CRD IV and CRR
8. NUMERICAL ANALYSIS
Benchmark Scenario
We need a benchmark scenario as a starting point to compare our results and investigate how yields vary with input parameters, for example because of uncer-tainty about the implementation of MREL or jurisdictional differences. To set plau-sible benchmark parameters for our calculations, we collect balance sheet data for 38 European banks. A description of our data set and more detailed information can be found in Appendix A. In addition, we base our input parameters on findings from existing research. Ideally, one should more accurately estimate each parameter value from information such as a bank’s balance sheet, stock returns, debt prices, and credit default swap spreads. However, as our goal is to make more general predictions regarding the drivers of credit spreads across banks in the EU, we choose not to do so. The parameters for our benchmark scenario are presented in Table 7 below.
Table 7: Benchmark Parameters
Parameters Value
Risk free rate r 2.0%
Volatility of assets σ 1.5%
Jump intensity λ 0.2
Mean jump size µY -1.5%
Jump volatility σY 2.0%
Tax rate κ 30.0%
Cost of resolution Z 2.0%
Payout rate δ 1.5%
PONV 6.0%
8.2.1. General Parameters
As the volatility of a bank’s assets is relatively low, we assume that the annual standard deviation of assets from the Brownian motion is 𝜎= 1.5%. The risk-free rate is 𝑟= 2% and is held constant throughout the period. This is chosen for com-putational simplicity. However, as we are interested in finding spreads, the choice of a fixed interest rate should not have a great impact on the obtained results, as mentioned in the literature review in chapter 5. The marginal tax rate is set to 𝜅= 30%.
8.2.2. Jump Parameters
The risk-neutral jump intensity is set to 𝜆= 0.2, corresponding to one expected jump per path, i.e. five years; and the risk-neutral mean jump size is 𝜇𝑌 =−1.5%.
The standard deviation of jumps is set to 𝜎𝑌 = 2.0%. This setup is close to Pen-nacchi’s (2010) and incorporates the risk of sudden drops in asset value, for example in a financial crisis. Furthermore, the negative jump mean value characterizes the asymmetric nature of a bank’s asset portfolio due to the large pool of debt claims, such as mortgages with limited upside, as explained by Nagel and Purnanandam (2015).
8.2.3. Costs of Resolution
To capture the costs of the resolution process, we include the random variable Z in our model. As our benchmark scenario, we assume that this variable is uniformly distributed on the interval [0,0.10]. The randomness of the variable incorporates a realistic feature of the resolution process, as costs in practice depend on the circum-stances, the resolution tools applied by authorities, and the market conditions at the time of resolution. In the interpretation of costs of resolution, we include the costs of potential haircuts, write-downs of assets, fire sales, and other uncertainties regarding what happens when the bank enters resolution. Furthermore, we include direct costs such as those of accountants, lawyers, and other restructuring costs.
8.2.4. Payout Rate
The payout ratio is set to 𝛿= 1.5% of total assets. Whenever payout restrictions are imposed on the bank, this rate is reduced by 0.25 percentage points. Thus, 𝛿 𝑡 = 0.015−0.0025𝟏𝑀𝐷𝐴(𝑡) . These values are set to represent plausible values of payouts, taking all liability classes into consideration. We will test the robustness of our model against these assumptions later.
8.2.5. Capital Requirements
The bank is subject to a number of capital requirements. Based on the current regulatory environment described in chapter 2 and market observations of Euro-pean banks, we assume plausible minimum capital requirements, which are shown in Table 8 below.
Table 8: Minimum Requirements
Requirement Amount Requirement Amount
Pillar 1 minimum requirement 8.0% 2x Pillar 1 minimum requirement 16.0%
Capital conservation buffer 2.5% 2x Pillar 2 requirement 3.0%
Counter-cyclical buffer 0.5% Combined buffer requirement 5.0%
Systemic risk buffer 2.0%
Pillar 2 Requirement 1.5%
Total Capital requirement 14.5% Total MREL 24.0%
The amounts are set as a percentage of RWA.
Minimum capital requirements The MREL
Specifically, we assume that the bank is subject to the Pillar I requirement of 4.5%
CET1, 1.5% AT1, and 2.0% Tier 2 of RWA. Furthermore, the bank is subject to a 0.5% CCyB, a 2.5% CCB, a 2.0% SIFI buffer, and a 1.5% P2R. In total, this is equivalent to a CET1 requirement of 11.0% in percentage of RWA.
As described in the previous chapter, our waterfall model is characterized by dif-ferent capital zones, each triggered by the bank’s assets falling below a regulatory threshold. The specific capital trigger levels are presented in Table 9 below.
Table 9: Trigger Points Trigger Trigger level Based on Consequence
MREL trigger 24% Total capital ratio Restrictions on payout MDA trigger 11% CET1 ratio Restrictions on payout
AT1 high-trigger 7% CET1 ratio AT1 high-trigger conversion to CET1 AT1 low-trigger 5.125% CET1 ratio AT1 low-trigger conversion to CET1
PONV 6% CET1 ratio The bank enters resolution
The triggers are breached when the ratio falls below the trigger level.
As the MDA trigger is set as the sum of the Pillar I CET1 requirement, the CBR, and the P2R (cf. chapter 2), MDA is equal to 11.0%. Based on market standards, the conversion triggers of high- and low-trigger CoCos are set to CET1 ratios of 7.0% and 5.125%, respectively. We set the MREL trigger to a total capital ratio of 24.0%, which corresponds to a requirement of two times the Pillar I requirement, two times the P2R, and one time the CBR, reflecting no additional adjustments made to the final MREL amount by the resolution authority.
8.2.6. PONV
We set the PONV to a CET1 ratio of 6.0%. As described in chapter 2, the PONV is a discretionary trigger point based on supervisors’ judgement about the individ-ual bank’s solvency prospects. Nevertheless, we do have some guidelines for an approximate trigger level.
The Pillar 1 minimum CET1 requirement is 4.5% of RWA. Therefore, a 4.5% CET1 ratio appears to be the lower boundary for the PONV. On the other end of the spectrum is the trigger point for high-trigger AT1 CoCos. As the latter are per-ceived as going-concern instruments (Avdjiev, et al., 2013), the PONV should be below 7.0% CET1. Thus, we believe that the market’s working assumption is that PONV is triggered somewhere between 4.5% and 7.0%; this is also our own as-sumption. Consequently, we set the PONV to 6.0% CET1. All of the capital zones are shown graphically in the figure below.
8.2.7. Balance Sheet Composition
With respect to the balance sheet composition, the liability side of the balance sheet is shown in Table 10 below. The balance sheet is based on our data set and ECB data containing information on the aggregate consolidated balance sheets of EU banks (ECB Data Warehouse, 2017). We assume that half of the bank’s liabilities consist of deposits. Furthermore, we assume that the bank optimizes its capital structure such that once minimum capital requirements have been met, the bank will rely on the cheapest source of funding, referred to as “efficient capital struc-ture.”
Table 10: Balance Sheet
Assets Liabilities
Total assets 100 Deposits 50.00
Senior 36.50
Tier 3 4.75
Tier 2 1.00
AT1 0.75
CET1 7.00
Total assets 100 Total liabilities 100
With regard to the level of CET1 capital, we assume that the bank keeps a man-agement buffer of 3.0% CET1 above the MDA trigger – that is, a “safety buffer”
14.0%. The assumption regarding the size of the management buffer is based on market observations and stated capital target ratios of banks within our data set.
8.2.8. Risk-Weighted Assets
We assume that RWA amount to 50% of total assets. This is based on market observations and is of course stylized, as RWA do vary in practice. The largest banks generally tend to have slightly fewer RWA than this level, whereas smaller banks have a higher ratio of RWA to total assets.
Sample Simulation
To provide an example of how the simulations are performed consider the figures below, which show our simulation approach. Figure 12 shows 20 simulated assets paths for our benchmark scenario. One path ends up in resolution at time 𝑡= 1.75, and another at time 𝑡= 3.25. The rest of the simulated asset paths does not reach the PONV before time 𝑡= 5. Figure 13 shows the cash flows to a bondholder in the three scenarios of Figure 12, where the dark blue bars illustrate the payoff structure on a bond of a bank that does not end up in resolution, and the light blue and the red bars represent the cases where the bank does reach the PONV.
In these cases, the principal is reduced by some amount due to the costs of the resolution, and coupons do not continue to be paid.
Figure 11: 20 Simulated Asset Paths
90 92 94 96 98 100 102 104 106 108 110
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00
Asset Value
Time, t
Figure 12: Hypothetical Bond Cash Flows
The way we obtain the price on a bond is to calculate the present value of the expected cash flows on each path. By simulating many paths and taking the aver-age, we can then obtain the market price. Because we in our model assumes that the bond is issued at par value at time zero we need to calibrate the model, such that the market value at time zero is indeed equal to the par value. We do this by iterating the coupon rate of the bond until the market value of the bond is equal to the book value. By subtracting the risk-free rate, from the equilibrium coupon rate we then obtain the spread.
Summary
We have now described our simulation framework and set up a benchmark scenario such that we can compare our results and investigate how yields vary with input parameters. To be able to generalize our results, we have set up the benchmark scenario such that it represents an average European bank. To set plausible bench-mark parameters for our calculations, we have collect balance sheet data for a number of European banks and examined the literature. The scenario is, however, still stylized. We will in the next chapter investigate the sensitivity of spreads to different input parameters, and examine which factors that drive credit spreads.
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00
Principal repaid at t = 5 PONV at t = 1.75 PONV at t = 3.25
CashFlow
Time,t