The Basel II IRB framework reviewed in Section 3.1 provides for asset correlations ranging from 3% (applied to Retail-Other exposures; see Equation (3.4) for details) to 30% (applied to the High Volatility Commercial Real Estate (HVCRE) asset class; see BCBS (2006a, p. 66) for details). For SMEs, the range maximum is reduced to 20%; see Subsection 3.1.3. Compared to these prudential regulatory levels, internally calibrated asset correlations derived in this Chapter within a single factor framework appear to be of a significantly lower level. This discrepancy in the overall level of internally calibrated asset correlations and those found in the Basel II regulatory framework retains a sharp focus both in the academic literature and practical implementations of portfolio credit risk frameworks.
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In particular, Chernih, Henrard, and Vanduffel (2010) review asset correlation results found in the literature and segregate them by source data type. Their survey – replicated in Table 4.3 – suggest that the type of source data (i.e., default data vs. market-based equity data) may play a significant role in the setting of overall asset correlation levels; see Table 1 and Table 2 in Chernih, Henrard, and Vanduffel (2010, p. 53). Citing this work, Frye (2008) observes that the maximum asset correlation obtained with observed defaults as the source data, is approximately 10%, with that figure dropping to 2.3% for some studies; see, for example, Hamerle, Liebig, and Roesch (2003b). This maximum figure of 10% asset correlations, when estimated over default data, compares to a minimum of 10% asset correlations when estimated over equity data, and is attributed to observed and conceptual differences in the underlying data; see Frye (2008). In addition, working with both default data, based on the observed number of defaults, and loss data, derived from provisions data, Duellman and Scheule (2003) show the default data provides the lowest overall levels of asset correlation.
Commenting on low asset correlation levels obtained in their respective studies, Dietsch and Petey (2004) and Duellman and Scheule (2003) suggest that the use of aggregated data may engender some over-diversification within their data sets and therefore be a possible source of low correlation values. Dietsch and Petey (2004) also suggest their shortened time series as a potential source of reduced asset correlations due to the lack of a full economic cycle over the time period considered.
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In contrast, our research benefits from the use of non-aggreagted data, specific to one institution targeting high-risk SME borrowers. In addition, we benefit from a time series with 12 years of data. Despite our longer time series, however, we observe that the period covered is comprised of a prolonged period of economic growth along with low volatilities in our observed default rates. In particular, Table 4.4 compares normalized default rate volatilise obtained in our study with those observed in Standard & Poor's (2011) over the period 1981 to 2010. As can be seen in Table 4.4, Financing Company normalized default rate volatilities are considerably lower than those observed over the Corporate defaults studied in Standard & Poor's (2011). The presence of lower volatilities may be a significant contributor to low asset correlation values.
While the 2008 - 2010 period added volatility to our data, the tameness of the Canadian 2001 - 2002 economic slowdown may explain lower asset correlations compared to other studies. Hamerle, Liebig, and Roesch (2003b) segregate their data into country and industry and estimate asset correlations using three models. Results for Canada reveal a maximum observed asset correlation of approximately 0.6% as found in the Agriculture sector; see Exhibit 2 in that paper, pg 22. For the Canadian Manufacturing and Services sectors, two sectors that together make up approximately half of the Financing Company’s lending portfolio (see, for example, Tables 2.5A and 2.5B), the authors estimate asset maximum asset correlations of approximately 0.3%. These results compare to roughly equivalent results for France, maximum asset correlations of approximately 2.0% for Germany and Japan, and 2.3% for the United States.
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Finally, the asset correlation estimation algorithm described in Subsection 4.1.1 corresponds to that found in Gordy (2000) and Dietsch and Petey (2004). Duellman and Scheule (2003) estimate asset correlations within a similar single factor framework using three algorithms, the third of which most closely resembles that used in this Chapter, and shows that this method provides for the highest values as compared to other algorithms. In comparison, Gordy and Heitfield (2002) find that this methodology presents the greatest degree of inefficiency when compared to more restricted methodologies.
Possible solutions in dealing with this phenomenon of low asset correlations may include the choice of time periods in which one or more full economic cycles are represented; the choice of high (or maximal) volatility periods, or the application of ad-hoc “conservatism” adjustments to the estimated correlations using external data which may provide required characteristics.
Asset correlation boost retaining observed relationships between SME borrowers
We perform an ad-hoc conservatism factor adjustment to the low level of asset corrlations obtained in our estimation. This exercise is similar to that in Dietsch and Petey (2002) wherein an SME portfolio credit risk model is designed and estimated from SME default data. Given findings of low overall asset correlation values, averaging approximately 2%, the authors input Basel II IRB asset correlations equal to 20% for Corporate borrowers and 8% for Retail borrowers; see Dietsch and Petey (2002, pp. 307- 308).
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In this Subsection, we take the average asset correlations across all loans in the portfolio under the Partial Implementation cases described in Subsection 3.3.2; specifically, see Table 3.6. For Cases 2, 3 and 4 average asset correlations are found to equal 7.5%, 15.0% and 11.3%, respectively. Next, a bounded log odds ratio adjustment is applied to all segments such that the overall estimated asset correlation of 0.34% is equal to pre- specified value. For example, suppose that we want to adjust our estimated segment asset correlations { } such that the overall asset correlation A is equal to some value B, subject to the condition that no segment asset correlation { } is less than some lower boundary value L or greater than some upper boundary value U. The applied adjustment to each segment asset correlation would then be given by the following:
( ( ⁄( )) )
( ( ⁄( )) ) ( )
where,
(
) ( ) ( )
The idea of these boosts, ultimately, is to provide internally measured asset correlations that can be practically applied within a prudentially concordant portfolio credit risk framework. An important aspect of this practicality is the level at which asset correlations are set with respect to the international regulatory requirements presented in
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Basel II and reviewed in Section 3.1. To that end, we use 3% and 30% as the lower and upper bounds, respectively, in our adjustment. Another important aspect is the embodiment of the credit characteristics in the patterns and relative differences of asset correlations among different segments of borrowers in an SME portfolio. Our work up to Subsection 4.2.2 focused on the latter, in this subsection we addressed the former and presented a simple and common method for the augmentation of asset correlation levels to those present in the nationally applied regulatory frameworks.
Table 4.7 presents the results of our boost by Risk and Size Group segmentations. In both cases, the overall portfolio asset correlation is adjusted to the average asset correlation obtained in the full AIRB implementation (Case 2), equal to 7.4%; see Subsection 3.4.1. As we will see later in this Chapter, the effects of this boost on the resultant loss distribution are non-negligible. Capital charge results using these boosted values are given in Section 4. 3. The boosted asset correlations presented in Table 4.7 range between 9.0% (for the 7 – >$1,000,000 SG segment) and 18.6% (RR 4-5 – SG $250,000 - $1,000,000 SG segment). As discussed above, patterns observed in Subsection 4.2.2 are maintained.
RG- and SG-based Partial Implementation Average Asset Correlations
Before moving on capital charge results we present an abridged restatement of Table 3.6 under RG and RG-SG calibrations of our PDs. Specifically, Table 4.12 presents restated average asset correlations under Cases 2, 3 and 7a. Results are presented by RG and SG
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segments and show the same patterns observed in Table 3.6. In Table 4.12 the Corporate asset class specification is now applied to one RG (>$1,000,000) so that under Case 2, controlling for RG, we observe identical asset correlations for the smallest three SGs – treated under the Retail-Other asset class – and a significantly higher average asset correlation for the largest SG. Restated average asset correlations are found to be generally lower than those calculated in Chapter 3.
Comparing results in Table 4.7 to those in Case 2 of Table 4.12 we find, as expected, a lack of Basel II-imposed patterns in our internally calibrated results. In addition, we find that for the vast majority of SG and RG segments, internally-calibrated boosted asset correlations are higher than the average asset correlation in Case 2. Exceptions to this observation occur in the RG 7 – >$1,000,000 SG segment (in which we find the lowest boosted asset correlations, recall) and the overall >$1,000,000 SG. Table 4.13 presents discrepancies between internally-calibrated boosted asset correlations and Case 2 average asset correlations as ratios of the former to the latter. Table 4.13 shows that the greatest discrepancies occur for smaller borrowers with high PDs, reflecting Basel II pre- calibrations, with the most closely matched asset correlations are those for the >$1,000,000 SG.