Noise Trading Feedback Models - When Traders Feed Off Each Other
Remember the dot-com bubble? Companies with zero profit, sometimes zero revenue, trading at insane valuations. Analysts invented new ways to justify the prices. “Forget earnings, count the eyeballs!” And for a while, it worked.
But here’s the thing. Those crazy stock prices didn’t just sit there being wrong. They actually changed the companies themselves. That’s the big idea of Chapter 6. Price movements feed back into the real value of the firm.
Wait, Prices Change Reality?
The efficient market people say: if noise traders push a stock price too high, rational traders will correct it. Price goes back to where it should be. End of story.
Feedback models say something different. Yes, the price might eventually go back to fundamentals. But those fundamentals might have shifted because the price moved in the first place.
Think about it like this. A company’s stock price shoots up. Now that company can hire better talent because everyone wants to work at the “hot” company. It can raise capital more easily. Suppliers give it better terms. Customers trust it more. The company actually becomes more valuable. Not because the business changed, but because the stock price changed, and that changed everything around the business.
And it works in reverse too. Stock tanks? Good employees leave. Suppliers tighten terms. Customers get nervous. The company gets worse. The falling price becomes a self-fulfilling prophecy.
Burton and Shah cover two models that formalize this idea. Let me walk you through both.
The Hirshleifer Model
David Hirshleifer, along with Subrahmanyam and Titman, built a model in 2006 that shows exactly how this feedback loop works. The setup has three types of players.
The firm. One company with stock that trades over three time periods. At the end, it pays out a final value to shareholders.
The investors. Two kinds. Rational ones who learn the true base value of the firm. And irrational ones who think they know what the firm is worth but are actually trading on noise, on signals that have nothing to do with fundamentals. Both types are split further into “early” and “late” traders based on when they get their information.
The stakeholders. These are the employees, suppliers, and customers. The key thing is they don’t know the true value of the firm. All they can see is the stock price. So they use the stock price as a signal for how much effort to put into the company.
Here is where it gets interesting.
Say the irrational traders get excited and bid the stock price way up. The stakeholders see the high price. They can’t tell if the price is high because the company is genuinely good, or because irrational traders are just being irrational. Their best guess? Probably a bit of both. So they invest more effort into the firm.
And that extra effort actually increases the real value of the company. The irrational hype created real value. The feedback loop is complete.
The Surprising Result
Here’s what really caught my attention. In this model, irrational traders can actually make money. Not just survive, but earn positive returns.
How? The early irrational traders know exactly how the late irrational traders will behave once they get the same noise signal. So the early ones front-run the late ones. The late irrational traders always lose money, yes. But sometimes the early ones make enough to more than cover those losses, partly because of the feedback effect.
And it gets even crazier. Under certain conditions, irrational traders can earn higher expected returns than rational ones. Not because they’re taking on more risk, which is the usual explanation. But because they actually have relevant information that rational traders don’t have. The noise signal matters because it feeds back into real prices.
Think about that for a second. The people trading on nonsense can sometimes beat the people trading on facts. Because the nonsense becomes reality through the feedback mechanism.
The Subrahmanyam-Titman Model
The second model, published in 2001, looks at the same feedback idea but from a different angle. It asks: why do companies spend so much money on investor relations just to prevent short-term stock price dips?
If the efficient market theory is right, short-term dips shouldn’t matter. The price will correct itself. So why bother?
The answer, according to Subrahmanyam and Titman, is cascades.
What Are Cascades?
Imagine a company with a bunch of stakeholders, say employees. Each employee has a minimum amount they need to be paid to stay. Some have low minimums, some have high ones.
And here’s the critical part. The value each employee gets from working at the company depends on how many other employees are there too. More coworkers means more resources, better projects, higher expected compensation. Fewer coworkers means the opposite.
This creates a domino effect.
Positive cascade: The employee with the lowest salary requirement joins. Now the expected value for the next employee goes up. So they join too. Then the next one joins, and the next. One hire triggers an avalanche of hires. Everyone joins even though only one person would have joined if they were making the decision alone.
Negative cascade: One employee with the highest requirements quits. Now the expected value for everyone else drops. The next most expensive employee quits. Then the next. One departure triggers a mass exodus. Everyone leaves even though almost all of them would have stayed on their own.
How Stock Prices Trigger Cascades
In the model, rational investors learn something about the true value of the firm and trade accordingly. But there’s also noise trading happening at the same time. A market maker sees the combined demand and sets a price.
Stakeholders see this price. But they can’t tell if a high price means the rational investors discovered something good, or if it’s just noise traders being noisy. Sound familiar? Same problem as in the Hirshleifer model.
If the price looks high, stakeholders update their beliefs. They think the firm is probably worth more than they assumed. The marginal stakeholders decide to associate with the firm. And if there are cascade conditions, that triggers more stakeholders to join. The company genuinely becomes more valuable.
If the price drops, some stakeholders leave. Others see them leaving and follow. The company actually becomes less valuable.
The researchers found two important things. First, cascades are more likely with volatile stocks. Big price swings are more likely to trigger stakeholder decisions that start the domino effect. Second, cascades are less likely when information is expensive. If it costs a lot to learn about the company, stakeholders know that price movements are mostly noise, not signal. So they don’t react as much.
What About the Company Itself?
The model also considers what happens when companies can control how much information the public sees. And the answer depends on whether you’re a startup or an established company.
Startups want attention. They need stakeholders to join. So they have an incentive to be more transparent, to attract analyst coverage, to get people looking at their stock. The upside of a positive cascade is huge for them.
Established companies worry more about the downside. They already have their stakeholders. A negative cascade would be devastating. So they might actually choose to be less transparent, to reduce the chances that a random price drop triggers a stakeholder exodus.
Think about that next time you see a hot startup doing flashy press releases while a boring Fortune 500 company releases the minimum required information. There might be a rational strategy behind both approaches.
The Honest Limitations
Burton and Shah are fair about the weaknesses of both models. The biggest criticism is that both rely on very specific mathematical assumptions. When a model needs that many specific functional forms to work, you start wondering if the results come from the underlying logic or just from the particular equations chosen.
Also, in both models, stakeholders make decisions based only on stock price. No interviews, no Glassdoor reviews, no industry research. Just the stock ticker. That’s a stretch. In real life, a job candidate at a dot-com company in 1999 probably did at least some homework beyond checking the stock price.
But the core intuition holds up. Stock prices are not just passive scorecards. They can actively change the thing they’re supposed to be measuring. And when irrational traders push prices around, the effects don’t stay confined to the stock market. They ripple out into the real economy.
Why This Matters
The big takeaway is uncomfortable for efficient market believers. If noise traders can change a company’s actual value by moving its stock price, then market efficiency has a deeper problem than just temporary mispricing.
It also raises a question that nobody has fully answered yet. If prices are distorted, then some companies raise capital at the wrong prices. Hot companies get too much money. Solid but boring companies get too little. Resources get misallocated across the entire economy.
That’s not just an academic curiosity. That’s real money going to the wrong places.
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