943 F.2d 428
34 Fed. R. Evid. Serv. 256
UNITED STATES of America, Plaintiff-Appellee,v.Adolph J. BARSANTI, Defendant-Appellant.UNITED STATES of America, Plaintiff-Appellee,v.Harold M. KLINE, Defendant-Appellant.UNITED STATES of America, Plaintiff-Appellee,v.Allen GRIFFEY, Defendant-Appellant.
Nos. 90-5341 to 90-5343.
United States Court of Appeals,Fourth Circuit.
Argued March 7, 1991.Decided Aug. 19, 1991.

Robert P. Watkins, Williams & Connolly, Washington, D.C., argued (Nancy R. Priess, Robert J. Shaughnessy, on brief), for defendant-appellant Kling.
Michael S. Lieberman, Dimuro, Ginsberg & Lieberman, P.C., Alexandria, Va., for defendant-appellant Griffey.
F. Michael Ballard, Fairfax, Va., for defendant-appellant Barsanti.
Paul George Cassell, Asst. U.S. Atty., Norfolk, Va., argued (Henry E. Hudson, U.S. Atty., on brief), for plaintiff-appellee.
Before ERVIN, Chief Judge, PHILLIPS, Circuit Judge, and BRITT, District Judge for the Eastern District of North Carolina, sitting by designation.
OPINION
ERVIN, Chief Judge:


1
Adolph J. Barsanti, Harold M. Kline, and Allen Griffey were indicted in an eleven count indictment in the Eastern District of Virginia.   They were charged with conspiracy, making false statements, and defrauding the United States.   All three were convicted of the conspiracy charges.   In addition, each was convicted of making false statements to the United States Department of Housing and Urban Development (HUD) and the Federal Housing Administration (FHA).   Barsanti, Kline and Griffey appeal their convictions asserting that numerous errors were committed by the district court during their trial and at sentencing.   We find that the district court committed no error in the trial or at sentencing;  therefore, we affirm the convictions and sentences of Barsanti, Kline, and Griffey.


2
* Barsanti and Kline were two individuals who began acquiring condominiums at the Carlton condominiums complex for investment purposes.   They acquired units with the assistance of two real estate agents at the Carlton, Griffey and Harriet Becker.   Barsanti and Kline invested in various units at the Carlton by obtaining low-downpayment, owner-occupant HUD mortgage insurance.


3
Section 234 of the National Housing Act authorizes HUD to insure mortgages covering one-family condominium units.  12 U.S.C. § 1715y(c).   Regulations implementing this program distinguish between "occupant" mortgagors and "non-occupant" mortgagors.   See 24 C.F.R. § 234.27 (1985).   A HUD-insured mortgage for an occupant mortgagor could cover as much as 97% of the value of the property.   A non-occupant's HUD-insured mortgage could cover no more than 85% of the value.


4
In five of the six transactions in this case, a basic pattern of events occurred.   An individual showed an interest in possibly purchasing a unit at the Carlton and subsequently made a deposit.   At the time he made his deposit, he was told that he could change his mind within 10 days and get a full refund.   The individual then changed his mind and attempted to get his deposit back.   At that time, the real estate agent told him that there would be a delay in getting his deposit back, and then the agent told him about a great deal whereby he could get his deposit back and in addition make some extra money.   The individual would buy the unit in a shared-equity arrangement with an investor (either Barsanti or Kline).   The real estate agent, coincidentally, just happened to know of an investor who might be interested in such an arrangement.   Together, the individual and the investor would apply for a HUD owner-occupant mortgage.   Then, just after the loan came through, the investor would buy the individual out for $1500.   Thus, the individual would make a small profit, and the investor would obtain a condominium with a small downpayment and a guaranteed loan.


5
When applying for the HUD-insured mortgage, both the individual and the investor filled out a form to be filed with HUD.   In the form, the parties made the following certified statements:


6
(b) One of the undersigned is the occupant of the subject property.


7
(c) All charges and fees collected from me as shown in the settlement statement have been paid from my own funds, and no other charges have been or will be paid by me in respect to this transaction.


8
Both the investor and the individual signed the above certifications;  however, the individual never moved into the condominium.   Neither did the investor;  therefore, there never was an "owner-occupant."


9
This basic chain of events occurred in five of the six transactions at issue in this case.   In the sixth transaction, a couple (the Ohris) entered into a purchase agreement for a unit at the Carlton and paid a $2,000 deposit.   They decided two months later that they wanted out of the deal.   Real estate agent Griffey put the Ohris in contact with Barsanti, who agreed to buy the Ohris' condominium from them.   The Ohris applied for the HUD-insured mortgage themselves;  they signed the certification that they would be owner-occupants.   Barsanti did not sign the certification.1  The Ohris had already moved out of the unit before they applied for the HUD insurance, however, and again there was no "owner-occupant" in this unit.   Barsanti bought the Ohris' condominium after the mortgage came through.   Barsanti could do this because owner-occupant mortgages are assumable.


10
On December 13, 1989, a grand jury in the United States District Court for the Eastern District of Virginia returned an eleven count indictment against Barsanti, Kline, and Griffey.   Count I charged all three with conspiracy to commit offenses against the United States including making false statements, mail fraud, misprision of felony, and defrauding the United States and its departments and agencies in violation of 18 U.S.C. § 371.   Counts II through VII charged the appellants with making, or causing to be made, false statements to HUD and FHA on documents known as "Certificates of Commitment for HUD Insured Mortgage" in violation of 18 U.S.C. §§ 1001 and 2.   Counts VIII through XI charged each of the appellants with mail fraud in violation of 18 U.S.C. § 1341.


11
The district court granted the government's pretrial motion to dismiss with prejudice Counts VI, VII, and IX through XI as to Barsanti;  Counts II through IV and VIII through XI as to Kline;  and Counts II, IV, V, and VIII through XI as to Griffey.   As a result, at trial in February, 1990 each of the appellants was charged with one count of conspiracy (Count I);  Barsanti was charged with four counts of false statements (Counts II, III, IV, and V) and one count of mail fraud (Count VIII);  Kline was charged with three counts of false statements (Counts V through VII);  and Griffey was charged with three counts of false statements (Counts III, VI, and VII).


12
After a jury trial, Barsanti was convicted on three of the false statement counts (Counts II, IV, and V);  he was acquitted on Count III.   Barsanti was also acquitted on the mail fraud charge (Count VIII).   Kline was convicted on three false statement counts (Counts V, VI, and VII).   Griffey was convicted on one of the false statement counts (Count III) and acquitted on two (Counts VI and VII).   All three were convicted on the conspiracy charge in Count I.   The district court denied appellants' motions for judgment of acquittal and for a new trial.


13
The district court held a post-trial hearing on whether the United States Sentencing Guidelines applied to the conspiracy convictions.   At the hearing, the court ruled that the conspiracy continued after November 1, 1987 by virtue of several acts by Barsanti and Kline.   The court explained:


14
I think the guidelines apply to Count 1.   I think the retention of the units under their insured mortgage status, the making of mortgage payments, receipt of rents from others, that is others than those who signed up as ostensible occupants, all are acts in furtherance of the conspiracy.


15
The court then ruled that the Guidelines were applicable to the conspiracy convictions.   The court then sentenced each of the appellants to a term of fourteen months imprisonment and a subsequent term of two years of supervised release.   The court also imposed fines as follows:  $20,000 each for Barsanti and Kline and $7,000 for Griffey.   This appeal followed, and the district court granted the appellants' motions to remain free on bond pending appeal.

II

16
The appellants were charged, inter alia, with making false statements to a federal agency in violation of 18 U.S.C. § 1001.2  The first issue raised by the appellants is whether the district court erred in refusing to let their expert witness, Philip Forest, testify concerning the allegedly false statements made by them.   According to the proffer of Forest's testimony, he would have testified regarding the meaning of (1) owner-occupant;  and (2) the language "this transaction" which was found in the (c) portion of the certification.


17
The trial court has broad discretion to determine whether to admit expert testimony, United States v. Portsmouth Paving Corp., 694 F.2d 312, 323 (4th Cir.1982), and will not be reversed absent a clear abuse of discretion.  Friendship Heights Assoc. v. Vlastimil Koubek, A.I.A., 785 F.2d 1154, 1159 (4th Cir.1986).   Thus, we must determine whether the district court abused its discretion in refusing to let Forest testify as to the two proffered subjects.


18
* According to the proffer of Forest's testimony, he would have testified that "the statutes and regulations of HUD with respect to owner occupancy was [sic] insufficient to put defendants on notice of any potential violation that any false statement made could not be material as a matter of law because of the vagueness and confusion of the owner occupancy requirement;  ..."   The government objected to the testimony, and the district court sustained the objection.   The court stated:


19
The issue in this case is whether there was a false statement made and conspiracy to do those offenses which are alleged in counts 2 through 8.   What the regulations say really don't have much to do with it....  [T]here is nothing ambiguous about the statement [made in certification (b) ].


20
Appellants argue that Forest's testimony was relevant to whether the statements made by them were false.   They cite to cases where expert testimony was deemed admissible to show that the statements that were made were not false.   See United States v. Race, 632 F.2d 1114 (4th Cir.1980);  United States v. Anderson, 579 F.2d 455 (8th Cir.1978), cert. denied, 439 U.S. 980, 99 S.Ct. 567, 58 L.Ed.2d 651 (1978).   In Race, this court noted that a defendant could not be "convicted under § 1001 for a statement ... which may be said to be accurate within a reasonable construction of the contract."  Race, 632 F.2d at 1116.   In Anderson, the Eighth Circuit held that the government has the burden in § 1001 cases of "negativ[ing] any reasonable interpretation that would make the defendant's statement factually correct."  Anderson, 579 F.2d at 460.   Appellants try to come within the holdings of Race and Anderson by arguing that "owner occupant" is vague and subject to a construction which would make their statements not false.   This argument is flawed.


21
Forest's testimony can be of no help to appellants.   They assert that Forest would have testified that there was no 30-day occupancy requirement and that no specific time for occupancy was required by HUD in its practice.   Even if this were so, Forest could not have testified that HUD did not require occupancy at some time.   In the six transactions at issue in this case, not one of the "owner-occupants" ever moved into the unit purchased after the settlement.   Thus, Forest's testimony would not help the appellants no matter how he defined "owner-occupant," short of saying it didn't require occupancy at all.   In other words, there is no reasonable interpretation of "owner-occupant" that would make the statements in certification (b) factually correct.


22
Under Federal Rules of Evidence 702, an expert may testify if his "knowledge will assist the trier of fact to understand the evidence or to determine a fact in issue."   Fed.R.Evid. 702.  "Rule 702 makes inadmissible expert testimony as to a matter which obviously is within the common knowledge of jurors because such testimony, almost by definition, can be of no assistance."  Scott v. Sears, Roebuck & Co., 789 F.2d 1052 (4th Cir.1986).   Here, part of the appellants' argument rests on the idea that the statement in certification (b) is nonsensical because people who apply for mortgages don't already "occupy" the houses they are trying to buy.3  Therefore, the statement "[o]ne of the undersigned is the occupant of the subject property" doesn't make sense.   This is an argument that doesn't require expert testimony.4  Counsel could make this assertion in closing arguments pointing out the inconsistency of the statement.   No expert testimony is required for the jury to understand this argument, and the court correctly determined that Forest could not testify as to the meaning of "owner-occupant."

B

23
Appellants also assert that Forest should have been allowed to testify regarding the meaning of the phrase "this transaction."   The proffer of Forest's testimony showed that he would have testified that "an agreement under a shared equity program that one party would in the event of a buyout pay the other party $1,500 for his interest in that property would under no circumstances violate certification (c) because it was not in connection with the mortgage transaction, and was further contingent, it did not definitely obligate either party to pay such amounts."   Further, he would have testified that a buy-out after closing would constitute a separate transaction from the initial purchase and issuance of HUD mortgage insurance.


24
Appellants argue that this testimony would have been helpful to the jury because the language "this transaction" in certification (c) was unclear.   The district court sustained the government's objection to this line of testimony, thereby prohibiting Forest from testifying as to the meaning of "this transaction."


25
With respect to certification (c), there may be a reasonable interpretation of "this transaction" which would make the appellants' statements factually correct.   The government's witness who worked at HUD testified that the phrase "this transaction" would cover the two transactions involved in this case:  the initial settlement where the owner-occupant and owner-investor bought the condominium and the subsequent buyout by the owner-investor of the owner-occupant's interest in the unit.   Forest apparently would have testified that "this transaction" meant only the initial settlement.   If that were so, the certification (c) statements made by appellants would not have been false.


26
Under the holdings of Race and Anderson, the district court erred in refusing to allow Forest to testify on this issue.   However, any error regarding certification (c) was harmless because the appellants were charged with making two false statements in violation of 18 U.S.C. § 1001:


27
1.  That one of the mortgagors was or would be the occupant of the property subject to the mortgage.


28
2. That all charges and fees collected from the mortgagors as shown in the settlement statement were paid from their own funds, and that no other charges had been or would be paid by the mortgagors in respect to the transaction.


29
There was overwhelming evidence that the appellants did make false statements about being occupants in certification (b).   Therefore, even if the statements regarding "this transaction" in certification (c) were capable of an interpretation making the statements factually correct, the appellants were still guilty of violating 18 U.S.C. § 1001 with regard to certification (b).   As a result, any error in excluding expert testimony on the certification (c) issue was harmless, and the district court's ruling excluding Forest's testimony is affirmed.

III

30
Kline argues that venue in Virginia was improper with respect to the false statement charges in Counts VI and VII.   Venue questions in criminal cases are not merely procedural issues, but implicate strong issues of public policy.  United States v. Martinez, 901 F.2d 374, 376 (4th Cir.1990) (quoting United States v. Johnson, 323 U.S. 273, 276, 65 S.Ct. 249, 251, 89 L.Ed. 236 (1944)).   The burden of proving that a crime occurred in the district where prosecuted is on the government.  United States v. Griley, 814 F.2d 967, 973 (4th Cir.1987).   However, the government does not have to prove where the crime was committed beyond a reasonable doubt;  it must only prove where it was committed by a preponderance of the evidence.  Id.


31
Venue in a criminal case is determined by the "nature of the crime alleged and the location of the act or acts constituting it."  United States v. Anderson, 328 U.S. 699, 703, 66 S.Ct. 1213, 1216, 90 L.Ed. 1529, 1532 (1946).   When Congress has not expressly provided where venue is appropriate, the court must decide based upon the statutory language:


32
When ... the statute defining the substantive offense "does not indicate where Congress considered the place of committing the crime to be, the locus delecti must be determined from the nature of the crime alleged and the location of the act or acts constituting it."  United States v. Anderson, 328 U.S. 699, 703, 66 S.Ct. 1213 [1216], 90 L.Ed. 1529 (1946) (citations omitted).   In determining the act or acts constituting the crime, we have commonly focused on the verbs employed in the statute defining the offense.


33
United States v. Blecker, 657 F.2d 629, 632 (4th Cir.1981).   Congress did not expressly provide for venue in 18 U.S.C. § 1001;  therefore, we must look to the verbs of the statute for guidance.   Section 1001 prohibits persons from


34
conceal[ing] or cover[ing] up by trick, scheme, or device a material fact, or mak[ing] any false, fictitious or fraudulent statements or representation, or mak[ing] or us[ing] any false writing or document knowing the same to contain any false, fictitious or fraudulent statement or entry, ...


35
18 U.S.C. § 1001.


36
In interpreting a similar statute, this court has held that venue is appropriate in a district where the statement "passed through."   See United States v. Blecker, 657 F.2d 629 (4th Cir.1981), cert. denied, 454 U.S. 1150, 102 S.Ct. 1016, 71 L.Ed.2d 304 (1982).   In Blecker, the defendants were charged with violating the false claims statute.  Id. at 632.   The relevant verbs in the statute were "makes or presents."  Id.  The statements at issue were made (prepared) in Maryland;  they were ultimately presented to a government agency in Washington, D.C.  Id.  In the interim, they passed through Virginia, as the defendants presented the statements to an agency in Virginia which in turn presented them to the government agency in Washington.  Id. at 632-33.   This court found that venue in Virginia was proper under a "passing through" theory:


37
"The last act taken by the defendants in committing the crime of submitting false claims to the government was the presentation of those claims to CSC at its Rosslyn, Virginia office with the knowledge that they would ultimately be transmitted to the GSA for payment....  Under these circumstances, we hold that venue properly lay in the Eastern District of Virginia."


38
Id. at 633.


39
The holding of Blecker is applicable to the facts before us.   Here, the false statements were signed by Kline in his attorney's office in Washington, D.C.   However, they were then sent to the mortgage bank in Virginia.   The bank in Virginia processed all the paper work and then sent it on to HUD in Washington, D.C.   Practically, a buyer such as Kline could not have sent the documents directly to HUD because he was applying for mortgage insurance from HUD.   By definition, there had to be a mortgage bank involved from which the buyer was trying to get a mortgage.   And as it happened in this case, that mortgage bank was located in Virginia.5


40
Under the theory of Blecker, the statements in this case were passed through a necessary intermediary in Virginia.   Kline made the statements in his attorney's office in Washington, D.C., knowing that they would go to the lending institution in Virginia and then on to HUD in Washington.   As a result, "pass through" venue in Virginia was proper, and the district court had venue for Counts VI and VII.

IV

41
All three appellants challenge the district court's ruling that the conspiracy continued after November 1, 1987, and that the Guidelines applied to their conspiracy convictions.   Congress expressly limited the applicability of the Guidelines to criminal offenses committed after November 1, 1987.  United States v. Polk, 905 F.2d 54, 55 (4th Cir.), cert. denied, --- U.S. ----, 111 S.Ct. 519, 112 L.Ed.2d 531 (1990).   However,


42
[i]n the context of an ongoing crime, courts have interpreted "offenses committed after" to mean offenses continuing after the effective date of the Guidelines.   Under this approach, a conspiracy begun before November 1, 1987 and continuing after that date, thus straddling the effective date, would be sentenced under the Guidelines.


43
United States v. Bakker, 925 F.2d 728, 739 (4th Cir.1991).


44
The appellants question the court's factual finding in this case that the conspiracy continued after November 1, 1987.   Our review of that finding is governed by 18 U.S.C. § 3742(e) which directs us to "accept the findings of fact of the district court unless they are clearly erroneous."


45
In this case, one of the objectives of the conspiracy was to obtain the low downpayment, 97% insured loans.   Appellants argue that once the loans were obtained and this objective was achieved, the conspiracy ended.   Since the loans were obtained before November 1, 1987, they argue that the conspiracy ended before November 1, 1987 and that the Guidelines did not apply to their convictions.   However, there were other objectives of the conspiracy which remained unfulfilled on November 1, 1987.


46
One of the advantages of the scheme was that profits would be made upon the ultimate sale of the units by Barsanti and Kline.   There was evidence at trial that the units had appreciated since they were purchased.   In addition to the profits on each unit, this scheme provided for another advantage for Barsanti and Kline.   Since the downpayments were so low, each was able to purchase several units.   If their downpayments had not been so low, and had the loans not been 97% guaranteed by the government, they might not have been able to purchase as many units.   Thus, they effectively multiplied the amount of profits they could make because of their ability to buy so many units.


47
There was evidence at trial that Griffey made a proposal to Barsanti and Kline to show them that if they held on to the condominium units for three years, they could make a 40% return on each unit.   This evidence shows that the conspiratorial agreement contemplated that the conspiracy would last for at least three years.   Since the units were purchased in 1984 and 1985, the conspiratorial agreement contemplated that the conspiracy would last past the effective date of the Guidelines on November 1, 1987.


48
In addition, evidence showed that BK Associates made mortgage payments on the units owned by Barsanti and Kline well after November 1, 1987.   BK Associates was a partnership entered into by Barsanti and Kline, established to manage the units owned by Barsanti and Kline.   BK Associates was intimately involved in the scheme whereby the owner-occupants appeared to be paying rent for the units, but in fact were not.   The ostensible owner-occupants paid rent to the condominium complex.   BK then reimbursed them for the "rent" they paid.   At the same time, other individuals who were actually living in the units paid rent directly to BK Associates for the units they occupied.   Tax returns for BK Associates for the years 1987, 1988, and 1989 showed that the partnership claimed interest expenses for "Seven Condo's [sic] at 4600 S. Four Mile Run Dr."   Those units were the Carlton units owned by Barsanti and Kline.   BK Associates claimed interest expenses in the following amounts:  $38,926.39 in 1987;  $39,071.07 in 1988;  and $28,594.89 in 1989.


49
The district court found that the conspiracy had objectives which continued after November 1, 1987 and that the conspiracy continued after the effective date of the Guidelines.   We must decide if that determination was clearly erroneous in light of the above evidence.


50
Appellants argue that the continued mortgage payments and possible profits from the sale of the units were merely "results" of the conspiracy and were not "objectives" of the conspiracy that would cause the conspiracy to continue after November 1, 1987.   They rely upon United States v. Doherty, 867 F.2d 47 (1st Cir.), cert. denied, 492 U.S. 518, 109 S.Ct. 3243, 106 L.Ed.2d 590 (1989), for support for this contention.   In Doherty, the defendants were charged with conspiracy to obtain promotions in the police department by stealing and selling police examinations.   The First Circuit had to determine whether each defendant's receipt of higher salary payments after a certain date could count as an overt act for statute of limitations purposes.  Id. at 61.   The court found that "the receipt of salary [was] a 'result' of, not an act in furtherance of, the conspiracy."  Id. at 62.   Appellants in this case rely upon Doherty's result and argue that the ultimate payoff for Barsanti and Kline when they sell their units is likewise a result, rather than an objective, of the conspiracy.


51
However, the language in Doherty calls for a different conclusion.   The First Circuit wrote:


52
[W]here receiving the payoff merely consists of a lengthy, indefinite series of ordinary, typically noncriminal, unilateral actions, such as receiving salary payments, and there is no evidence that any concerted activity posing the special societal dangers of conspiracy is still taking place, we do not see how one can reasonably say that the conspiracy continues.   Rather, in these latter circumstances, one would ordinarily view the receipt of payments as the 'result' of the conspiracy.


53
Id. at 61.   In this case, there were continued concerted activities by Barsanti and Kline which continued after November 1, 1987.   Specifically, BK Associates continued to make mortgage payments, receive rents, and manage the properties owned by Barsanti and Kline well after the Guidelines were enacted.   Unlike the unilateral activities in Doherty, the activities by Barsanti and Kline with regard to their condominium units were done through a well-organized partnership.   Thus, Doherty does not call for the result urged upon us by appellants under the present facts.


54
We find the reasoning of United States v. Mennuti, 679 F.2d 1032 (2d Cir.1982), persuasive.   In Mennuti, the defendant was involved in a scheme to destroy private residences to get insurance money.   Part of the agreement was that Mennuti would purchase the property from the landowner at a bargain price after the insurance money was received.   Mennuti argued that the object of the conspiracy was to get the check from the insurance company, and that the conspiracy ended when the check was received.   The Second Circuit disagreed:


55
Mennuti asserts that the object of the conspiracy was to acquire control over the [insurance] check and that when the check was acquired, concededly outside of the limitations period, the conspiracy ended.   We think it abundantly clear, however, that the scope of the conspiracy was not limited to receipt of the insurance check.   The conspiratorial agreement also included a payoff to each conspirator, which in Mennuti's case was the exclusive right to purchase the property at a bargain price after the house was destroyed....  [E]ven if the main objective of the conspiracy in this case was to defraud [the insurance company], the conspiracy continued until its other objectives, including Mennuti's own payoff, were achieved.


56
Id. at 1035-36.


57
Similarly, in United States v. Walker, 653 F.2d 1343 (9th Cir.1981), cert. denied, 455 U.S. 908, 102 S.Ct. 1253, 71 L.Ed.2d 446 (1982), the Ninth Circuit held that a conspiracy to commit fraud continued long after the false statement was made to the government agency.   There, the statement was made during a bid-rigging scheme.   The court stated:


58
[T]he fraud here involved a false statement to a government agency and the later enjoyment of the fruits of that deception and was properly charged as a § 371 fraud.   Therefore, the last overt act of this conspiracy was not the filing of the false certificates, because the agreement itself aimed beyond merely defeating the government process of competitive bidding and encompassed the ultimate objective of making excess profits to be shared among the co-conspirators.


59
Id. at 1347.   In this case, one of the objectives of the conspiracy to defraud HUD was that Barsanti and Kline would make money when they ultimately sold their units.   This objective had not been accomplished on November 1, 1987.


60
As this court has held, conspiracy is an ongoing crime, and if a criminal conspiracy is established, it is presumed to continue until its termination is affirmatively shown.  United States v. Sheffer, 896 F.2d 842, 844 (4th Cir.), cert. denied, --- U.S. ----, 111 S.Ct. 432, 112 L.Ed.2d 416 (1990).   Further,


61
[d]uring sentencing, the district court's findings of fact should be based upon a preponderance of the evidence.   The court of appeals should "give due regard to the opportunity of the district court to judge the credibility of the witnesses, and [must] accept the findings of fact of the district court unless they are clearly erroneous."  18 U.S.C. § 2742(d).


62
Id.  In this case, the district court found that the conspiracy continued after November 1, 1987.   There was ample evidence to support that finding, given that Kline and Barsanti were still reaping the benefits of their investments well beyond November 1, 1987.   In addition, they were doing so through continued concerted activity in the form of BK Associates.   We hold that the facts support the district court's finding that the Guidelines applied in sentencing Barsanti and Kline.


63
With respect to Griffey, we find that application of the Guidelines as to him was also correct.  "A defendant's membership in a conspiracy is presumed to continue until he withdraws from the conspiracy by affirmative action."  United States v. West, 877 F.2d 281, 289 (4th Cir.1989).   To prove withdrawal, a defendant must provide evidence that he acted to defeat or disavow the purposes of the conspiracy.  Id.  Here, Griffey has made no such showing.   Although his active conduct in the conspiracy had ceased before the effective date of the Guidelines, we have found that the conspiracy itself continued after that date.   Since Griffey offered no evidence that he acted to defeat or disavow the purposes of the conspiracy, we hold that the Guidelines were correctly applied to him.

V

64
Griffey asserts that the district court erred by denying his motion for judgment of acquittal after the jury sent a question to the court during deliberations.   The jury's question was as follows:


65
Pg. 16, para 21, under Unit 316 appears to be in error.   The date of Dec. 21, 84 is inconsistent with other dates for this unit and is not supported by the evidence.   The evidence indicated that only the Ohris signed the HUD Certificate.   Please Clarify Count III.


66
The court responded by referring the jury to the portion of its charge relating to the use of the phrase "on or about" in the indictment.   The court further referred the jury to the charge on aiding and abetting.   Afterwards, the jury found Griffey guilty of Count III (the Ohris sale) and acquitted Barsanti.6


67
We review the giving of supplemental instructions under an abuse of discretion standard.   See United States v. Lozano, 839 F.2d 1020, 1024 (4th Cir.1988).   It is entirely proper for the court to refer the jury back to the court's original charge.   See United States v. White, 794 F.2d 367, 370 (8th Cir.1986).   The court in this case properly tried to assist the jury by referring them to portions of the original charge which he thought might assist them.   This was not an abuse of discretion.


68
In this case, there was only one possible problem with the jury's verdict.   That problem was the variance between the date of the indictment regarding the Ohris transaction and the date which the evidence showed that the transaction actually occurred.   The indictment alleged that the false statements in the Ohris transaction occurred "on or about December 21, 1984."   Evidence at trial showed that the certification by the Ohris was signed on April 26, 1985, some four months later.


69
Looking only at the variance between the dates, it appears that there may be a fatal variance between the indictment and the evidence.   However, on further reflection, the variance was not fatal.


70
Rule 52(a) of the Federal Rules of Criminal Procedure requires us to disregard a variance if it does not affect substantial rights of the defendant.  United States v. Quicksey, 525 F.2d 337, 341 (4th Cir.1975), cert. denied, 423 U.S. 1087, 96 S.Ct. 878, 47 L.Ed.2d 97 (1976).   The test of substantiality is found in Berger v. United States, which requires


71
(1) that the accused shall be definitely informed as to the charges against him, so that he may be enabled to present his defense and not be taken by surprise by the evidence offered at trial;  and (2) that he may be protected against another prosecution for the same offense.


72
295 U.S. 78, 82, 55 S.Ct. 629, 630, 79 L.Ed. 1314, 1318 (1935).  Berger also directs that if an examination of the entire record shows that the variance did not appear to have caused prejudice, the error must be regarded as harmless.  Id.


73
In this case, the indictment relating to Count III was sufficiently clear despite the erroneous date so that it passes the two prongs of Berger.   The indictment informed Griffey that he was being charged with false statements in connection with the sale of Unit 316.   There was only one transaction involving Unit 316, and that was the transaction with the Ohris.   Therefore, although the date was four months wrong, Griffey knew what transaction was involved in the count and to whom he sold Unit 316.   Griffey was sufficiently informed about the charge relating to Unit 316 that he could prepare a defense without being surprised.   For the same reason, namely that there was only one transaction involving Unit 316, there is no danger of double jeopardy.   Thus, the variance in this case was not an error requiring a judgment of acquittal.   See Quicksey, 525 F.2d at 341.

VI

74
Griffey asserts that the government proved two conspiracies rather than a single conspiracy as alleged in the indictment.   Therefore, he asserts that his conviction should be reversed.


75
"The government bears the burden of proving the single conspiracy it charged in the indictment.   On appeal, this court must determine whether the evidence, when viewed in the light most favorable to the government, Glasser v. United States, 315 U.S. 60, 80, 62 S.Ct. 457, 469, 86 L.Ed. 680 (1942), supports the jury's finding of a single conspiracy."  United States v. Hines, 717 F.2d 1481, 1489 (4th Cir.1983).   If the evidence shows that there was more than one conspiracy, we must reverse the verdict only where proof of the multiple conspiracies prejudiced substantial rights of appellants.  Id. at 1489-90.   A defendant's rights would be infringed if the jury would have been confused into imputing guilt to members of one conspiracy because of the illegal activities of the other conspiracy.   See id. at 1490.


76
The evidence showed that there was a single conspiracy in this case.  "A single conspiracy exists where there is 'one overall agreement,' ... or 'one general business venture.' "  United States v. Leavis, 853 F.2d 215, 218 (4th Cir.1988) (citations omitted).   Whether there is a single conspiracy depends upon the overlap of main actors, methods and goals.  Id.  Here, there was one general business venture, evidenced by the establishment of BK Associates, which was the conduit through which the money travelled.   The ostensible owner-occupants who "bought" the units paid "rent" checks in order for it to look like they were living in the unit they purchased.   BK Associates then immediately wrote them reimbursement checks for the identical amount.


77
Appellants argue that the Ohris transaction was so different from the other transactions that it constituted a separate conspiracy.   We disagree.   The key players were the same.   Barsanti and Griffey were involved with the ostensible owner-occupants, who in this case happened to be the Ohris.   The only reason this transaction differed from the normal routine was that the Ohris got a little further along on the purchase track by themselves than did the rest of the individuals involved in the scheme.   This does not mean that this one deal constituted a separate conspiracy.


78
Further, even if we were to hold that there were two conspiracies, the appellants cannot show that they were prejudiced in any way.   The jury was not likely to have imputed guilt from this transaction which was otherwise unwarranted.


79
In sum, the evidence showed the existence of a single scheme to defraud the government through its agency HUD.   But even if the evidence showed two conspiracies, there was almost a complete overlap in the players.   Thus, there was no risk that the jury would improperly impute guilt from one conspiracy to the other.   As a result, there was no fatal variance between the indictment and the proof at trial.

VII

80
At sentencing, the court imposed a three-level increase upon Griffey, Kline and Barsanti in their base offense level calculations pursuant to § 3B1.1(b) of the Sentencing Guidelines.   Section 3B1.1(b) requires an increase in a defendant's base offense level if he was a "manager or supervisor (but not an organizer or leader) and the criminal activity involved five or more participants or was otherwise extensive."   United States Sentencing Commission, Guidelines Manual, § 3B1.1(b) (Nov. 1989).   Griffey asserts that increasing his sentence under § 3B1.1(b) was error.  "The trial court's determination that the defendant played an aggravating role in the offense is essentially factual, and therefore is subject to the 'clearly erroneous' standard of review."  United States v. Sheffer, 896 F.2d 842, 846 (4th Cir.), cert. denied, U.S. ----, 111 S.Ct. 432, 112 L.Ed.2d 416 (1990) (citations omitted).


81
The court stated at sentencing:  "It is justified to assess a three-level enhancement because they did manage and supervise the criminal activity.   The criminal activity involved five or more participants, the three themselves [Barsanti, Kline and Griffey], of course, plus Ms. Becker, Behbahani, Adel, Ohri[s], Tippitt and Strother7 and I think they should get the three [level] enhancement."   Evidence at trial showed that Griffey talked first with the individuals who expressed an interest in purchasing units at the Carlton.   He then arranged for them to enter into equity-sharing agreements with Barsanti and Kline.   Without his introduction and encouragement, the individuals would not have met Barsanti and Kline.   Nor would they have made the purchases of the units;  for each of the individuals had decided not to purchase the units and had requested their deposits back.


82
There was ample evidence that Griffey was an essential link in the conspiracy, managing and supervising and arranging for the deals to be struck.   The district court found that he managed and supervised at least five persons, and this finding was not clearly erroneous.

VIII

83
A final issue in this case is raised by Griffey.   He asserts that the district court should have held a hearing due to a newly discovered violation by the government based upon the government's failure to provide him with some material which he was entitled to receive under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963).   The evidence which Griffey asserts was Brady material was as follows.   He declares that Becker contacted him by telephone after the trial and told him that she had told the prosecutor during her debriefing that the only person she told that the Adels would not live in Unit 123 was Marge Murray.   Griffey avers that this was exculpatory evidence in that it tended to show that Becker had not told Griffey that the Adels would not be occupants.   Thus, presumably, Griffey did not know that they did not intend to occupy the unit they were purchasing.   Griffey filed an affidavit with the court to this effect.


84
In response, the government filed an affidavit of Becker denying that she had only told Marge Murray that the Adels were moving out.   She also denied having made the statement which Griffey alleged that she made.   The court determined that no evidentiary hearing was required to resolve this issue.   The court stated:


85
I don't think an evidentiary hearing is necessary, Mr. Rhoades.   I think that it is arguable at best that this is Brady material, or improperly withheld evidence of the prosecutor.   The affidavit dispells (sic) that, in my mind.   So the motion for a new trial on those grounds will be denied.


86
The district court is not required to hold an evidentiary hearing to resolve whether there was a withholding of Brady material when it "would add little or nothing to the proceedings."  United States v. Wilson, 901 F.2d 378, 382 (4th Cir.1990).   The district court had before it conflicting affidavits as to whether the statement was made by Becker.   Griffey's affidavit said that Becker made the statement to him.   Becker's affidavit said that she did not make that statement to Griffey and that she "would not have said such a thing to Mr. Griffey because it was not true."   An evidentiary hearing would have added nothing to the proceedings.   The court had to decide which affidavit to accept, and it did so.   We fail to see what an evidentiary hearing would have accomplished.   Therefore, we hold that no evidentiary hearing was required under these facts and that the district court did not err in refusing to hold such a hearing.

IX

87
To summarize, first we find that the district court did not err in refusing to admit expert testimony offered by the appellants.   Second, we find that venue in Virginia was proper in this case under the principle of "pass through" venue.   Third, we find that the Guidelines applied to the conspiracy convictions in this case because the conspiracy continued after November 1, 1987.   Fourth, we find that the district court properly referred the jury back to the original jury charge when answering a question from the jury.   Fifth, we find that there was no fatal variance between the indictment and the evidence shown at trial since the evidence showed the existence of only one conspiracy.   Sixth, we find that the district court properly increased the base offense levels of Barsanti, Kline, and Griffey as they managed or supervised five or more participants.   Finally, we find that the district court did not err in refusing to hold an evidentiary hearing regarding the alleged Brady material.   For all of the above reasons, the convictions and sentences in this case are affirmed.


88
AFFIRMED.



1
 The jury acquitted Barsanti in the count charging him with false statements in this transaction.   However, they found Griffey guilty, presumably on a theory of aiding and abetting the Ohris in making false statements


2
 Section 1001 provides:  "Whoever, in any matter within the jurisdiction of any department or agency of the United States knowingly and willfully falsifies, conceals or covers up by trick, scheme, or device a material fact, or makes any false, fictitious or fraudulent statements or representations, or makes or uses any false writing or document knowing the same to contain any false, fictitious or fraudulent statement or entry, shall be fined not more than $10,000 or imprisoned not more than five years, or both."  18 U.S.C. § 1001


3
 In the proffer, counsel stated:  "Mr. Forrest [sic] was further expected to testify that with respect to the certificate of commitment marked as Government's Exhibit 1-A, that the language in the certification made no sense in connection with the statutes and regulations governing owner occupancy because the certification statement asked whether the purchaser was an occupant of the property.   In the context of a settlement where the purchaser has not yet purchased the property in most cases he cannot be the occupant of the property, and so the form made no sense."


4
 Counsel for Kline conceded as much at trial.   He stated:  "Your Honor, it seems to me the question about owner-occupancy is one that is clear and may not be denied for expert testimony on that."


5
 The HUD agent who testified at trial stated that HUD got its information to evaluate loans from the lending institutions, with 95% of the information being hand-delivered by couriers on a daily basis.   He further testified that if the packet of information lacked a particular item and therefore could not be processed, HUD would send the packet back to the lending institution, not to the buyer.   Factually, the statement had to go through the lending institution in order to get to HUD


6
 These verdicts are not as inconsistent as they seem at first.   In the Ohris transaction, the Ohris made the false statements alone;  Barsanti did not sign the certification, apparently because the Ohris were financially well enough off that they could get the loan without Barsanti's help.   In apparent reliance upon his promise to buy them out, they continued with the purchase, even after deciding they did not want to own the condominium unit after all.   Since Barsanti did not make a false statement, he was acquitted.   Griffey, on the other hand, was found guilty.   The government proceeded on a theory of aiding and abetting against Griffey.   Here, Griffey introduced the Ohris to Barsanti, and talked the Ohris into continuing to purchase the condominium even after they made it clear that they did not intend to move in and did not want to own the unit


7
 Behbahani, Adel, Ohris, Tippit and Strother were all ostensible owner-occupants.   Becker was a real estate agent who played a role similar to that of Griffey


