autocorrelation of CDS spreads and selecting the assets based on historical returns. The strategy that gives the lowest return is the one using the estimated CDS spreads with the MA approach including all assets that yield a negative return of -0.47% for the entire sample period. Examining the sub periods it can be detected that a large part of the return is obtained during the period of the European sovereign debt crisis. Before the financial crisis almost no positive returns can be observed.
Table 6: Total percentage return from the strategies
Sharpe ratio Return Sharpe ratio Return Sharpe ratio Return All assets All assets All assets
Threshold CG MA CG MA CG GARCH CG GARCH AR(1) AR(1) CG MA CG GARCH AR(1)
Nov 2005-Dec 2006 (Before Financial crisis )
0 -2.05% -1.36% -2.72% -2.49% -1.11% -1.16% -1.69% -2.29% -2.05%
0.01 0.04% 0.07% -2.63% -2.45% -1.69% -1.57% -0.22% -2.19% -2.05%
0.02 -0.04% -0.10% -2.55% -2.40% -1.57% -1.49% -0.06% -2.11% -1.83%
Jan 2007- Dec 2008 (Financial crisis)
0 0.73% 4.26% -1.60% -2.10% 13.60% 16.58% 2.52% -2.21% 8.97%
0.01 1.88% 2.08% -0.49% -1.77% 14.00% 15.75% 0.68% -2.04% 8.80%
0.02 0.74% 0.58% -0.86% -1.75% 13.10% 13.77% -0.09% -2.05% 7.59%
Jan 2009 - Dec 2014 (European sovereign debt crisis)
0 22.03% 25.67% 10.49% 9.45% 57.31% 89.24% 6.14% 9.19% 30.97%
0.01 -1.39% -0.44% 10.95% 12.26% 49.75% 76.88% -0.91% 9.29% 26.77%
0.02 0.13% -0.28% 9.64% 10.61% 39.91% 56.03% -0.31% 8.90% 18.94%
Nov 2005- Dec 2014 (Whole trading period)
0 20.43% 29.30% 5.38% 5.64% 76.68% 118.03% 7.01% 4.39% 39.79%
0.01 0.51% 1.70% 7.53% 8.18% 67.85% 101.57% -0.47% 4.76% 35.10%
0.02 0.82% 0.19% 4.09% 4.30% 55.78% 74.88% -0.46% 4.46% 25.63%
The table presents the total return expressed in percentage. The period covered is before the financial crisis, during the financial crisis, during the European sovereign debt crisis as well as the whole trading period. The signals are either based on the CreditCredes (CG) estimated CDS spreads or the observed CDS spreads. The CreditGrades is estimated using two different volatility estimators; Moving Average (MA) or GARCH. Three different selection criteria are used; Sharpe ratio, return and all assets.
Obtaining returns on a risk adjusted basis can be attained by estimating the Sharpe ratio. The results of the estimations are presented below in Table 7. The highest Sharpe ratio was obtained by the same strategy that produced the highest total return. None of the strategies using GARCH estimated volatility manages to produce a positive Sharpe ratio for the whole period. On the other hand, the MA approach without threshold does produce a positive Sharpe ratio. The impact of including the thresholds on the Sharpe ratio is not always negative as can be seen during both the financial and the European crisis. For instance, the strategy using AR (1) and highest return increases the Sharpe ratio when the threshold is introduced. This indicates that the strategies’ volatility drops with the introduction of a
threshold, hence lowering the risk of the strategy.
The results regarding the Sharpe ratio and the total return indicate that the best performing strategies are the strategies that are based on the autocorrelation. These results are in line with Avino and Nneji (2012) finding that strategies based on autocorrelation outperforms those based on a structural model. Table 7 also displays that it is possible to find
positive Sharpe ratios using portfolios consisting of single named CDS spreads. Our results recommend using selection criteria instead of trading all assets. Both portfolio selection methods applied in this study increase the performance compared to trading all assets. This confirms our belief that it would be beneficiary to select the best performing assets into the trading portfolio.
Table 7: Sharpe ratios for the strategies
Sharpe ratio Return Sharpe ratio Return Sharpe ratio Return All assets All assets All assets
Threshold CG MA CG MA CG GARCH CG GARCH AR(1) AR(1) CG MA CG GARCH AR(1)
Nov 2005-Dec 2006 (Before Financial crisis )
0 -0.65 -0.38 -0.49 -0.47 -0.29 -0.34 -0.61 -0.68 -0.86
0.01 -0.43 -0.20 -0.47 -0.46 -0.40 -0.39 -1.37 -0.67 -0.94
0.02 -5.69 -2.79 -0.49 -0.48 -0.45 -0.45 -2.42 -0.68 -1.00
Jan 2007- Dec 2008 (Financial crisis)
0 -0.12 0.01 -0.17 -0.09 0.12 0.13 -0.02 -0.13 0.10
0.01 -0.17 -0.04 -0.16 -0.09 0.12 0.13 -0.14 -0.12 0.10
0.02 -0.49 -0.24 -0.18 -0.09 0.12 0.11 -0.38 -0.13 0.08
Jan 2009 - Dec 2014 (European sovereign debt crisis)
0 0.09 0.10 0.03 0.05 0.22 0.22 0.04 0.05 0.21
0.01 -0.15 -0.09 0.04 0.06 0.20 0.21 -0.22 0.06 0.20
0.02 -0.23 -0.19 0.02 0.03 0.17 0.18 -0.36 0.05 0.16
Nov 2005- Dec 2014 (Whole trading period)
0.00 0.01 0.06 -0.05 -0.01 0.17 0.18 -0.01 -0.02 0.14
0.01 -0.16 -0.07 -0.04 0.00 0.15 0.17 -0.18 -0.02 0.13
0.02 -0.38 -0.23 -0.06 -0.02 0.14 0.14 -0.37 -0.02 0.10
The table presents the Sharpe ratio. The period covered is before the financial crisis, during the financial crisis, during the European sovereign debt crisis as well as the whole trading period. The signals are either based on the CreditCredes (CG) estimated CDS spreads or the observed CDS spreads. The CreditGrades is estimated using two different volatility estimators; Moving Average (MA) or GARCH. Three different selection criteria are used; Sharpe ratio, return and all assets.
Byström (2006a) found significant autocorrelation in the iTraxx index, which is exploited in a trading strategy. This study confirms the autocorrelation being viable not only for the iTraxx index but also for the single name CDSs. His research was implemented in the beginning of our sample period. According to the results in our study, this was the weakest period which indicates not only the presence of autocorrelation but also a stronger relationship.