SAMPLE REDESIGN FOR THE

1

• SAMPLE REDESIGN FOR THE
• FDICS 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 (n1n2)
• 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
• L3 was generally superior to L2.
• However, because of the requirement of nh gt 1,
• L3 was not much better unless N gt 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 gt 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
• dachapman_at_fdic.gov