RDP 9409: Default Risk and Derivatives: An Empirical Analysis of Bilateral Netting 6. Results

6.1 Data

The data used to test the various methods for setting a capital charge consists of interest rate swap and forward rate agreement portfolios obtained from a number of Australian banks. In some cases the portfolios are complete – covering all counterparties. In other cases, those counterparties conducting the most business with the bank were selected. For the bulk of the portfolios, maximum credit exposure was calculated using the interest rate model and methods detailed in Section 3 and Appendix 1. However, in the case of five portfolios, credit exposure was calculated by the banks themselves using their own interest rate models and aggregation methods. The number of contracts and counterparties in each portfolio are presented in Table 8.

Table 8: Bank Portfolios

Bank	Counterparties		Contracts
1	214		1,302
2	270		1,635
3	32		283
4	43		773
5	45		316
6	22		93
7	255		1,687
Total – RBA model		881
8	141		1,490
9	262		1,625
10	54		164
11	248		1,587
12	120		–
Total – banks' own models		825
Total		1,706

6.2 Add-Ons

To test the alternative forms of add-ons, each was regressed against maximum potential exposure. Maximum potential exposure was calculated as the difference between maximum credit risk and the current net mark-to-market if positive and zero otherwise. Here, we are testing the ability of the add-on to cover the worst case increase in a portfolio's value.

For each bank's portfolio, the set of contracts with each counterparty are treated as separate sub-portfolios. This paper focuses on the structure of the portfolios made up of the contracts between a bank and one counterparty, rather than the portfolio of contracts across all counterparties. Traditionally credit risk analysis has looked at a total portfolio and argued that since swap portfolios are generally built up so as to avoid any market risk, a swap portfolio can be approximated as a collection of matched pairs of the swaps.^[17] The difficulty with this when addressing the effect of netting is that, in most cases the set of contracts with each counterparty are not fully offsetting and the extent to which they are offsetting determines the impact of netting on both current and potential credit exposure. Hence, the capital charge is calculated for each counterparty.

For each bank we regress (across counterparties) the capital charge against maximum potential exposure. That is, for each bank and each method of calculating an add-on, we estimate the equation:

where:

Add-on is the capital charge for potential exposure; and

The R² from these regressions are reported in Table 9. Note that the regressions are estimated without the inclusion of a constant, hence it is possible to obtain negative R² values. A common problem in cross sectional regression analysis is heteroscedasticity where the variance of the regression errors is not constant. In most cases it was found that the error variance increased with the size of the counterparty portfolio. Hence, the heteroscedasticity was corrected for by performing weighted least squares estimation using the sum of notional principal for each counterparty as a scaling factor.

In total, twenty separate methods were tested as a capital charge for potential exposure. They fall into seven broad groups.

1. The standard Basle add-on together with two different ways of calculating net mark-to-market. The first alternative calculates the net mark-to-market (Net RC) as the sum of the market value of all contracts in the portfolio if this sum is positive, and zero otherwise. This is the conventional way of calculating net credit exposure. It can be seen that except for one bank the net replacement cost performs poorly compared to the Basle approach. The second ‘net’ calculation (ABS Net) is to take the absolute value of the sum of the market value of the portfolio's contracts. This provides a much better measure of potential exposure, outperforming the conventional net measure in every case. It is more highly correlated with potential exposure than the Basle measure in a number of cases, but overall fails to out-perform the Basle add-ons.
2. The second group of capital charges are those suggested by ISDA and are denoted in Table 9 as ISDAC1, ISDAC2 and ISDAC3. They are calculated from equations (3) and (4), using the conventional definition of net (the sum of the contracts' market values if positive and zero otherwise) and gross (the sum of the positive market values in a portfolio). ISDAC1 is calculated from equation (3). ISDAC2 is calculated using equation (4) with β set equal to 0.25 (the value suggested by ISDA as being appropriate). A grid search was used to find an optimal value of β at 0.35. ISDAC3 is calculated using that value of β. For all banks, ISDAC2 and ISDAC3 are more highly correlated with potential exposure than ISDAC1.
3. The third group of measures, comprising ISDA1 and ISDA2, are also calculated from equations (3) and (4), but are based on the absolute net-to-gross ratio (that is, the absolute value of the sum of all contracts' net market value divided by the sum of the absolute market value of each contract). In this case, a grid search confirmed 0.25 as the appropriate value for β. These measures strongly out-rank those using the conventional net ratio in all cases except one. Because very few counterparties have a net market value of zero there is little difference in the explanatory power of the two formulations (ISDA2 outranking ISDA1 in five of the nine banks).

4. The fourth set of add-ons measure the capital charge as a function of short and long positions. First, the maximum of the sum of the Basle add-ons on all short and long contracts was taken. Second, the absolute difference between the total add-ons on short and long contracts was considered (this is denoted short/long net in the table). Finally, a weighted sum of the Basle add-ons (that is, the short/long gross add-on) and the short/long net position is calculated. The respective weights were determined by regressing the two components of the weighted sum against maximum potential exposure. The optimal weights estimated were 23 per cent of the net add-ons and 2 per cent of gross add-ons. This reflects a strong correlation between the swap rates in the portfolios. Moving from the net short/long to the weighted short/long adds little to the explanatory power of the capital charge. The net add-ons tend to perform better than the maximum of the short and long add-ons.
5. The fifth group of add-ons approximate the short/long approach by splitting the portfolio between positively and negatively valued contracts. On the whole, these measures performed much like the short/long add-ons. The short/long approach appears to be slightly better at tracking potential exposure. The positive/negative approach can be expected to be a reasonably good proxy for the short/long add-ons given that swap rates have steadily declined for the four years prior to the date these portfolios were selected and that the average remaining term to maturity of the contracts is quite short (three-quarters of the contracts have a remaining term to maturity of less than three years). Further details of the maturity profile of the portfolios is presented in Table 11. Once the interest cycle moves beyond a turning point the performance of this set of add-ons can be expected to deteriorate. Moreover, while the interest rate cycle is fairly smooth, other asset prices such as foreign exchange rates tend not to follow such smooth cycles and so this approach may not be appropriate for foreign exchange and derivatives written against other commodities.
6. The sixth group are those based on the time band approach, the first being based on the gross time band, the second, on net time bands. In all cases, except one, the gross time band out-performs the Basle add-ons. Overall, the net time bands outperform the gross time band add-ons. However, the net add-ons perform poorly for several banks.

7. The final group of add-ons are based on the linear function, equation (5). The gross measure (simply summing the add-ons for each contract) outperforms Basle and is on par with the detailed time bands gross result. The net measure, which nets the add-ons across all contracts for each counterparty does particularly well – overall outperforming the net time bands method. A weighted sum of the gross linear add-ons and the net linear add-ons, with weights of 3 per cent and 22 per cent respectively, improved slightly on the net add-on.

The results presented in Table 9 suggest that the Basle method outperforms the other measures in group 1 and those in group 2, but is itself outperformed, overall, by the measures shown under groups 3, 4, 5, 6 and 7. The one approach which appears to correlate most closely with potential exposure is the weighted linear addon. The net linear add-on also performs particularly well.

These overall results hold, broadly speaking, for individual bank portfolios. There were, however, exceptions. The weighted linear add-on, the best overall measure, performed very poorly in the case of one bank (bank 10). In contrast, despite the inability of the ABS Net measure to track potential exposure across all banks, it generated relatively good results in the case of some individual banks (banks 4, 8 and 9).

6.3 Total Capital Charge

To test whether a total capital charge should be based on equation (1) (Basle preferred method) or equation (2), both measures were calculated using the Basle add-ons and were regressed against the modelled total credit exposure. For each bank and each method of setting a total capital charge, we estimate the equation

where:

Add-on is the total capital charge; and

The R² from these regressions are reported in Table 10. From Table 10 it can be seen that while the two approaches have practically the same explanatory power, the current Basle approach consistently outperformed the alternative. This comparison was performed using different methods of calculating the add-on, with the same result. This seems to be due to the fact that the add-ons tend to underestimate the increase in exposure and the standard, more conservative, approach to the calculation of the capital charge compensates for this.

The scenario approach, looking at the worst case credit exposure from current rates, and from up and down shifts in the yield curve, provides similar explanatory power as the Basle approach.

In the light of the results of the add-on tests, the following add-ons were included in a test of the total capital charge:^[18]

• the absolute value of net mark-to-market;
• the absolute net-to-gross ratios;
• the time band approach;
• the short/long approach; and
• the linear approach.

The results show that the variation in total exposure across counterparty portfolios is so dominated by current exposure that there is little to distinguish between the different add-on approaches. Overall, none of the formulations dominate the current Basle proposal by any significant margin.

These results are based on a comparison of the capital measures with the maximum potential exposure and maximum total exposure. In other words, capital is held to cover the possibility of counterparty failure at the worst possible time. A less stringent assumption is that a counterparty fails on any given day during the life of its contracts. In this case, it is more appropriate to consider the capital coverage in terms of average potential exposure and average total exposure. The results using these assumptions are presented in Appendix 2. The conclusions reached from this are broadly consistent with the results obtained from the analysis of maximum exposure. However, the relative performance of the net linear method improves somewhat.

6.4 Offsetting Contracts

The above results were obtained using static portfolios. One possibility is that the recognition of netting within the capital standards may provide an incentive for banks to enter into a greater number of offsetting contracts.

To test the effect of banks taking on a higher proportion of offsetting business, only those counterparties with two-way deals with banks 1 to 7 were selected and the capital charges were tested on this sub-sample. The results of this are presented in Table 12. Again, when considering the add-ons alone, the ISDA, the time band, the short/long and the linear approaches outperform the current Basle add-ons. The net and weighted linear methods are most strongly correlated with potential exposure. In the test of the total capital charge, however, there is no great difference in explanatory power between any of the proposed methods (the Basle method included).

6.5 A Different Yield Curve

All the preceding results obtained took the beginning of 1994 as the starting point for the interest rate simulations. This was, in all likelihood, close to the trough in the Australian interest rate cycle. To test the sensitivity of the results to the level of interest rates the credit risk calculations were performed a second time using rates at the beginning of 1992 (initial short rate 7.4 per cent and long rate 9.75 per cent) for one actual portfolio and one randomly generated portfolio.^[19] The results, for both the 1994 and 1992 credit risk calculations are shown in Tables 13 and 14.

Turning first to the comparison of the add-ons with potential exposure, when the 1992 interest rate scenario is adopted, the performance of the net time band, the short/long and the linear add-ons improves. In the case of the total capital charge, however, the explanatory power of all formulations falls significantly, except the linear approach. The linear and scenario approaches appear to be most robust to the shift in the yield curve, however the scenario approach clearly outranks the linear approach under the 1994 interest rate scenarios.

This result introduces a note of caution in interpreting the results and in imposing a capital charge; the level of interest rates can have an effect on outcomes.

Footnotes

For example, Board of Governors of the Federal Reserve System and Bank of England (1987). [17]

The current exposure and the add-on were combined using the method proposed by Basle, that is using equation (4). [18]

The size of the randomly generated portfolio was doubled by creating an exactly offsetting deal for each initial deal. Hence the net market value of the total portfolio is zero. [19]