CRD IV and CRR
9. NUMERICAL RESULTS
higher default risk. The volatility parameter is therefore tested to see how our model captures this relationship.
Figure 14 shows how credit spreads calculated from our model on T3, and T2 bonds vary with the asset diffusion volatility, 𝜎. When volatility of assets is less than 1%, we observe that spreads on all debt tranches are low and stable. However, as the volatility increases, spreads on T2 and T3 rise rapidly. The spread widening is driven by a higher frequency of default. Hence, the probability of default increases as asset fluctuations become larger.
Figure 13: Volatility of Assets
A key result obtained from Figure 14 above is the effect of incorporating jumps in the asset value into our model. Without the possibility of jumps, all bonds would be entirely default-free and carry a zero credit spread for low levels of asset volatil-ity. When jumps in bank asset values are permitted, however, credit spreads be-come positive even for low levels of asset volatility. On the other hand, this also means that whenever the volatility of assets is lower than around 1%, credit spreads are driven by the jump risk, while the diffusion risk becomes the main driver of spreads for higher levels of volatility.
Figure 15 shows that the relative spread ratio between T3 and T2 remains notably stable at around 1.80x for changing levels of volatility. This can be attributed to the fact that increasing volatility impacts the PD, but not the LGD. This is an
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important result, as it tells us that while higher asset volatility results in higher absolute spreads, it does not drive relative spreads.
Figure 14: Spread Ratio - Volatility of Assets
The results regarding the volatility of assets show that spreads are significantly affected for high values of asset volatility, thereby capturing the fundamental rela-tionship of risk and return. Furthermore, we see that the volatility of assets affects the absolute spread on T3 and T2 due to its impact on the PD and not the LGD.
Initial CET1 Ratio
We observe that banks in Europe usually choose to hold an amount of CET1 capital above the minimum requirement. This amount is defined as a “management buffer,” and serves as a buffer to prevent regulatory measures being triggered in only mildly challenging times. Empirically, we see considerable differences in the CET1 buffer level above minimum requirements. Since the most significant regula-tory measures are triggered by the CET1 ratio, it is important to understand how credit spreads vary with the bank’s initial level of CET1 capital.
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Relative Spread
T2/T3Ratio
Sigma (%)
Figure 15: CET1 Ratio
Figure 16 shows how credit spreads vary for different levels of CET1 capital at 𝑡= 0. The case of an initial 11% CET1 ratio represents a situation where the bench-mark bank at 𝑡= 0 has just enough capital to comply with the MREL requirements and the MDA, i.e. the bank has no buffer. In this case, the spreads obtained on T3, and T2 are 168bps, and 301bps, respectively. When a bank has no CET1 buffer above requirements, it is more likely to be affected by negative shocks and adverse market conditions, which means that it is more likely to end up in PONV before time T. Thus, increasing the CET1 buffer should make a bank more resilient and hence decrease the riskiness for bondholders.
This is indeed what the results of our model suggest. Increasing the CET1 buffer decreases the spreads on all debt tranches, and as the buffer continues to increase, the spreads on T3 and T2 fall at a decreasing rate. This dynamic can be explained intuitively. Increasing the buffer from the 11% level has a large effect on spreads, as the benefit of the buffer is greatly captured. As the CET1 buffer continues to increase, the incremental benefit of a buffer increase declines, as a bank is so well capitalized that it does not experience much risk of default. Thus, we see a dimin-ishing marginal effect on spreads as the initial CET1 ratio increases.
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Figure 16: Spread Ratio - CET1
In contrast to absolute spreads, the ratio between T2 and T3 spreads is stable when changing the CET1 buffer. While this may seem surprising, there is an intuitive explanation for this result. Increasing the CET1 buffer lowers the PD, as it is the CET1 ratio that governs the default trigger. Although the PD is lowered signifi-cantly, the CET1 tranche will still be the same at default, as the default boundary is set at 6% CET1 ratio. Since we do not change the costs of resolution, the expected recovery will also be the same, and therefore we do not see any impact on the spread ratio between T3 and T2.
High- and Low-Trigger AT1
The trigger levels of a bank’s AT1 instruments are contractually defined for each bond issue. As the intention of AT1 capital is to provide a going-concern loss ab-sorption buffer, we investigate the effects on spreads by changing the AT1 amounts issued as high- and low-trigger instruments.
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Relative Spread
T2/T3Ratio
CET1 (%)
Figure 17: High- and Low-Trigger AT1
Figure 18 shows that altering the allocation of AT1 capital between high- and low-trigger CoCos does indeed affect credit spreads on T3 and T2. In the case where the full amount of AT1 is issued as high-trigger CoCos, we obtain credit spreads on T3 and T2 of 74bps and 136bps, respectively. If, instead, all CoCos are issued as low-trigger instruments, we find that T3 and T2 credit spreads increase by 14%
and 15%, respectively, to 84bps and 156bps.
The aim of AT1 instruments is to absorb losses and thus reduce the likelihood that a bank will experience severe financial distress. Our results suggest that the con-version feature of AT1s does in fact make banks more resilient, thus decreasing the PD. At the same time, however, the results also show that AT1 capital has the greatest effect when it is issued as a high trigger. With regard to the T2/T3 ratio, we see no effect of altering the allocation of high- and low-trigger CoCos.
Amount of AT1 and T2
Thus far, we have assumed that the bank optimizes its capital structure such that it will use the cheapest available sources of funding given the regulatory capital requirements. In other words, it will hold only the minimum required amount of both AT1 and T2 debt. However, this assumption might be too simplistic for banks in Europe. For example, in 2016 Danske Bank had 2.9% AT1 and 2.7% T2, which
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and the amount of capital ranking junior to it in the creditor hierarchy, changing the amount of AT1 and T2 should affect the spreads on T2, T3, and senior. There-fore, we now relax our assumption regarding the capital structure of the bank, and calculate spreads for different levels of AT1 and T2.
Figure 18: AT1 Ratio
Figure 19: Tier 2 Ratio
As one would expect, Figure 19 and 20 show that increasing the tranche sizes of both AT1 and T2 will result in lower spreads on the three debt tranches. However,
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AT1 (%)
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the results also show that increasing the T2 tranche has less of an effect on the T2 spreads than increasing the AT1 tranche. The waterfall model can explain this result. Increasing the AT1 tranche provides the T2 bondholders with a greater loss cushion. Thus, the loss attachment point is increased, which lowers the LGD on the T2 tranche. At the same time, the increased amount of AT1 lowers the PD by converting a greater amount of capital into equity when the high trigger point is reached, preventing the bank from going into resolution. However, increasing the T2 tranche does not change the loss attachment point, but only increases the ability to distribute losses across the T2 tranche, thereby having less of an effect on the T2 spreads.
Senior and T3 spreads are similarly affected, as changing either the AT1 or T2 tranche size will increase the capital cushion for senior and T3. These results con-firm the Morgan Stanley survey finding that the stack size below the T3 tranche matters for how market players estimate the T3 spread (Morgan Stanley, 2017).
Figure 20: Relative Spread - AT1 and Tier 2
The different T2 spread effects can also be seen in the spread ratio, as the ratio increases faster when the T2 is increased instead of the AT1. Changing the amount of AT1 and T2 therefore reveals that T3 instruments for a bank with a higher AT1 and T2 tranche can expect lower spreads, ceteris paribus.
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Initial Capital Above Benchmark (%)
Costs of Resolution
A main uncertainty when assessing the credit risk of bank bonds concerns the costs of the resolution process. As these costs affect the expected recovery of each liability class, it is important to measure how the magnitude of the costs affects both abso-lute and relative credit spreads. Our benchmark scenario considers random costs of resolution that are uniformly distributed on the interval 0,0.10. However, to iso-late the spread effects of changing the cost parameter, we need to eliminate the randomness and keep costs constant. Therefore, the following presents the results when the costs are held fixed per simulation.
Figure 21: Costs of Resolution
Figure 22 clearly displays the developed waterfall, and illustrates the loss attach-ment/detachment mechanism of the CLO approach. It shows how losses start to be incurred on the next tranche in the waterfall once the tranche below has been exhausted. After the CET1 and AT1 tranches have been depleted, the T2 tranche is the next to attach losses. As this tranche is relatively thin, increasing the costs of resolution quickly wipes it out. As the T2 tranche starts to reach the detachment level, spreads start to flatten out and remain constant for higher cost levels. At this point, the T3 loss attachment level is reached and the tranche starts to absorb losses, resulting in increasing credit spreads on T3. Finally, when the T3 tranche has been exhausted at a loss level of around the 9-10% of assets, senior bondholders start to incur losses and credit spreads on senior rise accordingly. Thus, the figure illustrates how the T3 gone-concern capital can be used to absorb losses when res-olution occurs. By adding the T3 tranche, many of the losses are absorbed by the
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T3, such that the senior tranche only incur losses in resolution for relatively high costs.
Figure 22: Spread Ratio - Costs of Resolution
The spread ratio between T3 and T2 reveals the same results. The ratio is high at low costs of resolution, but as costs increase and T3 and T2 spreads converge, the relative spread ratio between the two tranches approaches 1.0x.
These results underline that pricing bank debt instruments is indeed a difficult task for market participants due to the great uncertainty regarding both the costs faced in resolution and the process itself. For T3, we see that a cost increase of only 1 percentage point can cause spreads to double. The results further show that the costs of the resolution process are a significant driver of relative spreads. This is important for investors to keep in mind when assessing the T3 valuations.
PONV
One of the main uncertainties regarding bank capital regulation is the PONV. The conundrum about the location of this undefined point makes accurate pricing of bank liabilities extremely difficult. This is also the case in our model. Because of this uncertainty, it is essential to understand the effect of changing the PONV assumption.
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T2/T3Ratio
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Figure 23: PONV
Figure 24 shows the absolute credit spreads for different level of the PONV. As evident, its level has a relatively large impact on the credit spreads on T3 and T2 bonds. This is highlighted further in Figure 25 that shows the percentage change in credit spreads for different increments in the PONV. When the PONV is changed from 4.5% to 6.0% spreads on T3 and T2 increases by 36% and 50%, respectively.
That the PONV decision influences spreads is not surprising, as we would expect a higher number of defaults when increasing the default boundary. However, the size of the relative spread increase caused by changing the PONV 1-2 percentage points is significant.
Figure 26 shows that the relative spread ratio between T2 and T3 increases when the PONV is set at a higher level. As the costs of resolution are unchanged, a higher amount of losses is absorbed by the equity and T2 tranches when the default bound-ary is set higher, which leads to a higher expected recovery of T3. We would even-tually see the same effect on T2 by raising the PONV boundary even more.
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Figure 24: Percentage Increase in Spreads from an Increase in the PONV
Figure 25: Spread Ratio - PONV
Important insights can be drawn from these results. One concerns the high sensi-tivity of both the T3 and T2 spreads on the location of the PONV. This suggests that pricing bank bonds is extremely difficult, as the default boundary is unknown in practice. At the same time, our results reveal that the location of the PONV is
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Increase of PONV above 4.5% CET1 (percentage points)
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MREL Requirement
There is still a significant amount of uncertainty regarding the exact implementa-tion of MREL, which is a result of doubt regarding the size of the requirements, local differences, and specific adjustments made to the MREL for the individual bank. Therefore, spreads are calculated under different MREL requirements, with the assumption that the T3 tranche will change accordingly.
Figure 26: MREL
Figure 27 above shows credit spreads for an MREL between 20% and 30% of RWA.
At 20%, the spreads on the T3, and T2 tranches are found to be 104bps, and 147bps, respectively. As the MREL is increased, we see a clear and linear decline in credit spreads on T3, while spreads on T2 are relatively unchanged. The spread tightening on T3 is due to the fact that the size of the T3 tranche increases as minimum requirements rise for the bank to comply with the higher requirements.
Since increasing the total T3 tranche will ceteris paribus increase the amount among which losses are distributed, the expected recovery of T3 and senior will increase correspondingly. As the whole tranche rank pari passu in the event of default, we see lower credit spreads.
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Figure 27: Spread Ratio - MREL
Note that T2 tranche spreads are unchanged for different levels of MREL. This is because T2 ranks below T3 in the waterfall. Thus, neither PD nor LGD of T2 is affected by increasing the amount of higher ranked debt.
Summary of Numerical Results
We have in this chapter investigated what drives credit spreads in our model, and how sensitive results are to changes in parameters. We have found that the vola-tility of assets has significant effect on absolute spreads, but not on the ratio be-tween T2 and T3. Next, we adjusted the balance sheet composition and found that especially the amount of AT1 and T2 affects relative spreads. Then we looked at the costs of resolution and the PONV. We found that these parameters have large effect on spreads, both in absolute terms and in relative terms. Finally, we found that changing the MREL affects the spreads on T3 as well as the relative spread ratio between T2 and T3, but not T2.
This has given us an indication of how T3 bonds should be priced relative to T2 bonds, or at least an idea of what impacts the relative spread between the two tranches, and we are now able to compare our results to what we observe in the market. Before we are ready to compare the results to our observations in chapter 4, we will need to test the robustness of them. This will be done in the next chapter.
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T2/T3Ratio
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