VAN GRAAFEILAND, Circuit Judge:

Charles Agee Atkins and William S. Hack appeal from judgments convicting them of violating and conspiring to violate 26 U.S.C. § 7206(1) and (2) and 18 U.S.C. § 371, following a jury trial before Judges Weinfeld and Lasker in the United States District Court for the Southern District of New York. The charges included the willful making and subscribing of false individual and partnership tax returns, § 7206(1), and aiding and assisting in the filing of false individual and partnership returns, § 7206(2). See United States v. Atkins, 661 F.Supp. 491 (S.D.N.Y. 1987). We affirm.

Appellant Atkins was the founder and principal owner of a limited partnership called The Securities Groups, one of whose functions was the creation of tax write-offs for investors in money market instruments, primarily United States government securities. Appellant Hack controlled a similarly occupied company called Mountain Associates. The word "securities" may be somewhat misleading because, in the main, no physical certificates changed hands in the transactions involved herein. As one witness explained it:

Well, there are no physical certificates. The treasury stopped issuing the physical certificates a number of years ago. And when we refer to deliveries, what we are referring to are book entries done on the Federal Reserve system computers. So that the computer in fact keeps track of where the securities are versus where cash is. So that all of these transfers are actually electronic transfers of treasury bills versus fed funds.

Indeed, as another witness pointed out, artificial transactions in treasury bills or notes could be conducted without first purchasing anything from the treasury:

But with these so-called artificial [sic] transactions, they didn't require one having to actually go out and buy anything from the treasury. A dealer would just put something on his books indicating a purchase of transactions or purchase of some volume of securities as of day one in a sale as of some later day and then have corresponding transactions with some other party that also is self-reversing in that way. And that could be done without any transactions actually having to exist or be delivered over the delivery network in the government securities market. It didn't require that treasury securities actually exist.

At one point The Securities Groups' balance sheet showed it with $24 billion of assets and liabilities, with less than a $100 million of capital.

Although the Groups' offering memoranda represented that the Groups intended to handle clients' investments for the primary purpose of realizing economic gains, its real purpose was to generate tax losses for investors who needed them to offset unrelated gains. Such investors were promised 4 to 1 tax write-offs based on an investment consisting of 25 percent cash and 75 percent notes.

Because there is little dispute as to the facts, we need not recount in detail the evidence produced at trial. The Government proved beyond a reasonable doubt that Atkins, with the conniving assistance of Hack and other unindicted accomplices, created, purchased, and sold millions of dollars in fraudulent tax losses for his companies and his customers. Appellants used two basic schemes in creating the fraudulent losses — rigged straddles and rigged repurchase agreements.

A straddle in the securities industry is the concurrent establishment of "long" and "short" positions in a security or securities. A person is "long" if he has contracted to buy a quantity of securities for future delivery, speculating on an advance in the market; he is "short" if he has contracted to sell securities that he may not yet own, speculating on a decline in the market. Prior to the enactment of the Economic Recovery Tax Act of 1981, Pub.L. No. 97-34, 95 Stat. 172, 323-26, dealers such as appellants, by going long and short at the same time, i.e., "straddling", could close out in one year the leg of the straddle that showed a loss and close out in the succeeding year the other leg showing the gain, thus deferring for one year the tax on the offsetting gain.

However, the ordinary straddle is not risk free because there is no assurance that the gain on the second leg will be equal in amount to the loss on the first leg. One witness described a straddle as the "simultaneous purchase and sale of similar but different instruments such that if the market interest rates moved, one side of the position would be profitable, while the other side would automatically lose money." See Lasker v. Bear, Stearns Co., 757 F.2d 15, 16-17 (2d Cir. 1985). Because The Securities Groups was engaging in transactions involving billions of dollars, it proposed to eliminate the possibility of what could be extremely large losses resulting from such market fluctuations.

To accomplish this, it found accomplices such as Hack who, for a fee, were willing to enter into "paper" or computer transactions giving the Groups substantial first leg losses and then, by means of additional "paper" transactions, adjusting the second leg so as to eliminate any gains or losses that otherwise might result from market fluctuations. As one witness described the process, "the entire transaction from start to finish would be arranged, we'd know the end result going into it, and the only economic risk would be the fee paid for the loss."

Another witness, describing a deal between the Groups and appellant Hack, testified as follows:

Q. In this particular transaction between The Securities Groups and Mountain Associates, was there any market risk?

A. No.

Q. And again, could you explain to the jury why that was the case?

A. Because I had told Mr. Hack that we were going to be putting these on for tax purposes, and that there was no intention on our part to either make or lose money, and that as the market moved before year-end, I would realize the losing portion and put the straddle back on, and basically end up the trade when all was said and done with zero profitability.

In general, the process thus briefly described works as follows: After the dealer puts the straddle back on, he enters into a new futures contract, the second leg of which would be the exact opposite of the second leg of the original straddle. In other words, if the second leg of the original straddle called for a long position, the second leg of the new straddle would call for a short one, and vice versa. This would insure that, no matter which way the market moved, the deferred gain on the original straddle would not be affected. See Sochin v. Commissioner, 843 F.2d 351, 352-53 (9th Cir.), cert. denied, ___ U.S. ___, 109 S.Ct. 72, 102 L.Ed.2d 49 (1988); Lasker v. Bear, Stearns Co., supra, 757 F.2d at 16-17.

There was no expectation of profit in the transactions above described, their sole purpose being the creation of artificial tax losses.

Repurchase agreements ("repos") are devices for financing the purchase or sale of securities. The securities form the collateral for the loan, and the interest on the loan may be either pegged to the interest rate to maturity of the underlying security ("repo to maturity") or permitted to float according to the prevailing market rate at any given time ("open" or "term" repo). In a repo to maturity transaction, there can be no profit or loss in connection with interest charges, since they coincide with the interest payable on the collateral security. In an open or term repo, there can be profit or loss, because the interest charges on the loan can be lower or higher than the interest payable on the collateral. The Groups eliminated the possibility of such profit or loss on transactions carried on its books as open or term repos by secretly using repo to maturity rates. They used the undisclosed repo to maturity agreements to purchase treasury bills maturing in the year following purchase, but redeemed them in December of the purchase year as if the financing was an open or term repo. The interest expense payable under these term or open repos generated the desired tax losses. At the same time, the secret repo to maturity agreements insured that no profit or loss due to market fluctuations would occur. Again, we use the words of one of the Groups' employees to describe how this fraudulent procedure worked:

Q. Could you describe for the jury what was said during that conversation and who was speaking?

A. Mr. Gubitosi said that he had come up with a plan to generate tax losses without using straddle situations.

Q. Could you describe what was said about that.

A. He described a method by which we were going to be, we being The Securities Groups were going to go long treasury bill securities and have a financing agreement against it. In fact, the financing agreement would be written on an open basis when in fact it would actually be a repurchase agreement to maturity taking out the risk.

Mr. Gubitosi was very happy that he had come up with this and said, "I don't know why we ever did straddle transactions to begin with, we never had to, we only needed a one side transaction."

Q. Do you recall how he described what you were going to do?

A. He basically said, "Here we have the traditional straddle transaction, we will take the short side, roll it up in a ball and throw it away, we don't need it anymore," meaning by that we could have the long position which would generate the gain the following year and we would have the financing agreements which would generate the loss in the current year.

Q. Would there be any risk in these transactions?

A. No.

Q. Why not?

A. The transactions when they are put on are basically financed to maturity even though the transaction would be listed as an open trade.

Q. Would it still appear as a transaction that had economic risk?

A. Yes.

Appellants used both of above-described devices, or variations of them, to create hundreds of millions of dollars in apparent losses. They also backdated or caused to be backdated a large number of documents in order to increase the amount of their fraudulent claims. For example, the backdating of a purchase or sale by six months would permit the creation of a half year of phantom interest expense. Appellants also falsified other documents that were needed to carry out their schemes, such as disguising kickback payments as trading losses; and they lied to their lawyers, their accountants, and their customers concerning the true nature of their machinations.

Although appellants do not, indeed cannot, contend seriously that the Government did not prove beyond a reasonable doubt their participation in the above described schemes, they contend that they were deprived of due process because they did not know in advance that their conduct was unlawful. In view of the proven falsification and backdating of documents, the secret oral agreements, the lies and the concealment of facts, this argument borders on the specious. See United States v. Ingredient Technology Corp., 698 F.2d 88, 96 (2d Cir.), cert. denied, 462 U.S. 1131, 103 S.Ct. 3111, 77 L.Ed.2d 1366 (1983); United States v. Carruth, 699 F.2d 1017, 1021 (9th Cir. 1983), cert. denied, 464 U.S. 1038, 104 S.Ct. 698, 79 L.Ed.2d 164 (1984); United States v. Winograd, 656 F.2d 279, 282-83 (7th Cir. 1981), cert. denied, 455 U.S. 989, 102 S.Ct. 1612, 71 L.Ed.2d 848 (1982); United States v. Fruehauf Corp., 577 F.2d 1038, 1067-68 (6th Cir.), cert. denied, 439 U.S. 953, 99 S.Ct. 349, 58 L.Ed.2d 344 (1978). "A mind intent upon willful evasion is inconsistent with surprised innocence." United States v. MacKenzie, 777 F.2d 811, 816 (2d Cir. 1985), cert. denied, 476 U.S. 1169, 106 S.Ct. 2889, 90 L.Ed.2d 977 (1986) (quoting United States v. Ragen, 314 U.S. 513, 524, 62 S.Ct. 374, 378, 86 L.Ed. 383 (1942)). Moreover, "[t]he doctrine of substance versus form is well ensconced in tax law." United States v. Crooks, 804 F.2d 1441, 1449 (9th Cir. 1986), modified on other grounds, 826 F.2d 4 (9th Cir. 1987).

Appellants' reliance on 26 U.S.C. § 165(c)(1) (losses allowed if incurred in a trade or business); § 108(a) of the Tax Reform Act of 1984, Pub.L. No. 98-369, 98 Stat. 494, 630 (losses from pre-1982 straddle positions allowed if entered into for profit); and § 1808(d) of the Tax Reform Act of 1986, Pub.L. No. 99-514, 100 Stat. 2085, 2817-18 (losses from pre-1982 straddles allowed when incurred in trade or business or in transaction entered into for profit), is misplaced. As former Judge Weinfeld correctly held in denying appellants' pretrial motion to dismiss, 661 F.Supp. at 495-96, none of these statutes has been applied to sham transactions such as are involved herein. See Forseth v. Commissioner, 845 F.2d 746, 748-49 (7th Cir. 1988); Enrici v. Commissioner, 813 F.2d 293, 296 (9th Cir. 1987) (per curiam); Mahoney v. Commissioner, 808 F.2d 1219, 1219-20 (6th Cir. 1987); United States v. Winograd, supra, 656 F.2d at 282-83.

Appellants' contention that transactions without economic substance and sham transactions are "fundamentally distinct legal concepts" and that a sham transaction is a "fictitious transaction that in fact never took place" demonstrates a lack of understanding of what, for tax purposes, a sham transaction is. A fictitious transaction may be treated as a sham; however, so also may a transaction that "has no business purpose or economic effect other than the creation of tax deductions." DeMartino v. Commissioner, 862 F.2d 400, 406 (2d Cir. 1988). "A sham transaction is one having no economic effect other than to create income tax losses." Neely v. United States, 775 F.2d 1092, 1094 (9th Cir. 1985); see also Knetsch v. United States, 364 U.S. 361, 365, 81 S.Ct. 132, 134, 5 L.Ed.2d 128 (1960); Bail Bonds By Marvin Nelson, Inc. v. Commissioner, 820 F.2d 1543, 1548 (9th Cir. 1987); Ballagh v. United States, 331 F.2d 874, 876-78, 166 Ct.Cl. 191 cert. denied, 379 U.S. 887, 85 S.Ct. 157, 13 L.Ed.2d 92 (1964). Appellants' further contention that the district court's charge on lack of substance has no place in a criminal prosecution is without merit. See United States v. Clardy, 612 F.2d 1139, 1152-53 (9th Cir. 1980).

Judge Lasker, who completed the trial when Judge Weinfeld became severely ill, charged the jurors that, in order to return verdicts of guilt, they must find that the transactions in question were "without economic substance", i.e., that they had no business purpose apart from the creation of a tax deduction, and that they were subject to no market risk. He stated further that a transaction has no purpose apart from creating a tax deduction if it is not intended "either to make or preserve any profit or to limit a loss in any way" and that it is subject to no market risk "if changes in market prices cannot have any effect" on it. Although Judge Lasker did not use the word "sham", he clearly charged the substance of the term as above defined, and the absence of specific terminology therefore is unimportant. See United States v. Ingredient Technology Corp., supra, 698 F.2d at 94; United States v. Philatelic Leasing, Ltd., 794 F.2d 781, 786 (2d Cir. 1986). The charge as given by Judge Lasker is substantially the same as the one we approved in United States v. Ingredient Technology Corp., supra, see 698 F.2d at 97 n. 9. We approve it as given below. Moreover, the proof overwhelmingly supported the jury's verdict.

We have carefully considered appellants' remaining arguments and hold them to be without merit. Accordingly, the judgments of conviction are AFFIRMED.