Predicting Stock Prices

Predictable Patterns or Random Noise: The History of Stock Price Forecasting.

For more than a century, investors, mathematicians, and economists have been locked in a high-stakes debate: Are stock prices predictable, or are we just staring into a financial abyss of random noise?

The quest to unlock the future of stock prices has shaped modern portfolio theory, birthed massive hedge funds, and created a fascinating timeline of intellectual breakthroughs.

Understanding this evolution is not just an academic exercise—it is the foundation of how institutional capital is managed around the world today.

The Foundation of Randomness: Bachelier, Brownian Motion, and Time

Long before Wall Street used supercomputers, a French mathematician named Louis Bachelier laid the groundwork for modern financial theory in his 1900 doctoral thesis, The Theory of Speculation.

Bachelier made a radical proposition: the mathematical expectation of the speculator is zero. He argued that stock price movements mirror Brownian Motion—the erratic, random drifting of particles suspended in a fluid.

From this, Bachelier derived a critical mathematical relationship: (2) stock prices vary according to the square root of time.

Where represents the expected range or volatility over a time horizon . This means that if a stock’s price volatility is expected to fluctuate by USD2 over one day, it will not fluctuate by USD4 over two days; instead, it will fluctuate by . This concept remains a cornerstone in option pricing models used by institutions like Goldman Sachs to price risk.

Decades later, this evolved into the Random Walk Theory, popularized by economist Burton Malkiel. The theory posits that stock price changes have the same distribution and are independent of each other.

Therefore, (2) past movement of stock prices cannot be used to predict future movement. 

In short, a blindfolded monkey throwing darts at a newspaper’s financial pages could select a portfolio that performs just as well as one carefully managed by experts.

The Efficient Market Hypothesis: The Ultimate Counter-Argument

How could prices be completely random if thousands of brilliant analysts are studying them? University of Chicago economist Eugene Fama answered this in the 1960s with the Efficient Market Hypothesis (EMH).

Fama argued that the randomness itself is proof of an efficient market.

In an efficient market, (3) all relevant information is immediately reflected in stock prices.

When new information emerges—such as Apple releasing a surprise earnings report or a sudden regulatory shift affecting Toyota—thousands of rational market participants instantly digest it and trade on it. Because news is inherently unpredictable, price changes must also be unpredictable.

• Weak Form Efficiency: Past price data is already reflected. Technical analysis is useless.
• Semi-Strong Form Efficiency: All public information is reflected. Fundamental analysis cannot beat the market.
• Strong Form Efficiency: All public and private (inside) information is reflected. No one can consistently beat the market.

The Believers in Trends: Dow Theory and the Forecasters

While academics preached randomness, practitioners insisted on patterns. The bedrock of technical analysis is Dow Theory, developed from the writings of Charles Dow at the turn of the 20th century.

Dow Theory states that (4) trends in stock prices persist until they lose momentum and go into reverse. 

Instead of treating each day’s price change as an isolated, independent event, Dow theorists see the market as moving in three waves: primary trends (tides), secondary reactions (waves), and minor ripples.

William Peter Hamilton, an early editor of The Wall Street Journal, advanced this thinking by asserting that (5) the market itself reveals what stock prices will do in the future. 

Hamilton argued that the combined price action of the market indexes acts as a barometer, digesting everything known to mankind and flashing signals of accumulation (buying) or distribution (selling) before the broader economy catches up.

Later, Robert Rhea refined this work, famously attempting to identify two “times and places for certainty” within market cycles:

1. The bottom of a bear market, when equities are deeply undervalued and accumulating them offers near-certainty of long-term returns.
2. The absolute peak of a bull market, when speculative mania makes a severe downturn mathematically inevitable.

Robert Rhea refined market cycle theory by identifying two periods of maximum certainty for stock prices.

The (6) absolute bottom of a bear market, where deep undervaluation guarantees long-term returns, and the absolute peak of a bull market, where speculative mania makes a crash inevitable.

The Empirical Reality Check: Alfred Cowles and 20-Variable Regressions

While Wall Street analysts claimed they could spot these trends, an eccentric businessman and economist named Alfred Cowles decided to test their claims with rigorous data. In his seminal 1933 paper, Can Stock Market Forecasters Forecast?, Cowles analyzed thousands of professional predictions.

Cowles took the debate a step further by using advanced statistical modeling. He tried to determine whether stock prices are predictable using linear regression with twenty variables—incorporating everything from industrial production and interest rates to historical price ratios.

His conclusion was a massive blow to the financial industry: the professional forecasters failed to outperform pure chance.

The 20-variable regression models showed that while certain (7) macroeconomic factors correlate with long-term trends, predicting short-term stock price movements with statistical consistency was virtually impossible.

The Modern Compromise: Smart Beta and Quantitative Realities

Where does this leave investors today? The reality lies somewhere between pure randomness and absolute predictability.

Global mega-funds like Renaissance Technologies or AQR Capital Management have proven that micro-inefficiencies do exist, but they are incredibly fleeting.

Modern quantitative finance uses machine learning models—far advanced from Cowles’ 20-variable regressions—to (8) exploit tiny behavioral biases and momentum anomalies before the market corrects itself.

For the everyday investor, the lesson of financial history is clear: trying to predict next week’s price movement is a gambler’s game governed by the square root of time.

True wealth generation relies not on outguessing a random walk, but on aligning with the long-term, fundamental growth of the global economy.