90% Confidence Interval

• The Bottom Line: A 90% confidence interval is a value investor's tool for defining a 'reasonable range' for a company's future value, replacing the fool's errand of single-point prediction with disciplined, probabilistic thinking.
• Key Takeaways:
• What it is: It's a calculated range of outcomes (e.g., for future earnings or intrinsic value) where you expect the true result to fall 90% of the time.
• Why it matters: It systematically builds a margin_of_safety into your analysis and forces you to confront uncertainty, which is the very essence of investing.
• How to use it: By calculating a plausible range for a company's value and only buying when the market price is significantly below the entire range.

Imagine you're listening to a weather forecast. A bad forecaster might say, “Tomorrow's high will be exactly 77 degrees Fahrenheit.” This is incredibly precise, but almost certainly wrong. A good forecaster, acknowledging the world's inherent unpredictability, would say, “We are 90% confident that tomorrow's high temperature will be between 74 and 80 degrees.” This second statement is a confidence interval. It doesn't give you a false sense of certainty. Instead, it gives you a range of plausible outcomes and a level of confidence in that range. It communicates both the likely result and the degree of uncertainty surrounding it. In investing, a 90% confidence interval does the exact same thing, but for business fundamentals instead of weather. Instead of predicting that “Steady Brew Coffee Co. will earn exactly $5.00 per share next year,” a value investor thinks in ranges. They might analyze the business and conclude, “Based on historical performance, management's skill, and potential economic headwinds, I am 90% confident that Steady Brew's earnings per share will fall somewhere between $4.50 and $5.50.” This simple shift from a single number to a range is one of the most profound and powerful tools in an investor's mental toolbox. It's an admission of humility. It acknowledges that the future is not knowable and that our job is not to be a fortune-teller, but a business analyst who prepares for a variety of outcomes.

“It is better to be approximately right than precisely wrong.” - Often attributed to Warren Buffett ¹⁾

The “90%” part is simply a common statistical convention. You could use an 80% interval (a wider, less certain range) or a 95% interval (a narrower, more confident range). For most investors, the exact percentage is less important than the discipline of thinking in ranges. The 90% level strikes a healthy balance—it's high enough to be meaningful but not so high as to create an impractically wide range.

The concept of a confidence interval is not just a statistical curiosity; it is the very embodiment of the value investing philosophy. Wall Street often promotes a culture of “false precision,” with analysts building elaborate models that spit out price targets down to the penny. Value investors know this is a dangerous illusion. Here’s why embracing the confidence interval is crucial.

• It Institutionalizes the Margin of Safety: This is the most important connection. Benjamin Graham's core principle was to buy a security for significantly less than your estimate of its intrinsic value. A confidence interval makes this process rigorous. If your analysis suggests a business is worth between $80 and $100 per share (your 90% confidence interval), applying a margin of safety means you wouldn't consider buying it unless the price offered by mr_market was, say, $60 or less. By buying below the entire range of plausible values, you give yourself a double buffer: one against your analysis being wrong, and another against the business facing unforeseen troubles.
• It Combats Overconfidence: Human beings are hardwired to seek certainty and overestimate their own predictive abilities. Forcing yourself to define a range—especially the lower bound of that range—is a powerful antidote to this hubris. It makes you ask the critical question: “What could go wrong here?” By defining a pessimistic (but still plausible) outcome as your lower bound, you ground your investment case in reality, not just optimistic projections.
• It Helps Define Your Circle of Competence: The width of your confidence interval is a fantastic indicator of how well you understand a business.
  • Narrow Interval: If you're analyzing a predictable company like a utility or a dominant consumer brand (e.g., Coca-Cola in the 1990s), you can forecast its future earnings with a relatively high degree of confidence. Your range might be quite narrow. This indicates the company is likely within your circle of competence.
  • Wide Interval: If you're trying to analyze a pre-profit biotechnology firm or a new technology company, the range of potential outcomes is enormous—from bankruptcy to a 100-fold increase in value. Your confidence interval for its future earnings would be so wide as to be useless. This is a clear signal that the company is speculative and likely outside your circle of competence.
• It Refocuses on Business Value, Not Stock Price: The confidence interval is an estimate of the underlying business's worth or earning power. The stock price is what the market is willing to pay for it at a given moment. This distinction is critical. Your job is to calculate the former and compare it to the latter. The interval provides a rational benchmark against which you can judge the often-irrational mood swings of Mr. Market.

While a statistician would use complex formulas involving standard deviations and sample means, a value investor can use a more practical, scenario-based approach to build an intuitive confidence interval. The goal isn't statistical perfection; it's intellectual honesty.

Let's say you're trying to estimate the intrinsic_value of a company. The most common way is to project its future free_cash_flow and then discount it back to the present. Here's how to turn that single-point estimate into a powerful confidence interval.

1. Step 1: Build Your Base Case. This is your most realistic, “best guess” scenario. Based on the company's history, industry trends, and competitive advantages, what do you believe is the most likely trajectory for revenue growth, profit margins, and capital expenditures? This calculation will give you a single number for intrinsic value, which will become the center of your range.
2. Step 2: Define Your Key Drivers. Identify the 2-4 most critical variables that your valuation hinges on. These are the assumptions that, if changed, would have the biggest impact on the final number. For a retailer, this might be same-store sales growth and gross margin. For a software company, it might be customer growth and churn rate.
3. Step 3: Construct the Lower Bound (Pessimistic Case). Now, stress-test your key drivers. What happens if a mild recession hits? What if a new competitor enters the market? What if a key raw material cost increases? Adjust the key variables in your model to reflect a reasonably pessimistic—not catastrophic—future. The resulting intrinsic value becomes the lower bound of your 90% confidence interval. This is arguably the most important number in your entire analysis.
4. Step 4: Construct the Upper Bound (Optimistic Case). Do the opposite. What if the company successfully launches a new product? What if it gains market share faster than expected? What if a tailwind benefits the entire industry? Adjust your key variables to reflect a reasonably optimistic outcome. This gives you the upper bound of your confidence interval.
5. Step 5: State the Interval. You now have your range. For example: “My analysis suggests a base case intrinsic value of $120 per share. However, considering potential risks and opportunities, my 90% confidence interval for the company's value is between $90 (pessimistic case) and $150 (optimistic case).”

The result of this exercise is far more than just three numbers. It's a framework for making a decision.

• The Width of the Interval: As mentioned, a narrow interval ($95-$105) suggests a stable, predictable business. A wide interval ($50-$250) suggests high uncertainty and risk. A value investor naturally gravitates toward businesses where they can construct a reasonably narrow and confident interval.
• The Position of the Stock Price: This is where the rubber meets the road.
  • Price is Below the Lower Bound: If the stock is trading at $65, it's significantly below even your pessimistic valuation of $90. This represents a potentially strong investment opportunity with a large margin of safety.
  • Price is Within the Interval: If the stock is trading at $110, it's within your range of fair value. It's not egregiously expensive, but it offers little to no margin of safety. A prudent investor would likely wait for a better price.
  • Price is Above the Upper Bound: If the stock is trading at $180, it's priced for a future that is even more optimistic than your best-case scenario. This is a clear sign of overvaluation and a situation to avoid or sell.

Let's compare two fictional companies to see the confidence interval in action.

• Steady Brew Coffee Co.: A mature company with a strong brand, thousands of established stores, and predictable single-digit growth.
• Fusion-X Energy Inc.: A development-stage company working on a revolutionary but unproven nuclear fusion technology.

^ Valuation Scenario Analysis ^

Investor Conclusion: An investor looking at Steady Brew can form a rational opinion. The range of values is relatively tight. If the stock trades at $70, it's clearly below the low end of the range, offering a margin of safety. If it trades at $110, it's fairly priced with no margin for error. The decision is based on price versus value. For Fusion-X, the concept of a value range breaks down. The interval is so wide that it provides no practical guidance. The outcome is nearly binary: it will either be a near-total loss or a spectacular home run. This is not investing; it's speculation. A value investor would recognize this as being far outside their circle of competence and move on.

• Promotes Intellectual Honesty: It forces you to admit you don't know the future and to consider a range of possibilities, especially negative ones.
• Integrates Risk Management: The concept of a margin_of_safety is baked directly into the process of comparing a stock's price to the lower bound of your value estimate.
• Improves Decision-Making: It provides a clear, rational framework for when to buy (below the range), hold (within the range), or avoid (above the range).
• Highlights Predictability: The process naturally filters for the types of stable, understandable businesses that value investors cherish.

• Garbage In, Garbage Out (GIGO): The confidence interval is only as good as the assumptions used to build the scenarios. If your base, pessimistic, and optimistic cases are all based on flawed analysis, the resulting range will be misleading.
• Subjectivity: The choice of what constitutes a “pessimistic” or “optimistic” scenario is inherently subjective. Two skilled analysts can arrive at different ranges for the same company.
• False Security: Simply having a range can make an investor feel safe, even if the entire range is wrong or if an un-modeled “black swan” event occurs. It is a tool to improve thinking, not a crystal ball.
• Analysis Paralysis: Some investors can get lost in building overly complex scenarios and forget that the goal is to find obvious bargains, not to model every conceivable future. A simple, back-of-the-envelope range is often more useful than a 100-tab spreadsheet.

• margin_of_safety
• intrinsic_value
• circle_of_competence
• scenario_analysis
• mr_market
• risk_management
• price_vs_value