Sep 01

BIS on Economic Capital Modeling

by David Harper, CFA, FRM, CIPM

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BIS just released a terrific summary of economic capital (EC) practices among banks. It contains much that is relevant to an FRM candidate. Four metrics are discussed, in increasing order of sophistication: standard deviation, value at risk, expected shortfall (ES), and spectral metrics:

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Value at risk (VaR) and expected shortfall are the two most widely used measures, but “ES is the methodologically superior risk measure, largely due to its coherence, which makes capital allocation and internal limit setting consistent with the overall portfolio measure of risk. However, ES does not lend itself to easy interpretation and does not afford a clear link to a bank’s desired target rating.”

For many banks, VaR’s lack of subadditivity is a genuine problem but “probably more of a concern for credit risk and operational risk than for market risk.” That’s because market risk tends to rely on normal (symmetrical) distributions but credit and operational risk distributions are typically skewed.

Economic Capital is…

….a common yardstick!

“In order to achieve a common measure across all risks and businesses, economic capital is often parameterised as an amount of capital that a bank needs to absorb unexpected losses over a certain time horizon at a given confidence level. Because expected losses are accounted for in the pricing of a bank’s products and loan loss provisioning, it is only unexpected losses that require economic capital.”

….used in relative performance measurement, where the most common risk-adjusted metrics are risk-adjusted return on capital (RAROC) and shareholder value added (SVA).

Confidence level varies by purpose

Banks target confidence levels do not necessarily match Basel II’s regulatory targets (i.e., 99.9% confidence level used for credit and operational risk under Pillar 1 of Basel II or with the 99% confidence level for general and specific market risk). Rather,

  • “Some banks use lower confidence levels for performance assessment of business units than for their enterprise-wide capital adequacy assessment. This approach is based on the view that economic capital measures calculated at high confidence levels focus on extreme events and do not always provide appropriate information for senior management.”
  • Instead of the solvency view implied by higher confidence levels, lower confidence levels imply a going concern (shareholder) perspective: “in which banks want to hold a capital buffer ‘on top’ of their regulatory capital and where it is the probability of eroding such a buffer (rather than all available capital) that is linked to a target rating. This would reflect the expectation (by analysts, rating agencies and the market) that the bank operates with capital that exceeds the regulatory minimum requirement.”
  • In short, “high confidence levels reflect the perspective of creditors, rating agencies and regulators in that they are used to determine the amount of capital required to minimize bankruptcy risk” while lower confidence levels to allocate capital and identify exposures.

Importance of dependency modeling in credit portfolio risk models

According to the survey, the “majority of banks” use one of the three following types of credit risk models:

  • Moody’s KMV (following their structural approach, Portfolio Manager uses asset correlations to infer joint default probabilities)
  • CreditMetrics (flexible in approaches; e.g., can use bond spread correlations)
  • CreditRisk+ (does not explicitly model correlations)

Consistent with Basel II’s asymptotic single-risk-factor (ASRF) model, the survey finds that…

“Most models of credit portfolio risk estimate asset correlations among obligors in terms of common dependence on systematic risk factors. The assumption is that these underlying factors – e.g. country, region or industry of a borrower – fluctuate over time and typically follow a (joint) normal distribution. All borrowers are linked to these underlying systematic risk factors to varying degrees and tend to move in a correlated way. Thus, by modeling dependencies, banks account implicitly for concentration (both single name and sectoral) because large parts of their books are subject to the same underlying risk factors or to multiple risk factors. “

This is the theory of the ASRF in Basel II’s IRB except that the ASRF dubiously accounts for correlation only to the single systematic risk factor which, BIS says, “may be interpreted as reflecting the state of the global economy.”

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