Condicionantes para el cambio

In this Subsection we will compare internally calibrated simulation-based capital charges using boosted asset correlations calibrated to RG-SG segments, to Basel II (Case 2) capital charges. Our results will show a lower capital charge of 7% as compared to 8.2% under Basel II. In addition, observing capital charges by overall SG, we note that internally-calibrated capital charges display a strictly decreasing pattern with increasing Size, as opposed to the Basel II U-shaped pattern in capital charges by Size. This decreasing pattern has particularly strong implications for the smallest SME borrowers who, under the internal calibration, receive capital charges equal to up to three times those under Basel II. By contrast, capital charges for the largest SME borrowers are approximately half what they would be under Basel II.

In order to adequately assess the impact of using internally calibrated asset correlations in the calculation of capital charges we turn again to Case 2, the full AIRB implementation. In Table 4.6 we observe that the use of Retail-Other asset classification results in significantly lower capital charges to the smallest SME borrowers as compared to their larger SME counterparts. Specifically, we observe that the smallest borrowers, those in the ≤$100,000 Size Group, are charged approximately three quarters the capital assigned to the largest SME borrowers, those in the >$1,000,000 Size Group. This discount in capital charges is enhanced by the negative relationship between asset correlations and PD, the positive relationship between asset correlations and Size, and the presence of lower maturities for smaller SME borrowers; see Chapter 3.

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In Case 3, recall, the use of the Retail-Other classification is dropped, as are Size and Maturity effects, however, the Corporate asset class correlation function’s inverse PD relation is maintained. This implementation reveals a sharp increase in capital charges to smaller SMEs so that the smallest borrowers are charged over twice the capital of the largest SME borrowers.

Table 4.8 presents capital charges by Risk Group and Size Group under Cases 2, 7b and 10, while Table 4.9 presents cross ratios of segment capital charges across Cases. Examining results by overall RG in Table 4.8 and using tabulated ratios in Table 4.9, we observe that for all RGs except the riskiest (RG 8-9), borrowers generally obtain a reduction in capital charges varying between 50% and 10%. For borrowers in the 8-9 RG, capital charges are increased by 70%. Examining results by RG-SG segment we observe that the highest surcharges are generally applied to those borrowers most benefitting from Basel II pre-calibrations, namely, the smallest and riskiest borrowers. Specifically, the highest surcharge observed is one of 280% for the 7 RG – ≤$100,000 SG segment while the highest capital reduction observed is one of 60% for the 1-3 RG – > $1,000,000 SG.

These results, obtained in Case 7b and compared to Case 2, take into account Size as a dimension in the calibration of PDs and asset correlations, and use a simulation-based model and allocation scheme to obtain capital results. Case 10 presents a case in which Size is not a dimension in calibration, and show an underlying base for results observed

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above. Namely, we observe that overall portfolio capital charges under Case 10 are identical to those of Case 2, and equal to 8.2%. For the smallest borrowers, overall SG capital charges are 30% higher under the boosted asset correlations implementation of Case 10 when compared to the Basel II implementation. For borrowers in the largest Size Group, this result is reversed so that the largest borrowers, as an overall group, receive a discount of 30% to capital charges.

Examining results by overall RG, we observe discounts ranging between 20% and 30% for all RGs except RG 8-9. For the riskiest borrowers we observe a surcharge of 10% over Basel II capital charges. Additionally, we observe, under both Case 10 and Case 7b, and for all RG – SG segments as well as overall, a greater dispersion in capital charge results as compared to Base II (Case 2). Specifically, we observe a range of capital charges from 3.6% (RG 1-3 – SG > $1,000,000) to 24.8% (RG 8-9 – SG ≤ $100,000) under Case 7b and 4.6% (RG 1-3 – SG > $1,000,000) to 21.1% (RG 8-9 – SG ≤ $100,000) under Case 10. This compares to capital charges ranging from 3.5% (RG 1-3 – SG $250,000 - $1,000,000) to 13.2% (RG 8-9 – SG > $1,000,000) under Case 2.

Our exercise in this Subsection compared capital charges under prudentially high pre- calibrated asset correlations (i.e., Case 2) to internally calibrated capital charges adjusted to prudential levels. Our use of Size as an explicit calibration dimension provided an alternative to pre-calibrated relationships in Basel II. Our comparison showed that pre- calibrations in Basel II provide discounts to smaller borrowers that are not reflective of their true relative riskiness, while providing a surcharge of capital to larger SME

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borrowers. We use a RG calibration of PD and asset correlation parameters in order to gauge the relative impact of internal calibrations and Size dimensionality in those calibrations. Our results show that the use of internal calibrations of parameters, removing pre-specified Basel II calibrations, yields the underlying changes observed while the addition of the Size dimensionality amplifies these underlying reversals.

These results are dependent on the specifications of the bounded asset correlation boost, such that if we were to use an upper bound of 20% asset correlation we would obtain different capital levels, but we expect that the patterns and overall results obtained in this Subsection would be maintained; see Subsection 4.2.3.