Transcript SAMPLE REDESIGN FOR THE FDIC’S ASSET VALUATION REVIEW David W. Chapman Federal Deposit Insurance Corporation For Presentation at the Third International Conference on Establishment Surveys Montreal,

SAMPLE REDESIGN FOR THE
FDIC’S ASSET VALUATION REVIEW
David W. Chapman
Federal Deposit Insurance Corporation
For Presentation at the
Third International Conference on Establishment Surveys
Montreal, Quebec, Canada
June 18-21, 2007
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Introduction
• The FDIC insures deposits for up to $100,000.
• Therefore, the FDIC tracks the financial
soundness of banks
• If a bank fails, the FDIC, as the receiver of the assets,
attempts to sell these assets ASAP
– This requires pricing asset (loan) pools
– Pool prices based on a prob. sample of loans
• The process of selecting a sample of loans, reviewing
them, and pricing loan pools, is the
Asset Valuation Review (AVR)
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Introduction (continued)
• An AVR has to be done quickly
• For about 15 years, have used software called
RAVEN (Risk Analysis and Value EstimatioN)
– Uses FoxPro software
– RAVEN is being rewritten
• Allows sampling methodology to be revised
• Organization of presentation
– Summary of current sampling methodology
– Recommended sampling changes
– Assessment of recommended changes
– Final recommendations/additional research.
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Current Sampling Methodology
• Basic design: Stratified random sample
• Strata defined by
– Loan type (about 8 or 9 pools)
– Loan size in terms of book value (large/small)
• Prior to defining size strata, the smaller loans
are removed from sampling
– Take out loans in bottom 10% of book values
– For these, the sample recovery rate is applied
– This introduces some bias but saves resources
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Current Sampling Methodology (continued)
• Remaining loans in a pool put into 2 size classes
– Iterative procedure: increments of 1% of loans
– For each split, derive ni needed to achieve a specified
precision target for estimating the total book value (as a
proxy for recovery value) for each size class
– Take split that yields the minimum n (=n1+n2)
• RAVEN allows a choice of three precision levels
– High: Estimate total book value
to w/n ± 10% w. 95% confidence
– Medium: to w/n ± 15% w. 90% confidence
– Low:
to w/n ± 20% w. 80% confidence
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Recommended Sampling Methodology Changes
• Introduce a certainty stratum
– Since not using PPS sampling,
no obvious way to define certainties
– Try simple approaches based on
book value coverage (10%, 15%)
• Increase the number of strata
– In general, more strata improve precision
– Recommend either two or three
noncertainty strata
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Recommended Sampling Methodology Changes (cont.)
• Revise methodology for defining strata
– Cochran (1977) discusses methods for
defining optimum strata
• Equalize WhSh across strata
(Dalenius and Gurney, 1951)
• Equalize Wh (yh – yh-1) (Ekman, 1959)
• These methods require “trial and error”
• Cum Sq. Root of f rule
(Dalenius and Hodges, 1959)
– Basically for grouped data
– Have looked at some more recent references
• These seem to be iterative or require assumptions
– Tested simpler methods based on equalizing
the sum of book values, or square roots
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Recommended Sampling Methodology Changes
(continued)
• Derive total n differently, based on
precision target for entire pool
• Revise available precision levels
– High: ± 5% with 95% confidence
– Medium: ± 10% with 95% confidence
– Low: ± 20% with 95% confidence
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Assessment of Recommended Sampling Methodology Changes
• Certainty stratum
– 15% cutoff worked better than 10%
– Need a maximum number of certainty loans (5)
• Number of size strata
– L=3 was generally superior to L=2.
– However, because of the requirement of nh > 1,
L=3 was not much better unless N > 15
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Assessment of Recommended Sampling Methodology Changes
(cont.)
• Stratum definitions
– Compared two simple approaches
• Equalize the sum of book values
• Equalize the sum of square root of book values
• Equalizing the sum of book values worked best
– Theoretical basis for observed conclusion
• Cochran (1961) stated that, for optimum strata,
CV across strata approx. equal
• This result, combined with the result that WhSh are
approx. equal for optimum strata, implies
equal book value sums across strata
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Final Sample Design Recommendations
• Define a certainty stratum
– Coverage of top 15% of book values
– Limited to 5 loans
• Number of Strata
– For N ≤ 5, take all
– For 6 ≤ N ≤ 15, define one certainty stratum and two
noncertainty strata
– For N > 15, define one certainty stratum and three
noncertainty strata
• Stratum boundaries
– Equalize the sum of book values across strata
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Final Sample Design Recommendations (continued)
• Recommendations for future research
– Review the method of defining certainties
– Consider additional methods of defining strata
including iterative procedures
– Consider basing n on the use of ratio estimation
of recovery value
– Investigate the bias and cost savings from
leaving out the bottom 10% of book values
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• To request a copy of my paper or for
comments/questions:
[email protected]
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