Under the Sentencing Guidelines, punishment for certain economic crimes depends on the value of the loss inflicted. This case involves a dispute as to how to measure the loss caused by the defendant's default on a fraudulently obtained loan. The government claimed that the loss was 39.5% of the loan's principal balance. The only evidence it offered to support that figure was that the Resolution Trust Corporation, as successor to the defrauded bank, had sold the loan as part of a portfolio of non-performing loans and had realized a price on the portfolio amounting to only 60.5% of the total of the principal balances. Defendant offered in opposition an appraisal that showed a range of values for the property securing his loan, the lowest of which was well above the principal balance. The district court accepted the government's view. We find that it erred in doing so. Because the average value of members of a set, without more, provides no evidence of the value of any particular member of the set, the government's evidence failed to prove a loss. We reverse and remand for resentencing without the Guidelines "point" attributable to this error.

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Fernando Leonzo pled guilty to one count of conspiracy to commit bank fraud in violation of 18 U.S.C. Sec. 371 (1988). At sentencing, the government argued for an enhancement of the base offense level on the basis of asserted losses in three separate transactions. Two of these, with losses totaling nearly $79,000, are undisputed; Leonzo concedes that the district court could properly add six points (for losses exceeding $70,000) and accordingly sentence him to up to 18 months. See U.S. Sentencing Guidelines Sec. 2F1.1(b)(1)(G) (1994).

The dispute here centers around a third transaction, which the government claims bumps the losses up into the next category, "More than $120,000". Id. Sec. 2F1.1(b)(1)(H). In May 1990 Leonzo obtained a $275,000 loan from Perpetual Savings Bank to refinance the mortgage on his home in Vienna, Virginia. He defaulted a year later, leaving nearly $274,000 of outstanding principal. In January 1992 Perpetual was declared insolvent and placed in the receivership of the RTC. The RTC put the loan into a portfolio of loans that had in common only the fact that they were non-performing; it sold the package at auction in September 1992 for 60.5% of the loans' aggregate principal balance.

In preparation for sentencing the government obtained a letter from the RTC reciting this information, which the RTC claimed proved that it had taken a loss of 39.5% of the loan's $273,704.42, or $108,057.88. This brought the total losses caused by Leonzo to well over $120,000. Leonzo responded with an appraisal by Long & Foster Real Estate, valuing the Vienna property at between $300,000 and $330,000. The low end of the range was more than $25,000 above the unpaid balance; the mid-range estimate was more than $40,000 higher. He also applied for funds under the Criminal Justice Act to meet the expense of securing an expert witness, a professor of finance at American University, who, according to Leonzo's application, would provide a written opinion about the RTC's loss calculation.

The district court denied the request for expert assistance as "not warranted" and accepted the RTC's loss calculation. Accordingly, the court added 7 points for the total amount of the losses. After adjusting for various increases and decreases that are not disputed, this yielded a total offense level of 14, with a resulting sentencing range, given defendant's criminal history category, of 15 to 21 months. The court sentenced Leonzo to 21 months.

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For "Offenses Involving Fraud or Deceit" the Sentencing Guidelines direct courts to consider the "actual loss to the victim", and instruct them to calculate the loss as follows:

[I]f a defendant fraudulently obtains a loan by misrepresenting the value of his assets, the loss is the amount of the loan not repaid at the time the offense is discovered, reduced by the amount the lending institution has recovered (or can expect to recover) from any assets pledged to secure the loan.

U.S. Sentencing Guidelines Manual, Sec. 2F1.1, Application Note 7(b) (1994). The government bears the burden of establishing "loss" under Sec. 2F1.1 by a preponderance of the evidence. See United States v. Salmon, 948 F.2d 776, 778-79 (D.C.Cir.1991). The district court implicitly found that the RTC had recovered only 60.5% of the value of the asset "pledged to secure the loan", resulting in a loss of $108,057.88.

The district court's loss calculation is a factual finding that we review for clear error. United States v. Holiusa, 13 F.3d 1043, 1045 (7th Cir.1994); see also United States v. Kim, 23 F.3d 513, 517 (D.C.Cir.1994). We find such an error here. The RTC letter provides no evidence about how much of the value of the Vienna property RTC actually recovered at auction. Many loss amounts, including zero, are consistent with the RTC's recovery of 60.5% for the portfolio as a whole, depending on the distribution of values within the portfolio. One learns almost nothing about the value of a specific house from knowledge that it is located in a zip code where houses are on average worth $300,000, and nothing about the verbal SAT score of a specific high school student from information that her class averaged 615 on the verbal SAT. Indeed, the only evidence in the record directly bearing on the value of the mortgaged property, the appraisal, suggests that the RTC may well have taken no loss at all. Accordingly, the sentence is vacated and the case remanded.

It remains to decide whether on remand the government may offer new evidence to support its claim of a loss on the Vienna loan exceeding $41,000, which would be necessary to carry the total losses over $120,000. We are convinced that it should not. The government had the burdens of production and persuasion, and we see no reason why it should get a second bite at the apple. No special circumstances justified, or even explained, the government's failure to sustain these burdens. As the Seventh Circuit noted in a case in which the government similarly "failed--failed utterly--to prove any loss to the victim of [the defendants'] fraud", "the Guidelines award bonus punishment points for different levels of proven loss beginning with $2,000. The government did not earn a bonus in this case." United States v. Schneider, 930 F.2d 555, 559 (7th Cir.1991); see also United States v. Abud-Sanchez, 973 F.2d 835, 839 (10th Cir.1992); United States v. Smith, 951 F.2d 1164, 1169 (10th Cir.1991). Accordingly, we remand for resentencing on the existing record, with only a 6-point increase under Sec. 2F1.1(b)(G). This of course moots defendant's argument that the district court erred in denying his application for CJA funds for an expert witness. Because the defendant's sentence is a relatively short one, the district court should resentence him quickly, to insure that he serves no more than the eighteen months maximum that a correct application of the Guidelines yields.

So ordered.