Show pageOld revisionsBacklinksBack to top This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong. ====== Lorenz Curve ====== ===== The 30-Second Summary ===== * **The Bottom Line:** **The Lorenz curve is a simple graph that reveals dangerous concentrations of power, whether it's wealth in an economy or, more importantly for investors, a company's revenue in the hands of too few customers.** * **Key Takeaways:** * **What it is:** A visual representation of distribution, comparing a perfect, even spread against the messy reality. * **Why it matters:** It exposes a critical, often overlooked business risk: customer concentration. A company overly dependent on a few clients has a fragile [[economic_moat]]. * **How to use it:** As a mental model to assess the quality and durability of a company's revenue stream when you're doing your [[due_diligence]]. ===== What is the Lorenz Curve? A Plain English Definition ===== Imagine you're hosting a pizza party for ten guests. In a perfectly fair world, you'd cut the pizza into ten equal slices, and everyone would get exactly 10% of the total pizza. If we were to plot this on a graph, showing the cumulative percentage of guests against the cumulative percentage of pizza they received, we'd get a perfect 45-degree straight line. This is the **Line of Perfect Equality**. Ten percent of the guests get 10% of the pizza, 50% of the guests get 50% of the pizza, and so on. But real life is rarely so neat. Now, imagine the party's "big shot" guest arrives and grabs half the pizza for themself. The remaining nine guests are left to squabble over the other half. The distribution is now highly unequal. Our graph would now show a line that sags deeply below the Line of Perfect Equality. This sagging line is the **Lorenz curve**. The bigger the gap between the Line of Perfect Equality and the Lorenz curve, the greater the inequality. Originally, economists used this tool to measure income or wealth inequality in a country. A country where the curve is close to the straight line is relatively equal. A country where the curve bows out dramatically has a massive wealth gap. But for a savvy investor, this concept has a powerful, and far more practical, application. Forget about countries and citizens for a moment. Think about a **company and its customers**. Is the company's "revenue pizza" being enjoyed by thousands of different customers, each taking a small, manageable slice? Or is one giant corporate customer eating 70% of it? The Lorenz curve gives us a brilliant mental framework to visualize this risk. A company whose revenue Lorenz curve sags dramatically is living dangerously, no matter how good its latest earnings report looks. > //"Risk comes from not knowing what you're doing." - Warren Buffett// This quote is the essence of why we care about the Lorenz curve. It helps us see a risk that many others miss: the risk of concentration. ===== Why It Matters to a Value Investor ===== A value investor's job is to buy wonderful businesses at fair prices. The "wonderful" part is all about durability, resilience, and a strong competitive advantage, or what we call an [[economic_moat|economic moat]]. The Lorenz curve, when applied to a company's customer base, is a powerful moat-assessment tool. Here’s why it's so critical: * **It Uncovers Hidden Fragility:** A company might boast impressive revenue growth and juicy profit margins. But if you discover that 60% of that revenue comes from a single client, the entire investment thesis becomes fragile. What happens if that client goes bankrupt, finds a cheaper supplier, or gets acquired by a competitor? The company's revenue—and your investment—could be vaporized overnight. A bowed Lorenz curve is a red flag for a brittle business model. * **It Measures the Quality of an Economic Moat:** A truly wide moat is often built on a diversified and loyal customer base. Think of Coca-Cola or Procter & Gamble. Their revenue comes from billions of small, repeat purchases made by millions of people. No single customer holds them hostage. Their revenue Lorenz curve would be incredibly close to the Line of Perfect Equality. Conversely, a company serving only a handful of large industrial clients has a much narrower, more precarious moat. Their pricing power is limited, and their future is tied to the fortunes and decisions of others. * **It Informs Your [[Margin_of_Safety|Margin of Safety]]:** Value investing isn't just about finding good companies; it's about buying them with a buffer against bad luck or miscalculation. This is the [[margin_of_safety]]. When you identify a significant customer concentration risk (a saggy Lorenz curve), you must demand a much larger margin of safety. The risk of a major client loss must be compensated for by a much, much lower purchase price. The Lorenz curve helps you justify //why// you need that discount. * **It Distinguishes Between High- and Low-Quality Earnings:** Not all dollars of profit are created equal. A dollar earned from a thousand loyal subscribers is of far higher quality than a dollar earned from a one-off, high-risk project for a single client. By mentally plotting the Lorenz curve of a company's revenue sources, you get a quick, intuitive read on the [[quality_of_earnings|quality of its earnings]]. Stable, recurring, and diversified revenue is the bedrock of a long-term compounder. In essence, the Lorenz curve helps us obey a cardinal rule of intelligent investing: **focus on the downside first**. It forces us to ask, "What could go horribly wrong here?" and provides a clear framework for spotting one of the most common and devastating business risks. ===== How to Apply It in Practice ===== You don't need a PhD in statistics or a graphing calculator to use this concept. For an investor, the Lorenz curve is primarily a powerful mental model. Your goal is not to draw it perfectly but to gather the data to understand its general shape. === The Method === Here is a step-by-step guide to applying the Lorenz curve concept in your research: - **Step 1: Go to the Source.** The most reliable place to find this information for publicly traded U.S. companies is in their annual report, the [[form_10k|Form 10-K]]. This document is filed annually with the Securities and Exchange Commission (SEC) and is a treasure trove of information. - **Step 2: Know What to Look For.** Use the "Ctrl+F" search function in the 10-K document. Search for key phrases like: * `"Major Customers"` * `"Significant Customers"` * `"Concentration of Revenue"` * `"Concentration of Credit Risk"` - **Step 3: Analyze the Disclosure.** By law, companies must disclose any single customer that accounts for 10% or more of their total revenue. The disclosure will look something like this: > //"For the year ended December 31, 2023, sales to Customer A and Customer B represented approximately 25% and 15% of our total revenue, respectively. No other single customer accounted for more than 10% of our revenue."// - **Step 4: Mentally Sketch the Curve.** Armed with this data, you can now visualize the Lorenz curve. * In the example above, just two customers make up 40% of the revenue! This means the bottom 99.9% of customers make up the other 60%. * Your mental graph would show a curve that starts flat and then shoots up at the very end. It's a classic, high-risk bowed curve. * Conversely, if the 10-K states, //"No single customer represented 10% or more of our total revenue,"// you can picture a curve that hugs the Line of Perfect Equality much more closely. This indicates a healthier, more diversified revenue base. === Interpreting the Result === A "bowed" or "saggy" curve is a warning sign that requires deeper investigation. Ask yourself: * **Who is the customer?** Is it a stable blue-chip company like Apple, or a struggling startup? * **What is the relationship?** Is it a multi-year, legally-binding contract, or a series of short-term purchase orders? * **Is the concentration increasing or decreasing?** Check the 10-K filings from previous years. A company that is successfully diversifying away from its large clients is a positive sign. A company becoming //more// dependent is a major red flag. From a value investor's perspective, the ideal result is a Lorenz curve that is as close to the Line of Perfect Equality as possible. It signifies a resilient business that isn't beholden to the whims of a single powerful customer. ===== A Practical Example ===== Let's compare two hypothetical companies to see the Lorenz curve in action. Both companies are in the business of manufacturing electronic components and have identical revenue and profit figures. ^ **Metric** ^ **Steady Circuits Inc.** ^ **Titan Tech Solutions** ^ | Annual Revenue | $500 million | $500 million | | Net Profit | $75 million | $75 million | | P/E Ratio | 15x | 15x | | Major Customer Disclosure (from 10-K) | "No single customer accounts for more than 2% of total revenue." | "Sales to one customer, a major smartphone manufacturer, accounted for 68% of total revenue." | On the surface, these companies look identical. They have the same valuation. However, a quick look at their customer concentration tells a completely different story. * **Steady Circuits Inc.:** This company sells to hundreds, perhaps thousands, of different device makers. Its revenue stream is robust and diversified. Its Lorenz curve is very close to the 45-degree line of perfect equality. The loss of any one customer would be a minor inconvenience, not a catastrophe. This is a low-risk, high-quality business. * **Titan Tech Solutions:** This company is, for all intents and purposes, a satellite of its single, giant customer. Its fate is entirely tied to the success of that one smartphone brand and the health of their commercial relationship. Its Lorenz curve would be extremely bowed, sagging far below the line of equality. This business is walking on a tightrope. What if the smartphone company decides to design its own components in-house, or finds a cheaper supplier in another country? Titan Tech's revenue could collapse, and its stock price would follow. A value investor would immediately recognize that Titan Tech is vastly riskier than Steady Circuits. Despite having the same P/E ratio, Titan Tech would need to trade at a massive discount—a huge [[margin_of_safety]]—to even begin to be considered an attractive investment. The Lorenz curve framework allows us to see this risk with crystal clarity. ===== Advantages and Limitations ===== ==== Strengths ==== * **Highlights "Hidden" Risk:** It forces you to look past headline numbers (like revenue and earnings) and scrutinize the underlying quality and sustainability of a company's business model. * **Intuitive and Visual:** You don't need complex math to understand the concept. The image of a "saggy" curve is a powerful and easy-to-remember shorthand for concentration risk. * **Promotes Deeper Analysis:** It's a gateway concept. Once you identify customer concentration, it naturally leads you to ask more important questions about contracts, competitive landscape, and customer relationships, which is the heart of deep [[due_diligence]]. ==== Weaknesses & Common Pitfalls ==== * **Not a Standalone Tool:** High concentration isn't automatically a death sentence. A company with a 20-year, iron-clad contract with the U.S. government is in a much different position than a company with a one-year contract with a fickle fashion brand. Context is everything. * **Data Can Be Limited:** While U.S. companies have the 10% disclosure rule, international companies or private companies may not provide this level of detail, making the analysis difficult. * **Can Obscure Other Risks:** A company can have a perfectly "flat" Lorenz curve but still be at risk. For example, a company that sells to thousands of small hardware stores still faces existential risk if its entire industry is being disrupted by a giant like Home Depot. The curve doesn't capture industry-wide or technological disruption risk. ===== Related Concepts ===== * [[economic_moat]] * [[margin_of_safety]] * [[risk_management]] * [[quality_of_earnings]] * [[due_diligence]] * [[form_10k]] * [[diversification]]