In 1976, a then 23-year-old Sanford (Sandy) J. Grossman, now Wharton emeritus professor of finance, jolted stock market investors from their conventional understanding of how price formation occurs. In his paper titled “On the Efficiency of Competitive Stock Markets Where Trades Have Diverse Information,” which the Journal of Finance published, he showed that the price of an asset, or stock, reveals to each trader information that is of higher quality than his or her own information.
That revelation occurs when “the competitive system aggregates all the market’s information in such a way that the equilibrium price summarizes all the information in the market,” Grossman explained in his paper.
The paper’s groundbreaking insight, which continues to be relevant to this day, was recently recognized with the 2025 Wharton-Jacobs Levy Prize for Quantitative Financial Innovation. The biennial award, endowed with a $2 million gift from Wharton alumni Dr. Bruce I. Jacobs and Kenneth Levy, recognizes outstanding quantitative research that has had a lasting impact on the practice of finance.
Grossman’s paper was selected for its “pioneering work on the interplay between market efficiency, information asymmetry, limits to arbitrage, active management and the impact of trading and liquidity on price formation.” The prize includes an $80,000 cash award and a sterling silver medal.
During the ceremony to present the prize to Grossman, Jacobs said, “When Ken and I established this biennial award in 2011, it was our hope that over time, the recipients would constitute an elite group of scholars and practitioners who’ve had a transformative impact on financial markets.” Jacobs and Kenneth Levy are principals and co-founders of Florham Park, NJ-based Jacobs Levy Equity Management. “Sandy now joins the elite group” of previous winners, he added; they include Nobel economics laureates Harry Markowitz and William Sharpe, financial economist Stephen Ross, and finance professors Narasimhan Jegadeesh and Sheridan Titman.
How Information Finds Its Way Into Asset Prices
Jacobs, Levy, and Wharton finance professor Christopher Geczy, who is also academic director of the Jacobs Levy Equity Management Center for Quantitative Financial Research, explained how Grossman’s paper transformed investors’ perceptions about the role of information in price formation.
“Sandy explained not only why investment management firms invest in acquiring proprietary information, but also why it’s necessary for the functioning of competitive markets.”— Dr. Bruce I. Jacobs
In remarks at the prize ceremony, Levy noted that the “Efficient Market Hypothesis” holds that all available information is immediately incorporated into the prices of a stock. “But how does this happen? And what are the limits, if any, to the forces that govern this process? Thanks to the extraordinary work of Sandy Grossman, we have answers to these perplexing questions, as well as important insights into the role of information in security markets and implications for active management.”
Levy said Grossman’s 1976 paper laid the groundwork for another landmark paper titled “On the Impossibility of Informationally Efficient Markets,” which Grossman co-authored with Joseph Stiglitz and published in the American Economic Review in 1980.
Levy summarized the paper’s main takeaway: “It begins with a view that stock prices have two roles: as an aggregator of collective knowledge, such that the current price of a stock summarizes all information in the market, and as a transmitter of that information. Uninformed traders who invest nothing in collecting information presume that current prices reflect the knowledge of informed traders.”
Drawing from that, Levy said Grossman’s paper explained “the sometimes-paradoxical interplay between informed and uninformed traders that results in the stock prices that we observe.”
“If the price system is perfectly efficient, it removes the incentive to gather information, because uninformed traders could do just as well as informed traders simply by observing current prices, and informed traders would have no incentive to expend resources collecting information if they can’t earn a return on it,” Levy said. “As a result, the price system would collapse.”
The Role of “Noise” in Price Discovery
But that setting changes when “noise” comes into play, Levy said. “When noise is added to the system so that prices no longer perfectly aggregate or transmit information, traders are somewhat in the dark as to why prices are changing,” he added. “Those who have the resources are now incentivized to collect proprietary information. The result is competitive prices — noisy and imperfectly efficient.”
Noise, in fact, is essential to make the case for investing in information. In his paper, Grossman pointed out the assumption that prices perfectly aggregate information “is not robust.” The lack of robustness comes about when there’s noise in some investors’ information about an asset, such as uncertainty about its value, he added. When there is noise, the price system does not aggregate information perfectly, “and the allocative efficiency properties of a competitive equilibrium may break down,” he explained.
“Thanks to the extraordinary work of Sandy Grossman, we have answers to these perplexing questions, as well as important insights into the role of information in security markets and implications for active management.”— Kenneth Levy
The upshot of that scenario is that “if information is costly, there must be noise in the price system so that traders can earn a return on information gathering,” Grossman wrote. But in a setting where there is no noise, and information gathering is costly, a perfect competitive market will break down because investors cannot earn a return on what they invest in gathering information.
“The price system can be maintained only when it is noisy enough so that traders who collect information can hide that information from other traders,” Grossman wrote in his conclusion. “When this occurs, some traders want very much to know why prices are, for example, unusually high. It is not enough for traders to observe only prices.”
Grossman’s work is especially significant considering the advance of quant trading, according to Geczy. “As quantitative finance is being reframed over different horizons, and over different speeds, the Grossman and the Grossman-Stiglitz ideas are very relevant over the definition of what is advantage over very high frequencies as well as how we think about edge over the medium-term and long-term,” he said. Those ideas inform the definition of the notion of alpha, which represents value-added or market-beating return, he noted.
Grossman’s paper also informs the debate over insider trading, a notable example of which in recent times is the 2022 investigation into Congressional stock trading, Geczy said. Its relevance resonates also with other episodes such as the 2021 meme-stock trading hype involving stocks such as GameStop and AMC which highlighted the role of information arbitrage. Geczy noted its relevance also for approaches such as the so-called “mosaic model,” where analysts combine public and non-public but immaterial information to gain insights, with the rider that the information is non-material and legally obtained. “Insider trading is one of the sexy areas for which the Grossman paper frames the importance of information as a baseline,” Geczy said.
Why Grossman’s Paper Is Evergreen
According to Geczy, Grossman’s paper continues to be important to this day because it introduced the concept of “the Efficiency Paradox,” which essentially says that markets must be just so irrational for them to generate profits for those who pursue the information to make them rational.
“[Grossman’s] framework … is still a backbone of modern models of information and trading, reminding researchers in a sense to treat predictability as compensation for costly information [and] that noise is an equilibrium necessity.”— Christopher Geczy
“The markets are a competitive space where actors are paid to make markets efficient through the discovery of information asymmetries and profit,” Geczy continued. “So the paradox is you have to have inefficient markets so you can have efficient markets.”
Grossman’s paper is especially relevant today in the context of the push for passive investing, Jacobs said. “As passive indices have claimed an ever-growing share of stock investment in recent years, many have questioned whether active management could or should continue.… Sandy explained not only why investment management firms invest in acquiring proprietary information, but also why it’s necessary for the functioning of competitive markets.”
Geczy noted the sheer breadth of the import of the paper: “Sandy’s paper on the efficiency of competitive stock markets, where trades have diverse information, has greatly influenced how we understand, characterize, and model the nature and value of private information in markets, the mechanics and value of trading, the roles of both information and noise, and the distinction between and among passive and active approaches to investing among a number of areas of influence. It also predated and provoked the also-monumental papers Sandy co-authored with Joesph Stiglitz (1980) and Oliver Hart (1981),” he said.
Geczy also explained how the paper has shaped investors’ understanding of the role of information. “[Grossman’s] framework, as many of us have learned in graduate school, is still a backbone of modern models of information and trading, reminding researchers in a sense to treat predictability as compensation for costly information — that noise is an equilibrium necessity, that prices can reveal a great deal about fundamentals but are not everything,” he said. Thus, it creates “space for informed trading, and active management — that alpha must cover costs, all of it setting the stage for modern views of liquidity provision and market resilience,” he added.
Geczy credited Grossman with bringing “a whole new way of thinking about trading,” and pointed out two dimensions of that approach. One, it allowed for special information and advantage to be held by some actors who could then, based on what we call private signals, gather information. Two, maybe trading itself reveals information.
“Trading is not just trading. Trading is itself information,” Geczy said. “Although this is a classic theoretical paper, it has had tremendous implications for how we do things today. It’s an incredible paper. Some academics say it’s among the top five papers ever written in finance.”
