# Presentation: 079127

## Basel II: A Case for Recalibration

- by
- Paul Kupiec
- FDIC-JFSR Basel II Symposium
- September 13, 2006
- Division of Insurance and Research
-  Federal Deposit Insurance Corporation.
***The opinions expressed are the author’s and are not the official views of the FDIC. ***

## Paper Objectives

- Evaluate U.S. implementation of Basel II AIRB against two primary supervisory goals:
- Enhancement of financial stability
- As standard for sound risk measurement practice

## Outline of Presentation

- Review origins of AIRB framework
- Examine AIRB calibration assumptions
- Implications of calibration: QIS 4 & QIS 5
- Evaluate AIRB as a risk measurement standard
- Implications of adoption

## How to set capital?

- Logic of the AIRB capital rule
- Need enough capital to “cover” credit losses that may materialize
- Basel II “soundness standard”—99.9 percent
- Capital       99.9 percent quintile of bank credit loss distribution
- Enough capital to sustain the bank should it experience a very large and improbable credit loss
- Important Flaw in this logic

## Origin of the AIRB rule 

- Exact representations of portfolio credit return distributions are complicated, *(e.g., Kupiec 2006b)*
- Oldrich Vasicek approximation for a portfolio credit loss distribution (late 1980s/early90s)
- Asymptotic single factor portfolio credit risk model
- Also called the Gaussian copula model
- Mimics structural model of credit risk but is far easier to compute

## Gaussian Credit Risk Model Assumptions

-     is a std Gaussian (normal)
-     determines default correlation
- Firm *i* defaults on its debt when
- The unconditional probability of default is

- • The loss given default, *LGD*, is exogenous to the model.

## AIRB Capital Rule

## Maturity Adjustment

*Ad hoc* adjustment calibrated so that AIRB mimics Moody’s KMV Portfolio Manager capital assignments for credits of different maturity.

## Regulatory Correlation Function

## Correlations and Capital

**For fixed PD & LGD**
**	****	**** ****lower correlation implies lower capital**
- Correlations calibrated by the BCBS using G10 bank data analysis that suggested [see BCBS July 2005] :
- (1) default correlation increase with firm size
- (2) default correlations decrease as *PD* increases.
- • Wholesale correlations set to mimic data patterns:
-  smooth function; bounded between 12% and 24%
- Retail correlations “reverse engineered”
- AIRB capital approx equal to capital assigned by the internal models of a group of large internationally active banks [See BCBS 2005, p. 14]

## What will happen to capital under AIRB?
Capital will fall...
....probably by a large amount unless there are floors and limits

**Capital will fall**...
- ....probably by a large amount unless there are floors and limits

## QIS 4 Results: US Banks

## QIS 4 Results

- QIS 4 shows:
- Aggregate minimum capital falls by 15.5%
- median bank drop is 26 percent
- median decline in required Tier I capital is 31 percent
- bank estimates for the required capital for nearly identical positions varied widely
- Syndicated loan analysis
- Mortgage portfolio survey

## QIS 4 

- Does AIRB fix “regulatory arbitrage”?
- **claim**: securitization activity is undermining the Basel Accord capital standards:
-  **“****regulatory arbitrage”**
- Jones (2000), Mingo (2000) JBF
- Greenspan & others in speeches

## AIRB capital for securitizations

## QIS 5 Results: Europe et.al. 

- Group 1 banks’ capital fell an average of 7.1% under the AIRB approach
- Group 2 banks, smaller primarily nationally- focused institutions, posted much larger declines
- Within Europe
- Group 1 banks’ average capital declined 8.3% under the AIRB
- Group 2 banks’ capital declined 26.6% on average under the AIRB

## Evidence suggests significant capital reductions under AIRB

_**Should we worry about this**_**?**** ****(multiple choice)**
-  No, AIRB is a well-formulated capital model
-  Yes, AIRB has significant flaws that result in understated capital requirements
-  Uncertain

## Discussion of AIRB Model & Calibration

## Correlation-PD Calibration Assumptions

- Data suggest default rate correlation increases as credit quality declines ---opposite of AIRB model
- Allen, DeLong and Saunders (2004), Cowan and Cowan (2004), Dietsch and Petey (2004), Das, Duffie, Kapadia and Saita (2004), others....
**Problem:** AIRB assumes fixed default threshold, but default threshold is probably random
- Cox (1977) stochastic barrier model
- double stochastic intensity models of Das, Duffie, et, al.
**Implies: **There are probably two correlations related to PD to worry about, not just one as AIRB assumes

## Examining AIRB Model Assumptions

- Evidence shows that LGDs increase when default rates are elevated
- Studies by Frye (2000), Schuermann (2004), Araten, Jacobs, and Varshney (2004), Altman, Brady, Resti and  Sironi (2004), Hamilton, Varma, Ou and Cantor (2004), Carey and Gordy (2004), Emery, Cantor and Arnet (2004)
- decrease in the recovery rates during recessions and periods of heightened defaults
- Implies a systematic risk component in LGDs

## Examining AIRB Model Assumptions

- Evidence shows that draw rates on revolving lines increase as credit quality declines
- Allen and Saunders (2003), Asarnow and Marker (1995), Araten and Jacobs (2001), and Jiménez, Lopez, and Saurina (2006)
- suggests that obligors draw down lines of credit as their credit quality deteriorates.
- Implies a systematic risk component in EADs

## How Good an Approximation is the Gaussian Credit Loss Distribution? 

**Portfolio default rate is the single driver of credit loss uncertainty in AIRB rule**
- AIRB loss rate distribution is inaccurate
- Missing systematic risks generated by stochastic LGD and EAD
- Correlations assignments questionable
-  Missing capital for concentration risk (pillar 2)
- Unexpected loss is likely much larger that AIRB synthetic distribution suggests

## Problem with AIRB logic....it forgets to pay interest on a banks funding debt

- Minimum Capital=UL+EL+Bank Interest Expense
*This problem compounds issues created because the AIRB model inaccurately measures the tail value of bank credit loss distributions *

## How important are these weaknesses in the AIRB approach?

## AIRB Rule Omits Capital for Bank Interest Expense

## Importance of Interest Expense

- Bank buys bond
- Bond cost $66.14
- Matures in 1-year, pays $70
- 99% Credit VaR Capital Calculation
- Only 1 percent of outcomes <$59.82
- $66.14-$59.82 = $7.32 = CVaR capital
- Actual probability of default is 1.7%

## Slide 27

## Omission of Interest Expense 

- Understates Capital Needs
- Makes AIRB capital rule procyclical
- Soundness Standard Varies over the Business Cycle
- Consider last CVaR example, but assume that the 1-year Treasury rate goes from 5% to 10%

## Procyclicality

- Bond now costs $63.07
- CVaR tail value $62.89
- CVaR Capital falls to $0.18 because interest rates increased by 5 percent
- When interest rates are 5%
- CVaR Capital = $7.32
- When interest rates go to 10%
- CVaR Capital = $0.18

## Slide 30

## CVaR Capital & Interest Rate

- CVaR rule sets lower capital solvency standard as the level of interest rates increase
- Problem—AIRB rule forgets to pay interest on bank debt
- this expense should be in the capital rule and increase as interest rates increase to maintain the target soundness standard

## AIRB Rule & Procyclicality

- As central bank is raising interest rates to curb bank lending—AIRB rule will cut soundness standard, increase implicit safety net subsidy, and stimulate bank lending

## AIRB does not recognize portfolio interest income

**Q:** Doesn’t this offset the problem of forgetting interest expense?
**Answer:** Partly, but not entirely

## Including interest income and interest expense

- If *YTM* is the yield to maturity on a generic credit in a portfolio

- Including capital for bank interest expense, Kupiec (2006a) shows capital rule is

## Slide 35

## When interest income and interest expense are recognized:

**Capital requirements are higher than AIRB rule**

## Recognizing Systematic Risk in LGDs

## Generalized Single Factor Gaussian Model [Kupiec 2006c]

*LGD *is random and driven by common factor
- Approximate unconditional *LGD *distribution to a get closed form expression for capital for ***any*** *LGD* distribution
- Step function approximation

## Slide 39

## Step size 5%

- Threshold value for latent variable

## Want better approximation? 

- Want better approximation?
- Make step size smaller

## Modeling Random LGD

- Use latent Gaussian factor for PD
- Default threshold
- Probability of default

## Introduce New Latent Factor for LGD

-        factor drives *LGD* realizations
- Thresholds for the increments in the step function approximation

## Define an Indicator Function for Each Step

## LGD Model

- Loss Rate on a Credit
- Conditional value of default indictor
- Conditional value of individual LGD step triggers

## Portfolio Loss Rate Distribution

## Interpretation

- when

- when

- “stress” or “downturn” *LGD*

- Stress *LGD* can be interpreted as an expected value of new *LGD *distribution:
*probability is shifted from lower LGD realizations to higher LGD realizations*

## Stress LGD Calculation

- Stress LGD=expected value of maroon distn

## Slide 49

## Capital when LGDs are Correlated

**Requires substantially more capital than Basel AIRB**
*Capital increases by about 30 percent going from ELGD to Stress LGD in example in paper*
- Recognizes interest income on portfolio
- Includes capital for bank interest expense
- Includes capital for LGD systematic risk

## Random EADs

- AIRB rule assumes *EAD*s are known quantities
- qualitative adjustments in NPR guidance
- When *EAD*s are random, they require additional capital if *EAD* realizations are correlated
*EAD* systematic risk changes the capital rule

## “Stress EADs”

- Step function approach to model random *EAD*s
- Method will produce a “stress *EAD*” that is larger than a simple average *EAD*
- EAD systematic risk requires additional capital
- Approch developed in Kupiec(2006c)

## Conclusions

- AIRB approach reduces minimum capital
- Capital reductions are not consistent with sound risk measurement practices
- AIRB rule ignores many basic risk factors that determine bank capital needs
- AIRB understates risk and bank capital needs
- Omitted factors are fundamentally important for understanding and measuring the risk in complex financial institutions
- A sound risk measurement standard should formally recognize these factors

## Can’t Pillar 2 Fix these Issues?

- Unlikely and risky “solution”
- Capital modeling for credit is new science
- Judgment plays key role as data are limited
- High quality human capital is scarce
- Standards are evolving & approaches vary
- Pillar 2 requires bank examiners to argue obscure theoretical issues with bank quants and high-dollar industry consultants
*Bad bet if you are using my money*

## AIRB capital becomes upper bound on bank internal capital estimates

**Senior management thinks a “good” risk manager gets bank business “done” using the least capital**
*Very few understand model details*
*Undercapitalization costs materialize later*
*Sound risk measurement practices that require more capital are always dismissed in bank internal debates when a recognized “benchmark” requires less capital **[Kupiec’s Law]** *
*Bankers never argue that regulatory capital requirements are too low*

## Legal Issues

- AIRB rule becomes safe harbor in legal debates
- Minimum standard for sound risk measurement practice no longer debatable in court
- Removes possibility to recover losses resulting from reckless financial management practices
- compliance with the AIRB establishes that firm followed “sound risk measurement policies”
**Removes market discipline**