Rating Matrices and Stability

Once the optimal boundaries for each rating class are determined, a rating classification can be attributed for each observation of the dataset. Tracking the evolution of the yearly observations of each firm enables the construction of one-year transition matrices. If, for example, a firm is classified as Baa in the fist period considered, in the next period it could either have an upgrade (to Aaa, Aa or A), a downgrade to (Ba, B, Caa), remain at Baa, default, or have no information in the dataset (Without Rating – WR).

The analysis of the transition matrix is helpful in order to study the stability of the rating system. The fewer transitions, i.e., low percentages in the off-diagonal elements of the matrix, the more stable the rating system. Furthermore, transitions involving jumps of several notches (for example, a transition from Aaa to Caa) are undesirable. Thus, a stable rating system is one whose rating transitions are concentrated in the vicinity of the main diagonal elements of the matrix.

Another relevant aspect of the transition matrix is the transition from each rating class to default. In terms of discriminatory power, a better rating system is one where the transitions to default rise at an exponential rate, from the higher rating to the lower rating classes.

30 _{The default rates for the higher rating class, resulting from the historical methodology, are 0%}

because historically there are no observed one-year defaults for the benchmark, in the period considered.

6. QUANTITATIVE RATING SYSTEM & PD ESTIMATION 39 Tables 7 to 9 present the transition matrices for the three models considered, with the class boundaries determined by the cluster methodology, while Tables 10 to 12 present the matrices based on the historical methodology:

Aaa Aa A Baa Ba B Caa D WR Aaa 41.15% 20.37% 4.71% 1.22% 1.06% 0.65% 0.00% 0.81% 30.03% Aa 19.13% 29.82% 15.93% 6.11% 3.49% 1.16% 0.07% 2.98% 21.31% A 7.15% 23.74% 25.84% 12.88% 8.25% 2.78% 0.08% 3.20% 16.08% Baa 2.31% 14.08% 19.47% 19.25% 17.60% 6.93% 0.33% 5.39% 14.63% Ba 1.21% 4.93% 10.85% 16.70% 29.69% 15.20% 0.43% 5.92% 15.06% B 0.37% 1.76% 2.61% 4.27% 18.30% 42.96% 2.40% 11.85% 15.47% Caa 0.00% 0.95% 0.95% 0.00% 3.81% 34.29% 9.52% 25.71% 24.76%

Table 7 – Model A - 1 Year Transition Matrix (Cluster Method)

Aaa Aa A Baa Ba B Caa D WR Aaa 42.43% 23.57% 1.72% 0.36% 0.27% 0.00% 0.09% 0.63% 30.92% Aa 13.42% 46.57% 14.09% 3.32% 0.38% 0.21% 0.04% 3.20% 18.76% A 1.58% 26.52% 32.79% 14.78% 2.19% 0.43% 0.43% 4.81% 16.48% Baa 0.46% 8.27% 24.22% 33.40% 8.27% 2.99% 1.04% 7.55% 13.80% Ba 0.14% 2.32% 9.71% 29.28% 21.16% 8.12% 3.77% 10.72% 14.78% B 0.00% 1.89% 2.95% 14.74% 21.47% 21.05% 7.58% 13.05% 17.26% Caa 0.00% 1.54% 0.00% 7.34% 11.97% 16.22% 18.15% 21.62% 23.17%

Table 8 – Model B - 1 Year Transition Matrix (Cluster Method)

Aaa Aa A Baa Ba B Caa D WR Aaa 26.67% 28.80% 7.20% 0.80% 0.00% 0.27% 0.00% 0.53% 35.73% Aa 7.10% 41.27% 19.01% 3.85% 0.74% 0.44% 0.07% 1.63% 25.89% A 1.15% 18.70% 40.28% 15.40% 3.72% 0.68% 0.10% 3.20% 16.76% Baa 0.25% 3.84% 23.96% 32.14% 13.96% 2.89% 0.50% 5.41% 17.04% Ba 0.07% 1.25% 9.42% 24.50% 29.29% 13.10% 1.62% 7.28% 13.47% B 0.09% 0.35% 2.26% 9.03% 23.00% 32.38% 6.34% 11.37% 15.19% Caa 0.00% 0.00% 1.15% 0.29% 5.48% 26.51% 23.34% 19.88% 23.34%

Table 9 – Model C - 1 Year Transition Matrix (Cluster Method)

Aaa Aa A Baa Ba B Caa D WR Aaa 13.33% 26.67% 16.67% 6.67% 0.00% 0.00% 0.00% 0.00% 36.67% Aa 1.44% 14.83% 25.84% 15.31% 0.48% 0.96% 0.00% 0.00% 41.15% A 0.40% 5.23% 34.97% 26.83% 3.52% 0.60% 0.00% 1.01% 27.44% Baa 0.04% 0.80% 13.43% 45.59% 16.65% 1.69% 0.00% 2.96% 18.84% Ba 0.04% 0.16% 1.65% 21.18% 44.64% 11.38% 0.04% 5.69% 15.22% B 0.00% 0.10% 0.26% 3.64% 22.44% 44.83% 0.26% 12.47% 16.00% Caa 0.00% 0.00% 0.00% 0.00% 0.00% 22.22% 0.00% 55.56% 22.22%

6. QUANTITATIVE RATING SYSTEM & PD ESTIMATION 40 Aaa Aa A Baa Ba B Caa D WR Aaa 18.97% 36.21% 12.07% 0.00% 0.00% 0.00% 0.00% 0.00% 32.76% Aa 2.85% 32.43% 24.32% 6.16% 1.05% 0.30% 0.00% 0.75% 32.13% A 0.07% 12.79% 35.91% 16.80% 6.75% 0.98% 0.00% 2.46% 24.24% Baa 0.00% 3.44% 22.66% 31.96% 21.35% 2.00% 0.00% 2.96% 15.63% Ba 0.00% 0.42% 5.65% 17.58% 43.55% 11.80% 0.04% 5.31% 15.64% B 0.00% 0.05% 0.76% 2.48% 20.88% 47.44% 0.43% 12.18% 15.77% Caa 0.00% 0.00% 0.00% 0.00% 5.00% 25.00% 0.00% 30.00% 40.00%

Table 11 – Model B - 1 Year Transition Matrix (Historical Method)

Aaa Aa A Baa Ba B Caa D WR Aaa 18.92% 29.73% 16.22% 0.00% 0.00% 0.00% 0.00% 0.00% 35.14% Aa 2.24% 21.41% 35.14% 3.83% 0.96% 0.32% 0.00% 0.00% 36.10% A 0.22% 5.17% 46.79% 14.62% 5.29% 0.84% 0.00% 2.08% 24.97% Baa 0.00% 1.13% 24.27% 33.36% 20.49% 2.06% 0.00% 3.18% 15.52% Ba 0.00% 0.21% 5.42% 18.13% 43.13% 11.77% 0.04% 5.33% 15.96% B 0.00% 0.05% 0.81% 2.49% 20.90% 47.51% 0.34% 12.13% 15.77% Caa 0.00% 0.00% 0.00% 0.00% 0.00% 22.22% 0.00% 38.89% 38.89%

Table 12 – Model C - 1 Year Transition Matrix (Historical Method)

Results based on the historical methodology are more stable and display higher discriminatory power than the results based on the cluster methodology. In terms of stability, the historical based results have less high level transitions. For example, none of the three matrices based on this methodology have transitions from the high classes Aa, A, Baa to lowest class Caa, while all of the three matrices based on the cluster methodology have such transitions.

In terms of discriminatory power, the matrices based on the historical methodology also present better results, since the transitions to default start at lower percentages for the higher classes and increase continuously to considerable higher percentages than the transitions based on the cluster methodology.

Regarding the results for each model, within each methodology, none of them produces a clearly more attractive rating matrix.

41

7

Regulatory Capital Requirements

Under the New Basel Capital Accord (NBCA)31, financial institutions will be able to use their internal risk assessments in order to determine the regulatory capital requirements. In the first pillar of the Accord – Minimum Capital Requirements – two broad methodologies for calculating capital requirements for credit risk are proposed. The first, the Standardized Approach, is similar to the current capital accord, where the regulatory capital requirements are independent of the internal assessment of the risk components of the financial institutions. Conversely, in the second methodology – the Internal Ratings-Based Approach – banks complying with certain minimum requirements can rely on internal estimates of risk components in order to determine the capital requirements for a given exposure. Under this methodology, two approaches are available: a Foundation and an Advanced approach. For the Foundation Approach, credit institutions will be able to use their own estimates of the PD but rely on supervisory estimates for the other risk components. For the Advanced Approach, banks will be able to use internal estimates for all risk components, namely the PD, Loss-Given-Defaults (LGD), Exposure-At-Default (EAD) and Maturity (M). These risk components are transformed into Risk Weighted Assets (RWA) through the use of risk weight functions32_.

Up to this point we have devised six alternative methodologies for determining one of the risk components, the PD. Assuming fixed estimates for the other risk components33 we are able to estimate capital requirements under the IRB Foundation approach, and compare them to the capital requirements under the current accord. Table 13 provides results for all six models:

31 _{Basel Committee on Banking Supervision (2003).}

32 _{Appendix 6 provides a description of the formulas used to compute the RWA for corporate}

exposures.

33 _{The parameters assumed are LGD = 45%, M = 3 years, EAD for SME = 0.3 Million Eur and EAD}

for large firms = 1.5 Million Eur. For the calculations under the current capital accord, it is assumed that all exposures have the standard risk weight of 100%.

7. REGULATORY CAPITAL REQUIREMENTS 42