Data streams illuminating trading screens in a financial marketplace.

Decoding Market Signals: How Cheap Information Reshapes Financial Landscapes

Rhea Morgan in Business & Economy December 2025 • 4 min read.

"Uncover the surprising ways that affordable information is changing how markets aggregate knowledge, creating both opportunities and challenges for investors."

Financial markets have long been studied to determine how accurately they reflect the collective knowledge of traders. The core question is whether market prices truly reveal and aggregate the private insights of those participating. Research from Hayek in 1945 laid early groundwork, with significant progress made by Ostrovsky in 2012, demonstrating that ‘separable’ securities aggregate information effectively when trading occurs over extended periods. However, this separability isn't foolproof; it can falter with slight alterations to market dynamics or shifts in traders' informational advantages.

This article explores the evolving role of costly signals in market efficiency. With rapid advancements in information technology, data acquisition and analysis have become increasingly affordable. The question is, can this new wave of accessible information lead to more effective markets? Recent tools, like ChatGPT, are adding considerable value for investors, assisting with tasks from processing data to picking stocks, thus inviting a closer examination of information aggregation within financial ecosystems.

Using Ostrovsky's dynamic trading model, enhanced with the ability for traders to acquire costly signals, this analysis examines the impact of cheap information on market behaviors. By allowing traders to purchase signal structures before trading, and considering a broad spectrum of information cost functions, including Shannon entropy, we aim to uncover the characteristics of securities that facilitate information aggregation. This approach provides insights into how the cost of information influences market efficiency and the potential acceleration or deceleration of information aggregation.

What Securities Truly Aggregate Information? The Role of 'k Separability'

Data streams illuminating trading screens in a financial marketplace.

In the financial markets, the concept of 'k separable securities' emerges as crucial for effective information aggregation, especially when information costs are a factor. These securities are both necessary and sufficient for aggregating information, thereby generalizing Ostrovsky's earlier findings from 2012. As the cost of acquiring information decreases, the securities that eventually become 'k separable' and aggregate information in all equilibria, irrespective of the information structures, possess a straightforward structure: they assign a distinct payoff at each state.

This characteristic—specifying a different payoff for every state—is generic for securities with unique values. The core message is that when information is readily available, markets tend to aggregate information more effectively. Yet, there remains a limited class of securities, those that specify the same payoff in two states, and either higher or lower payoffs in two other states, that never become 'k separable' and may consequently fail to aggregate information even with minimal costs.

Arrow-Debreu (A-D) Security: This security pays out a fixed amount if a specific state occurs and nothing otherwise. It's a fundamental building block but offers limited information.
Three-Payoff Security: This security offers three possible payouts: a high payout in one state, a low payout in another, and a medium payout in all other states. This provides slightly more information than an A-D security but still has limitations.

This classification reveals that only securities with very specific payoff structures are always separable. These securities are not very informative, as they can only predict whether one or two states have occurred. This is problematic because combining multiple A-D securities to create a composite, more informative security does not solve the issue, as it will be non-separable for some information structures. Therefore, the classification of securities is based on payoff structure—always separable, 'k' separable for some 'k', and 'k' non-separable for all 'k'.

The Future of Market Efficiency: Navigating the Information Age

In conclusion, this research highlights the critical role of cheap information in shaping financial markets. By understanding the 'k separability' of securities, investors and market designers can better navigate the complexities of information aggregation. As technology continues to drive down the cost of information, the insights from this analysis will become increasingly vital for fostering efficient and transparent markets.

About this Article -

This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

This article is based on research published under:

DOI-LINK: https://doi.org/10.48550/arXiv.2406.07186,

Title: Information Aggregation With Costly Information Acquisition

Subject: econ.th

Authors: Spyros Galanis, Sergei Mikhalishchev

Published: 11-06-2024

Everything You Need To Know

How does cheap information impact market efficiency, according to the research?

The research suggests that the decreasing cost of information, driven by advancements in information technology, significantly impacts market efficiency. Cheaper information can potentially lead to more effective markets. The analysis, utilizing Ostrovsky's dynamic trading model, examines how traders' behaviors change when they can purchase signals at a lower cost, affecting information aggregation. This could result in faster or slower information aggregation depending on the specific characteristics of the securities and the cost of the information.

What are 'k separable securities,' and why are they important for information aggregation in financial markets?

'k separable securities' are crucial for effective information aggregation, particularly when information costs are a factor. These securities are necessary and sufficient for aggregating information, generalizing previous findings. They have a straightforward structure, assigning a distinct payoff at each state. This characteristic ensures that when information is readily available, markets tend to aggregate information more effectively. The classification of securities is based on their payoff structure: always separable, 'k' separable for some 'k', and 'k' non-separable for all 'k'.

Can you explain the role of Arrow-Debreu (A-D) securities and Three-Payoff securities in information aggregation?

Both Arrow-Debreu (A-D) securities and Three-Payoff securities are examples of how different payoff structures impact information aggregation. An A-D security pays a fixed amount if a specific state occurs and nothing otherwise; it is a fundamental building block but offers limited information. Three-Payoff securities offer three possible payouts: a high payout in one state, a low payout in another, and a medium payout in all other states, providing slightly more information than an A-D security. The research indicates that only securities with very specific payoff structures are always separable. The limitations of these securities highlight the challenges of creating more informative financial instruments.

How has the understanding of information aggregation in financial markets evolved from Hayek's work to Ostrovsky's model?

Hayek's 1945 research laid the early groundwork for understanding how market prices reflect collective knowledge. Significant progress was made by Ostrovsky in 2012, who demonstrated that 'separable' securities aggregate information effectively when trading occurs over extended periods. This means that certain securities, under specific conditions, can efficiently incorporate private insights from traders into market prices. This concept has evolved with the inclusion of cheap information and its impact on market dynamics, with the analysis building upon Ostrovsky's model by considering how the cost of acquiring signals affects market behaviors and information aggregation.

What are the implications of 'k separability' for investors and market designers in the era of cheap information?

Understanding 'k separability' is crucial for investors and market designers, especially with the increasing availability of cheap information. For investors, it means recognizing the types of securities that are most effective at aggregating information under different cost structures. They can then use this knowledge to build more informed investment strategies and potentially identify market inefficiencies. For market designers, it highlights the importance of creating and structuring securities that facilitate efficient information aggregation, promoting market transparency and efficiency. As technology continues to lower the cost of information, the insights derived from the analysis will become increasingly vital for navigating the complexities of financial markets.