Estimation of the Asset Correlation for Corporate counterparties: Where math meets intuition
Arjun Sunder S, CA,FRM
Credit Risk Models|IRB|IFRS-9|Basel III| Regulatory Reporting |Model Risk Management| ICAAP |Stress Testing| Econometric models
A.???? Introduction
A couple of weeks back, I had the opportunity to reread the Explanatory note on the Basel II Internal Rating Based (IRB) risk weighted functions published by Bank for International Settlements (BIS) in July 2005.? Once again, I was deeply impressed by the conceptual clarity of the authors.? I would strongly recommend this publication to all risk managers, who are engaged in development or validation of regulatory risk models in credit risk domain because of 2 reasons.
a.????? The paper explains the thought process behind the calibration of risk weight function used for estimation of capital requirements (K) in a very lucid manner, so that you can understand clearly the components, which drives the capital requirements and Risk weighted assets (RWA) under IRB approach
b.????? It helps you to explain the drivers behind RWA movements in a non-technical language to senior stakeholders or auditors, who may not be fully proficient in quantitative techniques applied in credit risk models. This is because the paper itself uses non-technical language to the extent possible.
The link for accessing this publication (hereinafter referred as note) is given in Comments section.
The Asset Correlation (R) is one of the components used in IRB risk weight function. In this context, R indicates the correlation of borrowers’ default risk with overall state of economy. In the upcoming sections, I intend to evaluate how closely the formula for estimation of asset correlation is aligned with bankers’ intuition/ commonsense.
B.???? Math
The formula for estimation of R (without size adjustments**) is given below.
Correlation (R) = 0.12 x (1-EXP (-50 x PD)) / (1-EXP (-50)) + 0.24 x [1-(1-EXP (-50 x PD))]
The table below sums the up the asset correlation computed in line with the above formula.
*PD estimates shown herein represent 1 year CDR published by CRISIL in their default and transition study. These figures are considered for illustrative purpose. In practice, even for AAA rated obligors floor PD of 0.03% is considered.
**In IRB RW function R is further adjusted for size of the entity judged based on turnover.
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On review of the table and the formula, following inferences can be made.
a.????? BIS has fixed lower and upper threshold for Asset correlation at 12% and 24% respectively.
b.????? When PD is 100%, asset correlation is floored at 12% and when PD is 0%, it is capped at 24%.
c.????? Correlation decreases exponentially as PD rises. The pace of decrease is determined by the so-called “k-factor”, which is set at 50 for corporate exposures.
?As observed in the Note, the upper and lower bound of correlation is fixed by BIS based after analysis of dataset shared by G-10 supervisors.
The following graph, reproduced from the Note also depicts this relationship nicely.
The asset correlation is measured in Y-axis and PD is shown in X-axis
C. Intuition/ Logic
The ratings are typically downgraded, when solvency or liquidity metrics of the entity worsens or when there is an adverse change in management. When such issues haunt an institution, general state of economy matters less. Even under a high growth, stable inflation economy, the risk of default of such institutions does not decline. Hence intuitively, lower asset correlation makes sense for counterparties with higher PDs. ?
Parting Thoughts
The Basel Committe prescribed supervisory estimates for asset correlation way back in 2005. ?These estimates have been kept constant since then. Shouldn’t these estimates be revised based on latest data/ empirical evidence? It is not clear whether BCBS has recommended to keep these estimates after factoring in the latest empirical evidence.
While risk of default of larger corporates tends to decline, with the progress in overall state of economy, the reverse is not always true. For e.g During economic slowdown induced by Covid, Indian large corporates were relatively less impacted as compared to mid corporates or SMEs.? May be that is the reason behind capping of asset correlation factor.?
May be Covid induced economic downturn is a wrong example to pick, considering the fact that many empirically proven relationships between predictive drivers (say unemployment rate) and default rate went for a toss during that period.?
Credit Risk Models|IRB|IFRS-9|Basel III| Regulatory Reporting |Model Risk Management| ICAAP |Stress Testing| Econometric models
2 个月https://www.bis.org/bcbs/irbriskweight.pdf
Assistant General Manager - Enterprise Risk Management at Commercial Bank of Kuwait
2 个月It is bound by 12% - 24% and moves between the band exponentially with respect to PD. To add to your observation, as PD increases the unexpected loss decreases and expected loss increases .
Senior Quantitative Risk Analyst at Handelsbanken - Quantifying the risks of tomorrow
2 个月Thank you for a nice post. The way I interpret the asset correlation is that at R = 0 the PD will be constant over the business cycle, while larger and larger R means more and more swings. As such, the Basel conclusion that lower PD typically means larger swings make sense if you think banks during good time might be to generous with good ratings. It however does not necessarily match up with observation, where you rather see that higher average risk also imply much larger variation over the credit cycle, as these companies essentially bet on "all going according to plan", while safer companies just keep steady though the cycle.
Corporate Banking Expert | Head of Credit Risk | Non-voting Commercial Credit Committee member| Helping stakeholders and investors make better decisions through building strategic financial plans and credit risk analysis
2 个月Insightful! The inverse relationship between TTC PD and R reflects how idiosyncratic and systematic risks interact. High TTC PDs are dominated by borrower-specific risks, reducing asset correlation, while low TTC PDs are more influenced by shared macroeconomic risks, increasing asset correlation. This relationship aligns with portfolio risk modeling principles, ensuring proper calibration of capital requirements.