Odd Lotters and the Odd-Lot Theory: What the Evidence Says

An odd lotter is an investor who buys or sells shares in small, irregular quantities, known as odd lots, rather than in the standard trading unit called a round lot. In US stock markets the round lot has traditionally been 100 shares, so an odd lot is any order of fewer than 100 shares. For most of the 20th century odd lotters were, almost by definition, small private investors who could not afford, or did not want, a full round lot.

The term matters in financial history because of the odd-lot theory, a once-popular technical-analysis idea that treated small investors as a reliable contrary signal. If odd lotters were selling heavily, the theory said, the market was probably near a bottom and it was time to buy. If they were buying heavily, the market was probably near a top. The theory was widely followed from the 1940s to the 1970s, studied in academic theses and journals, and then largely abandoned.

This article explains what odd lots are, how odd-lot trading worked, where the odd-lot theory came from, what researchers found when they tested it, why it fell out of use, and how odd lots have come back into focus in today's electronic markets. It also covers what more recent research says about whether small investors really are "wrong" at turning points.

This article is educational. It is not financial advice and does not recommend any trading strategy.

Key terms

The phrase "odd lot" is older than its financial use. It is used outside finance for any irregular quantity or package of goods, such as a batch of unmatched items at an auction.

How odd-lot trading worked

Why round lots existed

Exchanges standardised trading in round lots because it simplified the matching of buyers and sellers. Quotes on the trading floor were for round lots, and most professional activity happened in round-lot units. A small investor who wanted, say, 25 shares did not fit into this system directly.

Odd-lot dealers

For much of the 20th century, odd-lot orders on the New York Stock Exchange were filled by specialist odd-lot dealer firms rather than matched directly with other investors. The Securities and Exchange Commission's 1963 Special Study of Securities Markets identified the two principal NYSE odd-lot firms as Carlisle and Jacquelin and DeCoppet and Co. The dealer acted as the counterparty to the small investor: it bought the investor's odd lot or sold one from its own inventory, and then balanced its position by trading in round lots on the floor.

The odd-lot differential

Odd-lot investors usually paid for this service through the odd-lot differential, a small extra charge on the price. A 1994 SEC order describes it as a fee, usually one-eighth of a point, that dealers charged on odd-lot orders. According to the New York Institute of Finance, the differential was generally one-eighth of a point and was not itemised on trade confirmations. At a time when US stock prices were quoted in fractions of a dollar, one-eighth of a point meant 12.5 cents per share.

Automation and the end of the dealers

Over time the NYSE replaced the odd-lot dealers. An NYSE rule filing describes how the Exchange removed separate odd-lot dealers and made specialists the counterparty to odd-lot executions under its Rule 124. An automated odd-lot system was introduced around 1991, according to a later SEC filing, and the Exchange subsequently moved to end the differential. The NYSE's 2008 filing describes the odd-lot system as having been created to replace the odd-lot dealers.

Why odd lotters were small investors

Until the late 20th century, odd lots were almost entirely the business of individuals. Institutions such as pension funds, insurance companies and mutual funds traded in large blocks. A 1961 Time magazine article reported that odd lotters accounted for 21.3 percent of total market volume in 1960, which shows how large the small-investor segment was in the post-war boom.

A study by Hsiu-Kwang Wu in the Journal of Financial and Quantitative Analysis (1972) analysed annual odd-lot data from 1937 to 1967. It found that odd-lot volume grew in absolute terms after the Second World War but that its share of the market fell. By 1967 odd-lot volume was 11.6 percent of round-lot sales.

Origins of the odd-lot theory

Garfield Drew

The odd-lot theory is most closely associated with Garfield Albee Drew, a Boston market analyst. According to the 1961 Time profile, which called him "a controversial Boston chartist," Drew graduated from Harvard in 1926 and went to Wall Street as a bond statistician, working there through the 1929 crash and the early Depression. He later said he left partly because "I became so disgusted with the dishonesty around me that I wanted to get out."

He joined Roger and Paul Babson's United Business Service in Boston, where he noticed that odd-lot transactions did not seem to move with general market trends. He published a treatise on his odd-lot research in 1940, later expanded it into a book, and founded an investment service built around the theory. By 1961 his weekly report, the Drew Odd Lot Studies, cost $95 a year and had about 4,500 professional subscribers, including Swiss banks, investment funds and senior executives at large US companies. Time reported that the service brought in about $350,000 a year for Drew and a partner.

The basic idea

Drew's reasoning rested on an unflattering view of the small investor. He believed that the public could not match professional investors in skill or information, and that small investors tended to be most wrong at market turning points: selling just before the market rose and buying just before it fell. If odd lotters were selling heavily, he argued, someone more knowledgeable, presumably professionals, must be buying. Heavy odd-lot selling was therefore a sign that a rise was coming.

Drew described the public as "disbelieving" early in a bull market and said that a "bearish market psychology" was typical at the start of an upswing. He told Time that he charted trends rather than predicting them, and that he used odd-lot data alongside other indicators rather than in isolation.

The indicators

Drew and his followers used several statistics derived from the daily odd-lot figures that exchanges published. The main ones were:

• The odd-lot balance: the relationship between odd-lot purchases and odd-lot sales. Drew's work included a "Balance Index" based on this.
• The odd-lot short-sales ratio: odd-lot short sales compared with total odd-lot sales or with total short sales. Because short selling is a bet that prices will fall, heavy short selling by small investors was read as extreme pessimism and therefore as a bullish signal. Drew's work included a "Short-Sales Index."

These measures were considered useful because the data were published regularly and came from a group, small investors, that was thought to be easy to read.

An illustrative calculation

The following example uses invented figures to show how the balance and short-sales measures worked. It does not describe any real trading day.

Suppose that in one week odd lotters bought 4,000,000 shares and sold 5,000,000 shares, of which 200,000 were short sales.

An odd-lot theorist would compare these figures with their usual ranges. A purchases-to-sales ratio well below normal, combined with an unusually high short-sales share, would have been read as small investors being unusually pessimistic, and so, under the theory, as a possible buying signal. The theory did not specify universal thresholds; analysts judged readings against historical norms.

Early study of odd-lot trading

Odd-lot trading attracted serious study even before Drew's work became well known. In 1939 the Brookings Institution in Washington published Odd-Lot Trading on the New York Stock Exchange by the economist Charles Oscar Hardy (1884 to 1948), a 192-page study issued as Publication No. 78 of its Institute of Economics and reprinted by Arno Press in 1975. Hardy's study appears among the references in Wu's 1972 paper, showing that later academic work on odd lots built on it. Its existence shows that, by the late 1930s, the odd-lot market was large enough to be treated as a distinct part of the exchange worth analysing in its own right.

Part of a wider contrarian tradition

The odd-lot theory belonged to a broader family of contrarian ideas about markets. The best-known statement of the general idea is Humphrey Bancroft Neill's The Art of Contrary Thinking, first published in 1954, a collection of short essays by a writer known as the "Vermont Ruminator." Its most quoted line is "When everybody thinks alike, everyone is likely to be wrong." Neill popularised the theory of contrary opinion in markets: the idea that when nearly everyone holds the same view, it is worth asking whether the crowd is wrong.

The odd-lot theory can be seen as an attempt to turn this loose principle into a measurable rule. Instead of judging the general mood, it picked one group, small investors, and one data series, their published odd-lot trades, and treated that group as the crowd to be faded. That precision made it attractive, and it also made it testable, which is ultimately why it could be shown not to work well.

The theory in practice: claimed successes and failures

Claimed successes

According to Time, Drew claimed that his odd-lot index had marked the exact market bottoms in the recessions of 1948 to 1949 and 1953 to 1954. In December 1960, odd-lot sales exceeded purchases by the largest margin since 1941, and Drew signalled a new bull market; his figures had begun pointing that way as early as October. Time also noted that in ten of the previous eleven years, odd lotters had bought more than they sold while the market rose, a pattern that did not fit neatly with the idea that they were always on the wrong side.

The 1958 episode

Critics pointed to the summer of 1958, when odd-lot purchases were high and the theory signalled that it was time to sell. According to Time, those who sold regretted it because the market went on rising. Wall Street critics argued that Drew relied too heavily on odd-lot figures, and many brokers felt he did not give odd lotters a fair assessment. Even in a sympathetic profile, Time described his record as mixed.

What the research found

The odd-lot theory was heavily analysed in the 1960s and 1970s. The results did not support its strong form.

Klein (1964): sales supported, purchases not

One of the first systematic tests was a doctoral thesis by Donald Joseph Klein at Michigan State University, The Odd-Lot Stock Trading Theory, submitted in 1964. Klein studied the twenty most active NYSE stocks each month over 1955 to 1961 and compared the results of three groups: odd-lot sellers, odd-lot buyers and round-lot traders, with the Dow Jones Industrial Average and the S&P 500 as benchmarks. He measured price change and dividend yield over six months, one year and two years.

Klein concluded that the complete theory was invalid. In his words, "The sales aspect of the theory was supported," "while the purchase side was challenged." In other words, the stocks odd lotters sold may have tended to do well afterwards, which fits the theory, but the stocks they bought did not reliably do badly, which the theory also predicted.

Kewley and Stevenson (1967) and the debate that followed

In 1967 T. J. Kewley and R. A. Stevenson published "The Odd-Lot Theory as Revealed by Purchase and Sale Statistics for Individual Stocks" in the Financial Analysts Journal, testing the theory at the level of individual stocks rather than the market as a whole. Kewley published a reply in the same journal in 1969, and Wu's 1972 paper lists these among a series of studies by Drew, Kaish, Kewley and Stevenson, and Hardy. The existence of replies and counter-replies shows that the theory's validity was actively contested in the professional literature during this period.

Wu (1972): a changing market

Hsiu-Kwang Wu's 1972 study is useful less as a test of the theory than as a record of how odd-lot trading itself was changing. It found:

Two of these findings undermined the theory. First, odd-lot short selling was so small, averaging under 2 percent of round-lot short sales, that its movements may say little about the market as a whole. Second, odd lotters were shifting from being net buyers to net sellers over time, a long-term trend that made short-term changes in the balance harder to interpret.

West and Murphy (1978): the data stopped meaning what it used to

In 1978, Stan West and Thomas T. Murphy argued in the Financial Analysts Journal that changes in market structure had distorted traditional stock market statistics, including odd-lot data. Their points included:

• The theory was built on a purchase balance. When the odd-lot theory was formulated, odd-lot statistics normally showed more buying than selling.
• Hidden flows into small investors' hands. Stock splits, stock dividends, mergers and dividend reinvestment plans moved large numbers of shares to small investors without ever appearing in odd-lot purchase statistics. As a result, "only two of the last 17 years have shown purchase balances."
• Specialists changed the arithmetic. Because certain specialist firms now handled odd lots, purchases no longer had to equal sales. Customers had been net sellers since 1970, while specialists accumulated odd lots and sold them off in round lots.

The implication was that a chronic odd-lot selling balance no longer meant small investors were unusually pessimistic. It reflected how shares reached and left their hands.

Burton Malkiel's verdict

The best-known summary verdict comes from the Princeton economist Burton Malkiel in A Random Walk Down Wall Street. Malkiel wrote that "the odd-lotter isn't such a stupendous dodo after all." He allowed that odd lotters' performance might be slightly worse than the stock averages, but concluded that knowing what they were doing was of no use in forming an investment strategy. That is roughly where most finance writers have left the theory since.

Summary of the classic evidence

Why the logic was weaker than it looked

Apart from the empirical tests, the reasoning behind the odd-lot theory had several weaknesses that help explain why it performed poorly.

The counterparty was often a dealer, not a smart professional

Drew argued that when odd lotters sold, more knowledgeable professionals must be buying. But in the odd-lot system of his time, the immediate counterparty to an odd-lot sale was usually the odd-lot dealer, which then balanced its inventory by trading round lots. The dealer was providing a service and earning the differential, not necessarily expressing a view on where the market was going. The chain from "odd lotters are selling" to "informed professionals are buying" was therefore indirect.

Small investors were not a single crowd

The theory treated odd lotters as a single group with a single mood. In practice, small investors bought and sold for many reasons unrelated to market forecasts: to pay bills or taxes, to invest a bonus, to reinvest dividends, or to settle an estate. Some small holdings arrived through stock splits, stock dividends or mergers rather than deliberate purchases. West and Murphy's 1978 analysis showed how much of this flow did not even appear in the purchase statistics.

Selective memory

Like many market indicators, the odd-lot theory was promoted partly through memorable hits, such as Drew's claims about the bottoms of 1948 to 1949 and 1953 to 1954. Misses, such as the 1958 sell signal, were easier to explain away. Systematic tests, which count every signal rather than just the famous ones, are the only reliable way to judge an indicator, and those tests did not support the theory.

Costs and timing

Even where part of the theory appeared to work, such as the sales side in Klein's study, turning it into profits required acting on weekly data, paying commissions, and holding positions for months. An edge that is small, irregular and slow to appear can easily disappear once costs and the difficulty of timing are counted.

Self-defeating publicity

Drew's service had thousands of professional subscribers. If a published signal is widely followed and genuinely predictive, traders acting on it tend to move prices before the predicted move arrives, weakening the signal. This does not prove that the odd-lot theory was wrong, but it is one reason widely publicised indicators tend to lose their edge over time.

Timeline

Why the odd-lot theory faded

Several forces combined to end the theory's popularity.

The evidence was weak

As shown above, tests did not support the full theory. At best, parts of it seemed to work some of the time, which is not enough to build a reliable strategy, particularly after trading costs.

Small investors moved into funds

By the 1990s, more individuals were investing through mutual funds rather than buying individual stocks, according to the Wikipedia article on odd lotters, which cites a 1996 New York Times article by Laura Pedersen. When the typical small investor's money flowed through a fund manager trading in large blocks, odd-lot figures no longer captured small-investor sentiment.

The data became contaminated

As West and Murphy showed, dividend reinvestment, stock dividends, splits and changes in how specialists handled odd lots meant the raw figures no longer measured what the theory assumed. A permanently negative odd-lot balance stopped carrying the same signal.

The market became more efficient and more electronic

The broader shift in academic finance towards the efficient market hypothesis, the idea that publicly available information is quickly reflected in prices, also counted against the theory. If odd-lot data were published regularly and widely followed, any predictable signal would be expected to weaken as traders exploited it. Later, as described below, odd lots stopped being mainly a small-investor phenomenon at all.

Odd lots in modern markets

Algorithms and odd lots

In today's electronic markets, the link between odd lots and small investors has been broken. Large orders from institutions are routinely split into many small pieces by trading algorithms to reduce their market impact, and many of those pieces are smaller than 100 shares. High share prices have also made odd lots common: for a stock priced in the hundreds or thousands of dollars, even a substantial dollar investment may be fewer than 100 shares.

A study by Maureen O'Hara, Chen Yao and Mao Ye, "What's Not There: Odd Lots and Market Data," published in the Journal of Finance in 2014, examined 120 Nasdaq stocks from 2008 to 2011. Its key findings were:

This turns the old odd-lot theory on its head. Instead of being the trades of the least informed investors, odd lots in this sample were disproportionately used by informed traders, precisely because small trades attract less attention.

Odd lots join the consolidated tape (2013)

Partly in response to concerns about missing data, US regulators changed the rules on reporting. A plan amendment filed with the SEC in September 2013 removed odd-lot transactions from the list of trades not reported to the consolidated tape, and the Commission approved it on 31 October 2013 (Release No. 34-70794). Odd-lot trades began appearing on the tape on 9 December 2013. They were included in daily volume but did not count as last-sale prices, and the SEC noted that they did not trigger short-sale restrictions or trading halts. The approval order concluded that including odd lots would improve post-trade transparency and price discovery.

Redefining the round lot (2020 and 2024)

The SEC has also changed what counts as a round lot. Its 2020 Market Data Infrastructure rules introduced new definitions of round lots and odd-lot information, and amendments to Regulation NMS adopted in September 2024 (Release No. 101070) revised them and accelerated their implementation. Under the amended definition, the round lot depends on a stock's price:

A stock's round-lot size is set from its average closing price on its primary listing exchange and adjusted semiannually, with the size flagged to the market through a "round lot indicator" in consolidated data. The compliance date for the new round-lot definition was the first business day of November 2025, and for the expanded odd-lot information, which adds data on the "best odd-lot order," the first business day of May 2026.

A hypothetical example shows how the tiers work. Imagine a stock whose average closing price over the relevant period was $600. Under the amended definition it falls in the $250.01 to $1,000.00 tier, so its round lot is 40 shares. An order for 30 shares of that stock is an odd lot; an order for 40 or 80 shares is a round lot (one or two units); and an order for 50 shares combines one round lot with a 10-share odd lot. Under the old fixed 100-share rule, all three of those orders would have been odd lots. In dollar terms, a single round lot of this stock is worth 40 × $600 = $24,000, compared with 100 × $600 = $60,000 under the old rule.

The practical effect is that, for high-priced stocks, many orders that used to be odd lots now count as round lots, and better information about odd-lot prices is distributed to the market. The old picture of the odd lotter as a small investor who could not afford 100 shares fits modern markets even less well.

Fractional shares

Brokers have also begun offering fractional shares, letting investors buy part of a single share. Robinhood announced fractional trading plans in December 2019, Fidelity began offering partial stock trades early in 2020, and Charles Schwab launched its "Stock Slices" product in June 2020, initially limited to S&P 500 companies. Schwab now lets clients invest in most US-listed stocks or exchange-traded funds for as little as $1. For an investor with a small amount of money, fractional shares make it possible to hold expensive stocks directly, without the round-lot barrier that once defined the odd lotter.

Are small investors really wrong? Modern evidence

The original odd-lot theory assumed that small investors are systematically wrong at turning points. Modern research using detailed trade data gives a more complicated answer.

Individuals as contrarians who provide liquidity

Ron Kaniel, Gideon Saar and Sheridan Titman studied a large cross-section of NYSE stocks in "Individual Investor Trading and Stock Returns," published in the Journal of Finance in 2008. They found that individuals tend to buy stocks after prices have fallen in the previous month and sell after prices have risen. In other words, individual investors themselves trade like contrarians. Strikingly, stocks that individuals bought intensely went on to earn positive excess returns in the following month, and stocks they sold intensely earned negative excess returns. The authors interpreted this as individuals being rewarded for providing liquidity to institutions that needed to trade quickly.

This is close to the opposite of what odd-lot theory predicted, at least over a one-month horizon.

Small trades, herding and longer horizons

Brad Barber, Terrance Odean and Ning Zhu, in "Do Retail Trades Move Markets?" (Review of Financial Studies, 2009), used small trades in transaction data as a proxy for retail activity and checked this against the records of large brokerages. They found that individual investors herd, buying and selling the same stocks at the same time. Over a one-week horizon, stocks heavily bought by small traders earned strong returns the following week. Over a longer horizon the pattern reversed: according to a summary of the paper, stocks heavily bought by retail investors underperformed stocks heavily sold by about 4.4 percentage points over the following year.

Putting the evidence together

The modern research suggests:

• Over short horizons, small investors are not reliably wrong; their trades can even predict returns in the direction they trade.
• Over longer horizons, the stocks retail investors crowd into may underperform, which is a weaker, more specific version of the idea behind the odd-lot theory.
• Because modern odd lots are heavily used by algorithms and informed traders, odd-lot statistics today are not a clean measure of small-investor behaviour at all.

None of this revives the original theory as a usable signal. It does show that the question it asked, whether the crowd of small investors is systematically wrong, is still studied, and that the answer depends heavily on the time horizon and how retail trading is measured.

The odd lotter as an investor today

Is trading in odd lots a disadvantage?

Historically, yes, to a modest extent. Odd lotters paid the odd-lot differential, usually one-eighth of a point per share, on top of commissions, and their orders were handled separately from the main market. Today the separate dealer system and the differential are gone, odd lots are reported on the tape, and many brokers charge no commission on online stock trades. The practical penalty for buying fewer than 100 shares has largely disappeared.

An illustrative cost comparison

The following example is hypothetical and uses simple, round numbers only to show how the old odd-lot differential affected a small investor.

Suppose an investor in the era of fractional pricing wanted 40 shares of a stock trading at $50.

The differential added 0.25 percent to the purchase, and the investor would typically pay it again when selling. For frequent small trades, such costs added up. In today's market, the same investor would usually pay neither the differential nor, at many brokers, a commission.

Sensible lessons from the history

The history of the odd-lot theory offers some general lessons about market indicators:

• A signal that seems to work in one period may stop working as market structure changes. The odd-lot balance changed meaning once dividend reinvestment, splits and specialist practices shifted the flow of small lots.
• Data definitions matter. Changes in what counts as an odd lot, and whether odd lots are reported at all, can change what a statistic measures.
• Anecdotes are not evidence. Claims that an indicator "called the bottom" are easy to make after the event; systematic tests, such as Klein's, often tell a different story.
• Contrarian thinking is not the same as a contrarian rule. Recognising that crowds can be wrong is reasonable; turning that idea into a mechanical rule based on one group's trades is much harder to justify.

Common misconceptions

"Odd lotters are always small, uninformed investors"

This was roughly true in the mid-20th century. It is not true today. O'Hara, Yao and Ye found that odd lots were heavily used in algorithmic and high-frequency trading and contributed a disproportionate share of price discovery, consistent with informed traders splitting orders to avoid detection.

"The odd-lot theory was proven to work"

Systematic tests did not support the full theory. Klein's 1964 thesis found it invalid as a complete theory, with only the sales side supported. Malkiel concluded that knowing what odd lotters did was not useful for investment strategy.

"Odd-lot trading is still a separate, more expensive market"

The separate odd-lot dealers and the one-eighth-point differential have gone. Odd lots have been reported on the US consolidated tape since 9 December 2013, and odd-lot price information has been expanded under the SEC's 2024 amendments.

"A round lot is always 100 shares"

Not any more. Under the SEC's amended definition, the round lot for US stocks is 100 shares only for stocks priced at $250 or less. It falls to 40, 10 or 1 share for higher-priced stocks.

"Small investors always lose"

Modern research is more nuanced. Kaniel, Saar and Titman found that stocks individuals bought intensely earned positive excess returns the following month. Barber, Odean and Zhu found positive short-term but negative longer-term returns following heavy retail buying. The results depend on the horizon and how retail trading is measured.

Frequently asked questions

What is an odd lotter?

An investor who trades shares in quantities smaller than a round lot. Traditionally, in the US, that meant fewer than 100 shares.

What is the odd-lot theory?

A contrarian market theory, associated above all with the Boston analyst Garfield Drew from the 1940s onward, that treated heavy odd-lot selling as a sign of a coming market rise and heavy odd-lot buying as a sign of a coming fall.

Does the odd-lot theory work?

The evidence says no, not as a reliable strategy. Academic tests in the 1960s and 1970s found at best partial support, structural changes distorted the data, and Burton Malkiel concluded that odd lotters were not much worse than the averages and that knowing their trades was not useful.

Why did people believe it?

It had an intuitive logic, it came with published weekly data, and its promoters could point to times when the signal had coincided with turning points, such as the bottoms Drew claimed to have identified in 1948 to 1949 and 1953 to 1954. Failures, such as the 1958 sell signal, received less attention from believers.

Are odd-lot statistics still published?

Odd-lot trades are now included in US consolidated market data, and the SEC's 2024 amendments expanded the odd-lot price information that is distributed. But because odd lots are now used heavily by algorithms and institutions, these figures do not measure small-investor sentiment in the way the old odd-lot statistics were thought to.

Is it bad to buy fewer than 100 shares?

Generally not, in today's markets. The separate odd-lot dealer system and the odd-lot differential no longer exist, and many brokers offer commission-free trades and fractional shares. Whether any particular investment is suitable is a separate question that depends on an investor's own circumstances.

Who was Garfield Drew?

Garfield Albee Drew was a Boston market analyst, a 1926 Harvard graduate and former Wall Street bond statistician, who developed and promoted the odd-lot theory. He published a treatise on odd-lot trading in 1940 and ran a weekly subscription service, the Drew Odd Lot Studies, which Time profiled in 1961 when it had about 4,500 professional subscribers.

What replaced the odd-lot theory?

No single indicator replaced it. Analysts interested in investor sentiment use other measures, and academic researchers study retail behaviour using detailed transaction and brokerage data, as in the work of Kaniel, Saar and Titman and of Barber, Odean and Zhu.

Sources

• Odd lotter (Wikipedia)
• "Business: Small Investor's Boswell", Time, 31 March 1961
• Donald J. Klein, The Odd-Lot Stock Trading Theory, Michigan State University thesis (1964)
• Hsiu-Kwang Wu, "Odd-Lot Trading in the Stock Market and Its Market Impact", Journal of Financial and Quantitative Analysis (1972)
• Stan West and Thomas T. Murphy, "New Caveats in Relying on Traditional Stock Market Statistics", Financial Analysts Journal (1978)
• O'Hara, Yao and Ye, "What's Not There: Odd Lots and Market Data", Journal of Finance (2014)
• Kaniel, Saar and Titman, "Individual Investor Trading and Stock Returns", Journal of Finance (2008)
• Barber, Odean and Zhu, "Do Retail Trades Move Markets?", Review of Financial Studies (2009)
• SEC 1963 Special Study of Securities Markets, Chapter VI (SEC Historical Society)
• SEC Release No. 34-71057 (odd lots on the consolidated tape)
• Davis Wright Tremaine: SEC amends Regulation NMS, round lot and odd lot changes (2024)
• NYIF: odd-lot differential explained
• Fortune: Schwab fractional shares launch (June 2020)
• Charles O. Hardy, Odd-Lot Trading on the New York Stock Exchange (Brookings, 1939), library record
• The Art of Contrary Thinking, Humphrey B. Neill (Goodreads record)
• Charles Schwab: fractional shares