Information Theory for Investors
Signal, Noise, Uncertainty, and the Economics of Knowledge
Financial markets are often described as mechanisms for allocating capital.
While true, this description only captures part of their function. At a deeper level, markets are information-processing systems.
Every trade reflects a belief. Every price represents a collective estimate regarding future outcomes. Every shift in valuation emerges from changing information, changing expectations, or changing interpretations of uncertainty.
Viewed through this lens, investing becomes less about predicting prices and more about understanding information itself. This is where Information Theory becomes remarkably valuable.
Originally developed by Claude Shannon in the mid-twentieth century, Information Theory was designed to study the transmission, storage, and measurement of information. Its influence extends across telecommunications, computing, cryptography, artificial intelligence, and increasingly, quantitative finance.
For investors, Information Theory provides a framework for understanding some of the most fundamental questions in markets:
What constitutes useful information?
How can signal be distinguished from noise?
Why do some insights create alpha while others do not?
How should uncertainty be measured?
Why does information lose value as it becomes widely known?
These questions lie at the heart of investing itself. At its core, Information Theory reminds us that financial markets are not merely driven by information, but also by changes in information.
Markets as Information Systems
Financial markets aggregate enormous quantities of information.
Participants continuously process:
corporate earnings
economic indicators
central bank policy
geopolitical developments
industry trends
behavioural signals
liquidity conditions
Prices emerge from the interaction of these interpretations. Importantly, prices are not records of the present, they are estimates of the future.
A stock price reflects collective expectations regarding future cash flows. A bond yield reflects expectations regarding inflation, growth, and monetary policy. A currency reflects relative expectations between economies.
In this sense, markets function as distributed information-processing networks. Millions of participants collectively attempt to estimate uncertain future states, the resulting prices become informational signals themselves.
What Is Information?
Information Theory defines information in a surprisingly specific way.
Information is not simply data, it is also a reduction in uncertainty. A piece of information possesses value only if it changes understanding.
Consider two headlines:
The first states that a company reported earnings exactly in line with expectations
The second states that earnings exceeded expectations substantially
The first headline contains relatively little informational value because market participants largely anticipated the outcome. The second contains greater informational value because it changes expectations. Markets respond less to absolute events than to surprises, information matters because it alters probabilities.
Signal Versus Noise
Perhaps the most important contribution of Information Theory to investing is the distinction between signal and noise.
Signal refers to information containing genuine predictive or explanatory value. Noise refers to randomness, distraction, or irrelevant variation. Financial markets generate vast amounts of both.
Every day investors encounter:
news headlines
analyst opinions
social media commentary
economic releases
price fluctuations
Most of this information possesses limited long-term significance. The challenge is not finding information, it is identifying information that matters.
Information Theory suggests that the value of information depends upon its ability to improve decision quality. Many market participants consume enormous quantities of data while gaining little additional understanding; therefore, more information does not necessarily imply more knowledge.
Entropy and Uncertainty
One of the central concepts within Information Theory is entropy.
Entropy measures uncertainty; a highly predictable system exhibits low entropy, a highly unpredictable system exhibits high entropy. Financial markets contain varying levels of entropy through time.
Periods characterised by:
stable economic conditions
consistent trends
coherent narratives
often exhibit lower informational entropy.
Periods characterised by:
volatility
uncertainty
conflicting information
regime transitions
often exhibit higher entropy.
For investors, entropy provides insight into the informational structure of the market itself. The objective is not merely predicting outcomes, it is understanding how predictable the environment has become.
Information and Alpha
Alpha can be viewed fundamentally as an information problem.
If all market participants possess identical information and interpret it identically, opportunities for excess return become scarce. Alpha emerges when informational differences exist.
These differences may arise from:
superior research
faster analysis
deeper understanding
behavioural insight
alternative data
unique interpretation
Importantly, alpha does not necessarily require exclusive information; it may simply require superior processing of publicly available information. The key is transforming information into insight more effectively than competitors.
The Economics of Information
Information possesses economic characteristics.
It is costly to acquire, it requires effort to analyse, and it may become obsolete quickly. Thus, its value changes depending upon who possesses it. This creates an informational economy within financial markets.
Investors continuously compete for:
knowledge
understanding
insight
informational advantage
However, information exhibits a unique property; once information becomes widely known, its value often declines. A trading opportunity known by few participants may generate substantial returns. The same opportunity known by everyone may generate none, the market rapidly incorporates widely disseminated information. This process drives much of market efficiency.
Information Decay
Information possesses a lifespan, new information enters the market and influences prices.
Over time:
participants react
prices adjust
opportunities narrow
The informational advantage decays. This process is analogous to alpha decay, the value of information depends partly on its exclusivity and novelty.
As information diffuses throughout the market, excess return opportunities often diminish; this is why timing matters. Information is frequently most valuable shortly after discovery and least valuable once consensus has formed.
Bayesian Updating and Markets
Information Theory aligns naturally with Bayesian reasoning.
Investors begin with prior beliefs regarding future outcomes. As new information arrives, beliefs are updated; the market itself functions similarly. Prices continuously adjust as participants revise expectations. This process highlights an important principle:
Investing is not about certainty, t is about updating probabilities intelligently
The best investors are often not those who predict perfectly, they are those who adapt most effectively when new information arrives.
Information Overload
Modern investors face an unusual challenge. Historically, the problem was insufficient information; today, the problem is excessive information.
Financial markets generate:
continuous news
real-time data
social media signals
alternative datasets
algorithmic analysis
This abundance creates informational overload.
Paradoxically, excessive information can reduce decision quality, as the ability to filter becomes more important than the ability to consume. Information Theory therefore encourages selectivity. The goal is not maximum information, it is maximum informational efficiency.
Market Prices as Information
One of the most important insights in finance is that prices themselves contain information. Every market participant acts according to beliefs, expectations, and incentives. The resulting transactions produce prices, these prices represent aggregated information from across the market.
Importantly, prices do not reveal perfect truth. However, they often contain information that no individual participant possesses independently. This is one reason markets can appear remarkably intelligent despite the imperfections of individual participants. The collective system often processes information more effectively than its individual components.
Information Theory and Risk
Risk can also be viewed through an informational lens, many forms of risk emerge because information remains incomplete.
Investors face uncertainty regarding:
future earnings
economic growth
policy decisions
behavioural responses
Risk therefore reflects informational limitations. As uncertainty increases, informational entropy increases. As informational clarity improves, perceived risk often declines. This relationship connects Information Theory directly to portfolio construction, risk management, and capital allocation.
The MorMag Perspective
At MorMag, Information Theory forms an important conceptual framework for understanding financial markets. Markets are viewed as adaptive information-processing systems in which prices emerge through the interaction of competing interpretations of uncertain future outcomes.
Within this framework, research focuses on:
signal identification
noise reduction
entropy analysis
informational asymmetry
probabilistic updating
alpha generation
The objective is not merely collecting information, the objective is transforming information into understanding. In increasingly data-rich environments, this distinction becomes critically important.
Beyond Finance
The significance of Information Theory extends beyond investing, many of humanity's most important systems involve the processing of information.
Economies, technologies, biological organisms, social networks, and artificial intelligence systems all depend upon information flows. Financial markets represent one of the most visible examples of this principle. Understanding information therefore improves understanding of markets themselves.
Conclusion
Information Theory provides one of the most powerful frameworks available for understanding financial markets because it addresses the fundamental currency of investing: information.
By distinguishing signal from noise, measuring uncertainty through entropy, analysing information decay, and explaining how markets process knowledge, Information Theory reveals why some insights generate value while others do not. Its importance extends beyond quantitative modelling, it offers a deeper understanding of how markets function as information-processing systems operating under uncertainty.
At MorMag, this perspective forms part of a broader investment philosophy grounded in probabilistic reasoning, complexity science, adaptive markets, and rigorous research.
Successful investing is not simply about possessing more information, it is about extracting more understanding from the information that already exists.
