
    UNITED STATES of America, Appellee, v. Paul RUSSO, Barbara Hosman, William Petrokansky, Defendants-Appellants.
    Nos. 372, 373, 374, Docket 95-1123, -1124, -1125.
    United States Court of Appeals, Second Circuit.
    Argued Oct. 27, 1995.
    Decided Jan. 11, 1996.
    
      Daniel Richman, New York City (James A. Cohen, Ian Weinstein, of counsel), for Defendant-Appellant Hosman.
    Terence J. Lynam, New York City (C. Fairley Spillman, Neil J. Welch, Jr., Akin, Gump, Strauss, Hauer & Feld, L.L.P., of counsel), for Defendant-Appellant Russo.
    Lawrence S. Bader, New York City (Mor-rillo, Abramowitz, Grand, Iason & Silber-berg, P.C., of counsel), for Defendant-Appellant Petrokansky.
    Alan B. Vickery, Assistant United States Attorney, Brooklyn, NY (Zachary W. Carter, United States Attorney, Peter A. Norling, Gordon Mehler, Assistant United States At torneys, of counsel), for Appellee.
    Before: FEINBERG, OAKES and CABRANES, Circuit Judges.
   OAKES, Senior Circuit Judge:

This is an appeal in a stock market manipulation ease. Paul Russo, Barbara Hosman, and William Petrokansky appeal from judgments of conviction entered February 28, 1995, by the United States District Court for the Eastern District of New York, Sterling Johnson, Jr., J., after a jury found them guilty of mail fraud under 18 U.S.C. § 1341 and securities fraud under 15 U.S.C. §§ 78j(b) and 78ff. Russo and Hosman were also found guilty of conspiracy to commit mail fraud and securities fraud under 18 U.S.C. § 371. Russo was sentenced to 18 months’ imprisonment, five years’ probation, and restitution; Hosman was sentenced to five years’ imprisonment with all but six months suspended and five years’ probation; and Petrokansky was sentenced to 12 months’ imprisonment and five years’ probation. The appellants argue that the district court’s instructions to the jury on several aspects of securities law were erroneous; that the district court improperly permitted testimony by the government’s expert witness; that the evidence against Hosman and Petrokansky was insufficient to convict them; and that the government’s rebuttal summation deprived them of a fair trial. We affirm.

BACKGROUND

As is typical in cases involving manipulation of stocks, the facts before us are extensive and detailed. For purposes of clarity, we divide them into three sections: the business framework, the manipulation scheme, and the trial. We consider all facts and inferences to be drawn from the evidence in the light most favorable to the government. United States v. Birnbaum, 373 F.2d 250, 252 (2d Cir.), cert. denied, 389 U.S. 837, 88 S.Ct. 53, 19 L.Ed.2d 99 (1967).

I. The Business Framework

All three defendants worked for Kureen & Cooper (“K & C”) a broker-dealer which traded in small stocks generally valued at under five dollars per share. Russo bought K & C in 1985 after another small broker-dealer firm he co-owned, Creative Securities, went out of business due to insufficient minimum capital. Russo installed himself as president of K & C and oversaw its operations. Hosman, who had worked with Russo since 1962 and moved with him from Creative Securities, managed the K & C office for Russo and was a K & C broker. She also served as one of K & C’s three directors starting in 1986. Petrokansky, who had also followed Russo from Creative Securities, was one of roughly 20 K & C brokers. Unlike the other brokers, however, Petrokansky had his own office and reported directly to Russo rather than to a manager.

As part of its business, K & C underwrote initial public offerings (“IPOs”) of penny stocks, including the IPOs of the stocks at issue in this case: Lopat and EAS. Both Lopat and EAS were new high-risk companies from which K & C received substantial commissions for its underwritings as well as warrants entitling K & C to buy large numbers of shares at set prices after one year. These warrants served as an incentive to K & C to establish markets for Lopat and EAS so that the price of each company’s shares would rise above the set warrant price. After handling the IPOs, K & C acted as the principal market maker for Lopat and EAS, holding itself out to the market as ready to buy and sell Lopat and EAS stocks at prices which it posted on NASDAQ.

K & C’s customer accounts and its own trading accounts were handled by Evans & Co. (“Evans”), a larger brokerage firm that acted as a “clearing broker” for approximately ten small broker-dealers like K & C. Pursuant to a clearing agreement, Evans performed all the processing and administrative functions associated with K & C’s trades. K & C would execute the trades by filling out buy and sell tickets, which were collected and processed by Evans at the end of each day. Evans would then send out confirmations and account statements to K & C’s customers for whom trades had been executed and to K & C for trading in its own accounts. Evans also provided K & C with a daily “trading slate” that documented all the activity in K & C’s account for the previous day.

II. The Manipulation Scheme

Despite the prospects for Lopat and EAS at the time of their IPOs, the stocks did not perform well. By August 1986, there were more customers selling Lopat and EAS to K & C than buying from the firm, putting K & C at risk of substantial losses. K & C was so thinly capitalized that if it bought stock, it had to sell most of it the same day in order to maintain the minimum net capital required by federal securities regulations. Given the low demand for Lopat and EAS, K & C feared that it would have to sell off the stock at reduced prices and risk triggering a snowball effect as more holders sold Lopat and EAS back to K & C before the price dropped further. K & C was therefore burdened with the problem of continuing to make a market for Lopat and EAS stock so as not to put itself out of business.

In response to this crisis, Russo came up with a complex scheme to manipulate Lopat and EAS stock so that much of it remained off the market and prices did not decline. The scheme involved both unauthorized placement of Lopat and EAS in customers’ accounts and the “parking” of Lopat and EAS stock in the accounts of K & C customers in exchange for guaranteed profits. The scheme also included a buy-up of Lopat and EAS that was financed with false credits in K & C’s trading account generated through short sales of other stocks. Russo enlisted Hosman and Petrokansky to implement the scheme, directing Hosman to place the unauthorized trades and Petrokansky to park the stock. Russo directed another K & C employee, Paul Miaño (“Miaño”), who was the firm’s head trader and cooperated with the government in the prosecution, to make the short sales.

A.The Unauthorized Placements

From August to October 1986, Hosman placed blocks of Lopat or EAS stock in K & C accounts without customers’ authorization by presenting buy tickets to Miaño. The stock would then be “sold” from K & C’s account to the customer’s account and K & C would receive credit for stock sold at the selling price quoted in NASDAQ. When the customer received confirmation of the sale and called to question it, he or she would be told that a mistake had been made. K & C, after prolonging payment by seeking a seven-day credit extension on behalf of the customer, would either buy back the stock or cancel the original trade. Hosman would then frequently take the same block of stock and place it in another customer account without authorization.

These unauthorized trades kept large blocks of Lopat and EAS stock off the market and out of K & C’s account for up to two weeks. K & C thus created an impression of interest in the stock that did not exist while at the same time avoiding the need to sell Lopat and EAS on the open market at prices below its offer prices.

B. The Parking

During the same period that Hosman made unauthorized placements of stock, Pe-trokansky engaged in another method of “hiding” Lopat and EAS stock from the market. On instructions from Russo, Petrokan-sky placed Lopat or EAS with customers by guaranteeing them that K & C would buy the stock back in one or two weeks at a small profit of an eighth or sixteenth of a dollar per share. When the time came to buy back the stock, Petrokansky presented sell tickets reflecting a higher price than the customer had paid or than was posted on NASDAQ that day. Petrokansky would often immediately park the same stock with a new customer.

Parking Lopat and EAS stock accomplished the same purpose as making unauthorized placements: it kept Lopat and EAS off the market and out of K & C’s account. In so doing, the parking created a false impression of Lopat’s and EAS’s vitality on the market and freed K & C from responsibility for the stock. Unlike the unauthorized placements, however, the parking bore a cost to K & C, namely, the profits it paid out to the customers who held the stock.

C. The Short Sales

In order to purchase and keep in inventory the Lopat and EAS shares that were being sold back by customers, as well as to finance the parking of Lopat and EAS stock, K & C needed a ready source of cash. The appellants found one when Russo inadvertently discovered that he could generate false cash credits from Evans in K & C’s trading account by making short sales of high-value stocks.

A short sale involves a seller agreeing to sell stock it does not own and then borrowing the stock from a broker to tender to its customer. The seller pays a fee while it borrows the stock and eventually must “cover” the short sale by returning an equivalent amount of stock to the broker. Short sales are closely regulated, and, according to the Federal Reserve Board margin rules, a seller is presently required to put up margin equal to at least 50% of the value of the stock it sells short. 12 C.F.R. § 220.19(a) (1995). In addition, any proceeds from the sale are frozen under the rules until the seller covers the short sale.

Through an accounting error, Evans credited K & C’s account for the short sales without freezing the proceeds to ensure coverage or demanding compliance with margin requirements. The mistake occurred because K & C did not notify Evans that it was making the sales, as required under the clearing agreement, and made them from its regular cash trading account rather than from a special margin account used for short sales, which K & C did not have. The effect of the error was to give K & C an unrestricted cash credit in its account for each short sale it placed.

The appellants used the cash credits to pay for the increasing number of Lopat and EAS shares held in K & C’s inventory. Russo authorized short sales so as to generate sufficient credit to offset the Lopat and EAS shares bought each day, eventually paying for over 400,000 shares of each through the false credits. The credits allowed K & C to keep in its inventory stock that otherwise would have been sold at a loss on the open market.

Together, the components of the manipulation scheme permitted K & C to balance out its trading account each day during the fall of 1986 while keeping large portions of Lopat and EAS off the market and creating an appearance of demand for the stock. The appellants used the components in tandem to keep K & C alive even though, if it had been acting honestly, the firm would have fallen below the minimum net capital requirements as early as September 1986. Because of the manipulation scheme, K & C did not close its doors until late December 1986. At that time, Evans had terminated the clearing agreement after discovering the fraudulent short sales and K & C’s practice of applying for extensions in connection with its unauthorized trades, and K & C had insufficient net capital to operate. After closing K & C, the appellants opened a new securities firm in the same office less than two weeks later.

III. The Trial

The government brought a nineteen-count indictment against appellants in December of 1991: one count of conspiracy to manipulate stock in violation of 18 U.S.C. § 371 (1994), sixteen counts of mail fraud in violation of 18 U.S.C. § 1341 (1994), and two counts of securities fraud in violation of 15 U.S.C. §§ 78j(b) and 78ff (1994). In the indictment, the government listed unauthorized placements, parking, and short sales as the three types of market manipulation engaged in by the appellants. The jury trial commenced on January 4,1994.

At trial, the government relied on an expert witness, Howard Spindel (“Spindel”), to describe the breadth and impact of the manipulation scheme. Spindel testified about K & C’s trading patterns, using charts and lists of stock movement to demonstrate how Lo-pat and EAS were kept off the market through unauthorized trades and parking. He also testified about the extent to which the false credits generated by short sales affected K & C’s inventory of Lopat and EAS stock. Spindel gave an expert opinion that the prices of Lopat and EAS shares would have significantly declined had K & C allowed the manipulated stock to reach the market.

The government’s evidence on the price movements of Lopat and EAS stock during and after the manipulation scheme reinforced Spindel’s conclusion. During the scheme, the price of Lopat remained flat at approximately three dollars per share while the price of EAS dropped gradually from one dollar and 19 cents per share to just under 94 cents. Two weeks after the scheme ended, the price of Lopat had dropped 42% and the price of EAS 59%, resulting in a loss of roughly four million dollars in the combined value of the outstanding shares. The prices continued to drop through the first months of 1987 even though Evans had taken over K & C’s accounts and continued to hold most of the stock off the market. By the end of May 1987, the price of Lopat had fallen to $1.25 per share and EAS stood at 40 cents.

After two and a half months of trial, the jury returned its verdict on March 16, 1994, finding Russo and Hosman guilty on all counts and Petrokansky guilty on five counts of mail fraud and two counts of securities fraud. A mistrial was declared as to the remaining counts against Petrokansky.

In this appeal, appellants seek reversal of their convictions on eight grounds: (1) that the district court erred in instructing the jury that it was permitted to convict for stock manipulation based on the fraudulent short sales; (2) that the district court inadequately instructed the jury on appellants’ defense to the short sale scheme; (3) that the district court erred in admitting the expert testimony of Spindel; (4) that the district court erred in refusing to instruct the jury on'the definition of stock parking; (5) that the district court erred in its instruction to the jury on artificial price levels; (6) that the evidence was insufficient to convict Hosman of conspiracy; (7) that the evidence was insufficient to convict Petrokansky of mail fraud; and (8) that the prosecutor’s rebuttal summation was improper.

DISCUSSION

I. The Short Sales Charge

The appellants’ objection to the jury instructions on short sales is in essence an objection to the legal theory advanced by the government. They contend that the short sales cannot serve as a basis for their convictions for conspiracy because those sales were not manipulative within the meaning of the law. Under the same rationale, they argue that their convictions for the substantive counts of securities fraud and mail fraud must be reversed. Because the jury instructions permitted conviction on any of the three types of manipulation charged by the government, including the short sales, the appellants argue that the instructions were erroneous. Given the substance of their argument, it is not necessary for us to examine the content or sufficiency of the instructions themselves. We instead turn our attention to whether the short sales theory of manipulation is well-grounded in law. As our inquiry involves a question of law, we review under a de novo standard. United States v. Brown, 52 F.3d 415, 420 (2d Cir.1995), cert. denied, — U.S. -, 116 S.Ct. 754, 133 L.Ed.2d 701 (1996).

Section 10(b) of the Securities Exchange Act prohibits the use “in connection with the purchase or sale of any security,” of “any manipulative or deceptive device or contrivance in contravention of such rules and regulations as the Commission may prescribe. ...” 15 U.S.C. § 78j(b) (1994). Section 10(b) is implemented by Rule 10b-5, the regulation at issue here:

Employment of manipulative and deceptive devices.
It shall be unlawful for any person, directly or indirectly, by the use of any means or instrumentality of interstate commerce, or of the mails or of any facility of any national securities exchange,
(a) To employ any device, scheme, or artifice to defraud,
(b) To make any untrue statement of material fact or to omit to state a material fact necessary in order to make the statements made, in the light of the circumstances under which they were made, not misleading, or
(c) To engage in any act, practice, or course of business which operates or would operate as a fraud or deceit upon any person,
in connection with the purchase or sale of any security.

17 C.F.R. § 240.10b-5 (1995).

The appellants advance a complex series of arguments regarding why their practice of short selling high-value stocks to generate false credits did not violate Rule 10b-5. Upon careful examination, however, their claim boils down to a simple assertion: the fraudulent short sales were not sufficiently connected to K & C’s purchases of Lopat and EAS stock to be considered part of the manipulation scheme. Because the short sales only deceived Evans and not those trading in Lopat and EAS, the appellants contend, the sales cannot be a manipulative device within the meaning of Rule 10b-5.

In response, the government argues (1) that the short sales were driven by K & C’s need to purchase Lopat and EAS in order to keep the stock off the market; (2) that there was a close correlation on any given day between the credit amount generated from the short sales and the number of Lopat and EAS shares purchased by K & C; and (3) that the short sales were used in concert with the unauthorized placements and parking of Lopat and EAS stock. Taken together, these facts are more than adequate, in the government’s view, to meet Rule 10b-5’s “in connection with” requirement. Under this construction, the use by K & C of ill-gotten funds to keep Lopat and EAS off the market deceived investors as to the true value of the stock and enabled K & C to manipulate the market. The government therefore contends that the short sale scheme was properly charged as a manipulative device in violation of Rule 10b-5.

We are thus confronted with two interpretations of Rule 10b-5’s “in connection with” requirement, one narrow and one broad. Although a review of the case law yields neither direct precedent nor a comparable set of facts to those presented here, we are not without guidance in deciding which interpretation to adopt. The law of the Supreme Court and this circuit regarding the scope of 10b-5 is extensive and supports the government’s position.

The Supreme Court has interpreted Section 10(b) and Rule 10b-5 expansively in accordance with congressional intent to minimize fraud in securities trading. As stated by the Court in Affiliated Ute Citizens v. United States, 406 U.S. 128, 151, 92 S.Ct. 1456, 1470-71, 31 L.Ed.2d 741 (1972), “[t]hese proscriptions, by statute and rule, are broad and ... are obviously meant to be inclusive.” The purpose of the Section and its implementing regulations is to prevent fraud, whether it is “a garden type variety of fraud, or present[s] a unique form of deception. Novel or atypical methods should not provide immunity from the securities laws.” Superintendent of Ins. v. Bankers Life & Casualty Co., 404 U.S. 6, 11 n. 7, 92 S.Ct. 165, 168 n. 7, 30 L.Ed.2d 128 (1971) (quoting A.T. Brod & Co. v. Perlow, 375 F.2d 393, 397 (2d Cir.1967)); see also Chiarella v. United States, 445 U.S. 222, 226, 100 S.Ct. 1108, 1113-14, 63 L.Ed.2d 348 (1980) (“Section 10(b) was designed as a catchall clause to prevent fraudulent practices.”); Ernst & Ernst v. Hochfelder, 425 U.S. 185, 208, 96 S.Ct. 1375, 1385-86, 47 L.Ed.2d 668 (1976) (Section 10(b) “enable[s] the Commission ‘to deal with new manipulative [or cunning] devices.’ ”) (quoting Hearings on H.R. 7852 and H.R. 8720 before the House Committee on Interstate and Foreign Commerce, 73rd Cong., 2d Sess., 115 (1934)). The Court has also held that Section 10(b) and Rule 10b-5:

embrace a ‘fundamental purpose ... to substitute a philosophy of full disclosure for the philosophy of caveat emptor and thus to achieve a high standard of business ethics in the securities industry’.

Affiliated Ute Citizens, 406 U.S. at 151, 92 S.Ct. at 1471 (quoting SEC v. Capital Gains Research Bureau, Inc., 375 U.S. 180, 186, 84 S.Ct. 275, 279-80, 11 L.Ed.2d 237 (1963)); see also Basic Inc. v. Levinson, 485 U.S. 224, 234, 108 S.Ct. 978, 984-85, 99 L.Ed.2d 194 (1988).

In Superintendent of Insurance, the Court applied its expansive approach in holding that Section 10(b) “must be read flexibly, not technically and restrietively.” 404 U.S. at 12, 92 S.Ct. at 169. This case examined the “in connection with” language of Rule 10b-5 and held that a company which had been bought through the fraudulent conversion of its own assets by an outside party had a cause of action for deceptive practices under Rule 10b-5. Id. at 12-13, 92 S.Ct. at 168-69. The Court rejected a narrower reading of “in connection with” proposed by the lower court in favor of an interpretation that asked whether the deceptive practices “touch[]” sales of securities. Id.

This circuit has followed the Supreme Court’s approach to Rule 10b-5 and its “in connection with” requirement. In In re Ames Dep’t Stores Inc. Stock Litigation, 991 F.2d 953 (2d Cir.1993), the court noted that its previous narrow view of this language had been repudiated by the Supreme Court in Superintendent of Insurance. Id. at 964-66. The court also stated that although many of the eases which followed Superintendent of Insurance involved difficult determinations of Rule 10b-5’s boundaries, frauds which “mislead[ ] the general public as to the market value of securities” and “affect the ‘integrity of the securities markets,’ as this court described them in Superintendent of Ins. [of State of N.Y. v. Bankers Life & Cas. Co.], 430 F.2d [355] at 361, fall well within the Rule.” Id. at 966. Although in Ames it was the company itself which had deceived the public about the value of its stock, the general proposition that “fraud can be committed by any means of disseminating false information into the market on which a reasonable investor would rely,” id. at 967; see also Basic Inc., 485 U.S. at 246, 108 S.Ct. at 991, is no less true when the deception is worked by the stock’s market maker, as in the instant ease.

As noted above, the government presented substantial evidence of the short sales’ integral role in the scheme to manipulate Lopat and EAS stock. In essence, the appellants were running a stock-kiting scheme in which they moved stock from account to account in order to create the appearance of market activity. While the short sales did not affect the markets for Lopat and EAS through actual trading, they enabled K & C to create a false impression of demand for the stock and to shield prices from the realities of the market. Without the money generated through the short sales, the appellants would not have been able to keep large blocks of Lopat and EAS off the market or finance the other elements of the kiting scheme, thereby misleading the public as to the value of Lopat and EAS stock. As this court said in Ames:

[i]f such a straightforward cause and effect is not a connection, then the Rule would not punish a particularly effective means of reducing the integrity of, and public confidence in, the securities markets.

991 F.2d at 967.

The appellants seek to distinguish the Ames ease by asserting that K & C’s fraudulent short sales could not have affected the trading decisions of Lopat and EAS investors because K & C made its purchases of Lopat and EAS stock on the open market. They analogize their practice to that of an investor who lied on his home loan application in order to get more money to buy stock. We find this analogy inapposite. K & C was the market maker for Lopat and EAS stock— there was no “open market” on which it could trade except for the one it created, and it could not have continued to make this market without the money generated by the short sales. Unlike the unscrupulous investor to whom the appellants unfortunately compare themselves, K & C could not separate its fraud from its purchase of Lopat and EAS stock.

The appellants make a similar mistake in arguing that they had no duty to disclose their deceit to the market and that therefore the short sales cannot be considered part of the manipulation scheme. Relying on Chiarella, they contend that the duty to disclose arises “because of a fiduciary or other similar relation of trust and confidence,” 445 U.S. at 228, 100 S.Ct. at 1114-15 (quoting the Restatement (2d) of Torts § 551(2)(a) (1976)), that was not present in this case. Chiarella, however, addresses the obligations of one who seeks to benefit personally from non-publie corporate information. It does not apply to those such as the appellants who seek to benefit personally from an illegal, self-created scheme. We drew this exact distinction in United States v. Regan, 937 F.2d 823, 829 (2d Cir.), amended 946 F.2d 188 (2d Cir.1991), and cert. denied, 504 U.S. 940, 112 S.Ct. 2273, 119 L.Ed.2d 200 (1992), holding that a broker who failed to disclose its depression of market prices in the absence of a fiduciary duty could not rely on Chiarella because it had been charged with market manipulation, not insider trading.

Given the weight of the case law and our mandate to interpret Rule 10b-5 expansively, we conclude that the fraudulent short sales made for the express purpose of financing the appellants’ stock kiting scheme served as a fraud on the market for Lopat and EAS stock. We therefore find that the short sales were sufficiently connected to the manipulation scheme as to constitute a violation of Section 10(b) and Rule 10b-5, and that the jury was properly instructed on the conspiracy, securities fraud, and mail fraud counts.

II. The Defense Theory Regarding the Short Sales

The appellants argue that the district court, in declining to give two of their proposed instructions, failed to instruct the jury adequately on their defense to the short sales charge. The absence of the instructions, appellants claim, prevented a balanced presentation of the defense’s theory of the case. We review the propriety of the district court’s instructions de novo. United States v. Dove, 916 F.2d 41, 45 (2d Cir.1990).

The appellants’ theory was that the short sales did not deceive Evans, and therefore were not fraudulent, because the sales were done openly with Evans’ knowledge. The instructions proposed by the appellants read in pertinent part:

The defendants contend that Evans was aware that Kureen & Cooper was selling short in the trading account and that Evans knew that it was giving immediate cash credit to Kureen & Cooper for the short sales.... The defendants further contend that the trade tickets for the short sales were not miscoded and were not deceptive.

The district court denied these instructions and instead instructed the jury in the following manner:

The defendants [] contend that the government has failed to prove beyond a reasonable doubt that they agreed to defraud Evans & Co. of money by deceiving Evans & Co. through short sales_if you find that the government has failed to prove beyond a reasonable doubt that Evans & Co. was deceived by short selling in the trading account, you may not convict on the conspiracy charge based on the alleged scheme to defraud Evans & Co. Additionally, if you agree with the defendants’ contention, you may not find that the defendants artificially affected the price of EAS and Lopat stock based solely on purchases of stock from money generated from the short sales.

The appellants characterize this instruction as “boiler-plate” language which did not convey the essence of their case.

The appellants bear the burden of demonstrating that their proposed instructions “accurately represented the law in every respect.” Dove, 916 F.2d at 45. We find that they have not met this burden because their proposed instructions would have misled the jury about the degree of deceit perpetrated against Evans.

First, while K & C’s trades were included in Evans’ computer-generated records, Evans cannot be said to have had true awareness of K & C’s practice or to have approved of it. K & C’s short sales of high-value stocks were clearly not legitimate—they occurred in a cash account without K & C ever putting up the required margins for such sales. The very fact that K & C stumbled onto the false credits by making a coding mistake on a sell ticket, and then failed to notify Evans about the mistake, indicates that the practice was not above-board. Moreover, Evans ended its relationship with K & C as soon as it became fully aware of the short sales and the generated credits. Thus, the appellants’ proposed instruction on Evans’ knowledge of the short sales and credits would have presented the jury with a false picture of K & C’s fraudulent activity.

Second, an instruction on the coding of trading tickets, as requested by the appellants, would have led the jury down the wrong path in determining whether fraud had been perpetrated against Evans. The issue was not whether the tickets were mis-coded, but rather that K & C had made short sales of high-value stocks from a cash account without sufficient margin and in violation of its clearing agreement with Evans. The appellants’ proposed instructions would therefore have misled the jury into thinking that if the tickets were not miscoded, the appellants had a valid defense to the charge of fraud.

We also cannot agree with the appellants that the district court’s instruction failed to adequately inform the jury of the defense theory that Evans was not deceived by the short sales. A defendant is entitled to a jury instruction on a defense theory “for which there is any foundation in the evidence,” United States v. Alfonso-Perez, 535 F.2d 1362, 1365 (2d Cir.1976) (citations omitted), but he is not entitled to have the exact language he proposes read to the jury. United States v. Dyman, 739 F.2d 762, 771 (2d Cir.1984), cert. denied, 469 U.S. 1193, 105 S.Ct. 969, 83 L.Ed.2d 973 (1985). The trial court enjoys broad discretion in crafting its instructions which is only “circumscribed by the requirement that the charge be fair to both sides.” United States v. GAF Corp., 928 F.2d 1253, 1263 (2d Cir.1991). In this case, the district court clearly stated that the jury could not find the appellants guilty of conspiracy to commit fraud through the short sales unless they found that Evans was deceived. This instruction fairly apprised the jury of the essence of the defense theory and resulted in no prejudice to the appellants.

III. Definition of “Parking”

The appellants next contend that the government changed its definition of stock “parking” throughout the case, creating a confusion that the District Court should have remedied through a jury instruction. They argue that the failure to give such an instruction deprived them of a fair trial in numerous ways, including permitting the jury to convict on an erroneous definition and denying a valid theory of defense.

While we recognize that the government was not wholly consistent in describing the conduct that constitutes stock parking, we find the appellants’ arguments unavailing. As an initial matter, we do not believe the government’s definition of “parking” varied sufficiently to confuse the jury or mislead the defense. Although the words used to describe “parking” changed during the course of trial, the essential concept behind the government’s theory of manipulation remained constant: K & C perpetrated a fraud on the market by divorcing the financial risk of owning Lopat and EAS from legal ownership of the stock. The evidence presented by the government fully supported this theory of manipulation and presented a clear picture of stock parking to the jury.

Moreover, we agree with the government that “parking,” as used in this prosecution, is not a legal term requiring jury explanation. Rather, it is a business term that describes conduct which may or may not rise to the level of a 10b-5 violation. Unlike the concepts of “agent” and “guilt,” which are offered by the appellants as examples of terms which require jury instruction, “parking” is not defined by an established set of legal criteria. “Parking” was simply used by the government as a means to describe some of the fraudulent activities of the appellants and requires no more guidance to the jury than other factual allegations. Thus, the district court did not err in refusing to give an instruction on the definition of “parking.”

Finally, we note that the appellants’ proposed instruction on parking, which focused on voting rights and alienability as indicia of stock ownership, would have diverted the attention of the jury to questions of little significance to the charge of stock manipulation. The issue in this case was whether the appellants manipulated the price of Lo-pat and EAS stock, not whether the customers with whom K & C parked stock could have sold it or voted it during the parking period. An instruction focusing on the technicalities of stock ownership would therefore have confused, if not misled, the jury, and the district court properly avoided this result by denying the appellants’ request.

Because the term “parking” was defined by various witnesses during the course of the trial and was otherwise used in a comprehensible manner, we find that a jury instruction defining the term was not necessary and that the appellants were not deprived of then-right to a fair trial by the absence of such an instruction.

IV. Instruction on Artificial Price

The district court instructed the jury on artificial price in the following fashion:

In order to find an intent to manipulate the price of EAS and Lopat stock, you must find that the defendant you are considering intended to raise the price of the stock to, or maintain the price of the stock at an artificial level, that is, to a level above the investment value of the stock as determined by available information and market forces (emphasis added).

The appellants objected to this instruction, proposing instead a definition of artificial price that required proof of the defendants’ belief that the stock was really worth less than the price at which they traded it. They now claim that the district court’s failure to give their proposed instruction deprived them of their right to a fair trial.

The appellants attempt to convince us that their subjective valuation of Lopat and EAS stock, i.e., what they believed to be the stocks’ true worth, should have been the sole determinant of whether the prices that resulted from their fraudulent activities were “artificial.” This argument finds neither support in the law — indeed, they cite none— nor in the facts of this case. It is clear that the appellants did not believe that Lopat and EAS were undervalued: the government established in numerous ways that the appellants were motivated by an intent to subvert the operation of normal market forces on the price of the stock rather than by legitimate investment concerns. Furthermore, the jury was repeatedly told by the district court in other instructions that it must find fraudulent conduct in order to convict the appellants. We therefore conclude that the appellants were not prejudiced by the district court’s instruction on artificial price.

V. Expert Testimony

The appellants argue that the district court improperly admitted the testimony of Howard Spindel, the government’s expert witness. They claim that Spindel was not qualified to testify as an expert in the area of stock pricing and had no factual basis for his testimony about the impact of unauthorized trades and parking of stock on the prices of Lopat and EAS. The appellants also contend that Spindel drew legal conclusions about the defendants’ state of mind in relation to the parking transactions.

We find little merit in the appellants’ arguments. First, the trial court has “broad discretion ... to determine the qualifications of witnesses [which] will not be disturbed unless its ruling was manifestly erroneous.” Eagleston v. Guido, 41 F.3d 865, 874 (2d Cir.1994), cert. denied, — U.S. -, 116 S.Ct. 53, 133 L.Ed.2d 18 (1995) (quoting McCullock v. H.B. Fuller Co., 981 F.2d 656, 657 (2d Cir.1992)). In light of Spindel’s extensive experience in the securities market as a consultant, a general securities principal, and the controller of a large options trading firm, as well as his expertise on the net capital rule, we see no error, manifest or otherwise, in the district court’s decision to admit him as an expert. With regard to the second claim, a review of the record demonstrates that Spindel’s testimony about the impact of the appellants’ trades and parks on the price of Lopat and EAS stock had an adequate basis in fact. Spindel provided numerous price charts and lists of stock movement that supported his statements about Lopat and EAS. Furthermore, his testimony “provid[ed] the groundwork in the form of an opinion to enable the jury to make its own informed determination.” United States v. Duncan, 42 F.3d 97, 101 (2d Cir.1994).

As to the appellants’ third contention, we have noted that “[pjarticularly in complex cases involving the securities industry, expert testimony may help a jury understand unfamiliar terms and concepts.” United States v. Bilzerian, 926 F.2d 1285, 1294 (2d Cir.), cert. denied, 502 U.S. 813, 112 S.Ct. 63, 116 L.Ed.2d 39 (1991). But we have also cautioned that expert testimony must not usurp the roles of judge and jury by offering legal conclusions. Id. The appellants argue that Spindel’s opinion on whether certain transactions were parking transactions involved the legal conclusion that the appellants intended to park stock. For support, they cite United States v. Scop, 846 F.2d 135, 139-40, modified, 856 F.2d 5 (2d Cir.1988), a securities fraud case where the expert improperly used specific statutory and regulatory language such as “manipulation” and “scheme to defraud” to describe the defendants’ actions.

In Scop, however, we stated that had the expert “merely testified that controlled buying and selling of the kind alleged here can create artificial price levels ..., no sustainable objection could have been made.” Id. at 140. We find that Spindel’s testimony fits this hypothetical because it focused solely on factual conclusions and did not involve any legal characterizations. Spindel gave no opinion as to whether the appellants had violated the securities laws and did not make any statements about their intent; he simply described certain stock transactions and his opinion of their effect on the market. We conclude, therefore, that the district court properly exercised its discretion in admitting the expert testimony.

VI. Sufficiency of the Evidence

The appellants claim that the evidence was not sufficient to convict Hosman of conspiracy or Petrokansky of mail fraud. We recently set out our approach to challenges of sufficiency of the evidence in United States v. Martinez:

It is well settled that a defendant seeking to overturn a conviction based upon insufficiency of the evidence bears a “heavy burden.” Not only must the evidence be viewed in the light most favorable to the government and all permissible inferences drawn in its favor, but if the evidence, thus construed, suffices to convince any rational trier of fact of the defendant’s guilt beyond a reasonable doubt, then [the] conviction must stand. The government’s case need not exclude “every possible hypothesis of innocence,” and it is the task of the jury, not the court, to choose among competing inferences. Moreover, the jury’s verdict may be based entirely on circumstantial evidence.

54 F.3d 1040, 1042-43 (2d Cir.), cert. denied, — U.S. -, 116 S.Ct. 545, 133 L.Ed.2d 448 (1995) (citations omitted).

Under this standard, we find that the evidence was sufficient to convict both Hosman and Petrokansky. The government presented ample evidence of Hosman’s participation in the conspiracy to manipulate Lopat and EAS stock, including her conducting of unauthorized trades, her involvement in the liquidation of K & C, her role in the management of K & C, and her knowledge of K & C’s trading activity. Similarly, the government showed Petrokansky’s intent to manipulate the stocks as required by the mail fraud statute, providing evidence of his payout for participating in the scheme, his special relationship with Russo, and his knowledge of Lopat’s and EAS’s artificially inflated prices. We therefore conclude that neither Hosman nor Petrokansky meet the “heavy burden” of demonstrating insufficiency.

VIL Prosecution’s Rebuttal Summation

The appellants claim that the government’s rebuttal summation violated Federal Rule of Criminal Procedure 29.1 by introducing new matters to which the defense could not respond. Specifically, they object to the prosecutor’s handwritten additions to a chart already in evidence and his allegedly abusive remarks about the defense. Upon review of the record, we find that the prosecution’s references to the defense need no discussion as they were relatively mild, like his remark that the defense was “trying to take the heat off their clients,” and clearly harmless. Compare United States v. Biasucci, 786 F.2d 504, 514 n. 9 (2d Cir.), cert. denied 479 U.S. 827, 107 S.Ct. 104, 107, 93 L.Ed.2d 54, 56 (1986) (where prosecutor called defense counsel “sleaze” and “you hypocritical son of a bitch”). The issue of the introduction of new matters, however, does warrant our attention.

In his rebuttal summation, the prosecutor added a column of numbers to a chart introduced at trial which purported to summarize the commissions paid to Miaño as a broker at K & C. He then used these new numbers to demonstrate that Miaño testified truthfully about the commissions, matching the amount of Miano’s adjusted net commissions shown on the existing chart with the new numbers reflecting payments made to Miaño by Russo. The comparison of these amounts undermined the defense’s accusation that Miaño had lied about receiving the commissions due to another K & C broker. Although Miano’s credibility and the amount of his commissions had been challenged by the defense in its summation, the prosecutor took a step beyond the existing evidence to create a new line of argument based on Russo’s payments to Miaño. We therefore cannot adopt the government’s characterization of the additional numbers as “simple arithmetic” in response to a door opened by the defense.

Instead, we find the prosecutor’s actions to be similar to those taken in United States v. Gleason, 616 F.2d 2, 25 (2d Cir.1979), cert. denied, 444 U.S. 1082, 100 S.Ct. 1037, 62 L.Ed.2d 767 (1980), where a prosecutor produced a new tabulation during his rebuttal. In that case, we found the prosecutor’s behavior improper, despite the argument that the tabulation was in response to the defense’s summation and based on exhibits already in evidence, because it effectively introduced “a new theory ... at almost literally the last minute of a long trial.” Id. at 26. Here, the prosecution’s re-organization of the numbers relating to Miano’s commissions created a similar “last minute” argument and was therefore improper.

A finding of impropriety, however, does not end our inquiry. As stated by the Supreme Court in United States v. Young, 470 U.S. 1, 11, 105 S.Ct. 1038, 1044, 84 L.Ed.2d 1 (1985):

a criminal conviction is not to be lightly overturned on the basis of the prosecutor’s comments standing alone, for the statements or conduct must be viewed in context; only by so doing can it be determined whether the prosecutor’s conduct affected the fairness of the trial.

Whether the prosecutor’s improper conduct requires reversal in this ease depends on whether the conduct substantially prejudiced the appellants so as to deny them a fair trial. United States v. Tutino, 883 F.2d 1125, 1136 (2d Cir.1989), cert. denied, 493 U.S. 1081, 110 S.Ct. 1139, 107 L.Ed.2d 1044 (1990). We assess the degree of prejudice through “three factors: the severity of the misconduct; the measures adopted to cure the misconduct; and the certainty of conviction absent the improper statements.” United States v. Modica, 663 F.2d 1173, 1181 (2d Cir.1981), cert. denied, 456 U.S. 989, 102 S.Ct. 2269, 73 L.Ed.2d 1284 (1982). Applying these factors, we conclude that the appellants were not substantially prejudiced in this case.

First, the introduction of a new chart column based on information already in the record does not strike us as severe misconduct, both because it represented a limited segment of the two and one-half hour rebuttal summation and because it did not reflect an ongoing pattern of disregard for appropriate conduct at trial. See Modica, 663 F.2d at 1181 (noting that four improper remarks made in rebuttal were aberrational misconduct that did not demand reversal). Second, while the district court did not take any direct measures to cure the effects of the prosecutor’s remarks, it did reiterate to the jury on several occasions that a lawyer’s comments could not be considered evidence. Finally, and most persuasively, we believe the case against the appellants to be sufficiently strong without the improper comments and the new chart column. Indeed, the new column related to statements of a government witness whose credibility the jury was entrusted to determine, not to any actions of the appellants themselves. These improprieties came after eleven weeks of trial during which substantial evidence was presented incriminating the appellants, and it is highly unlikely that the prosecutor’s misconduct had a decisive role in the appellants’ conviction.

Because the appellants were not substantially prejudiced by the improper conduct of the prosecutor in his rebuttal summation, we hold that the misconduct was harmless error which cannot sustain a reversal of the convictions in this case.

CONCLUSION

We have considered all of the appellants’ arguments in support of reversal of their convictions and find them unpersuasive. The judgment of the district court is therefore affirmed. 
      
      . These stocks are known on Wall Street as “penny stocks” and are traded over the counter through the National Association of Securities Dealers Automated Quotation system (NASDAQ).
     
      
      . The Federal Reserve Board allows brokers to request extensions for payment for stock purchases from the New York Stock Exchange pursuant to Federal Reserve Board Regulation T, 12 C.F.R. § 220.8(d) (1995).
     
      
      . Evans had three types of trading accounts, designated Type 1, Type 2 and Type 3. Type 1 accounts were regular cash accounts in which Evans permitted brokerage firms to conduct short sales of penny stocks; Type 2 accounts were regular margin accounts; and Type 3 accounts were regular margin accounts through which brokerage firms made short sales of high-value stock. K & C did not have a Type 3 account with Evans nor did K & C's clearing agreement with Evans permit it to engage in short sales of high-value stocks. K & C did not have sufficient capital to put up the margin for such short sales as required by Federal Reserve margin regulations. See 12 C.F.R. § 220.19(a) (1995).
     
      
      . However, we find specious the appellants’ argument that short sales could be made out of Type 1 cash accounts as well as Type 3 credit accounts and that therefore K & C’s tickets were not miscoded. While short sales of penny stocks for which K & C was the market maker were permissible in its Type 1 account, short sales in high-value stocks required a Type 3 credit account, which K & C did not have under the clearing agreement with Evans.
     
      
      . The Fifth Circuit has noted that ”[t]he better practice would be to instruct the jury on the meaning of all terms of operative significance.” United States v. Anderton, 629 F.2d 1044, 1049 n. 5 (5th Cir.1980). While that may be a worthy aspiration, it is evidently not the law of this circuit as appellants cite no Second Circuit cases for the proposition that all significant terms must be defined in instructions to the jury and we find none.
     
      
      . Rule 29.1 addresses the order of closing arguments. The 1974 Advisory Committee Note states:
      The rule is drafted in the view that the fair and effective administration of justice is best served if the defendant knows the arguments actually made by the prosecution in behalf of conviction before the defendant is faced with the decision whether to reply and what to reply.
     