Archimedes' Principle

• The Bottom Line: A great investment, like a solid object in water, must displace less cash (its price) than the weight of the future earnings it generates (its value).
• Key Takeaways:
• What it is: A powerful mental model that uses the ancient Greek principle of displacement to visualize the core relationship between the price you pay for an asset and the intrinsic value you receive.
• Why it matters: It masterfully simplifies the goal of investing by forcing you to focus on a business's long-term, cash-generating power (the “buoyant force”) rather than its volatile, short-term stock price. This is the essence of value_investing.
• How to use it: Before buying any stock, ask yourself: “Is the stream of future cash I expect to receive from this business 'heavy' enough to justify the pile of cash I must give up to own it today?”

Legend has it that over two thousand years ago, the Greek mathematician Archimedes was tasked with determining if a king's new crown was made of pure gold or if a deceitful goldsmith had mixed in cheaper silver. Puzzling over the problem, he stepped into his bathtub and noticed the water level rise. In a flash of insight, he realized that a submerged object displaces a volume of water equal to its own volume. He understood that a pure gold crown would be denser and displace less water than a larger, mixed-metal crown of the same weight. Overjoyed, he supposedly leaped from the tub and ran through the streets naked, shouting “Eureka!” (“I have found it!”). The physics principle he discovered states that the upward buoyant force exerted on a submerged object is equal to the weight of the fluid it displaces. If the buoyant force is greater than the object's weight, it floats. If it's less, it sinks. So, what does a naked Greek in a bathtub have to do with your investment portfolio? Everything. This principle provides one of the most elegant and powerful analogies in all of finance for the value investor. Let's translate it:

• The Bathtub: Your investment portfolio.
• The Water: Your cash, ready to be deployed.
• The Object (The Crown): The company or stock you are considering buying.
• The Displaced Water: The price you pay. When you buy a stock for $10,000, you are “displacing” that much cash from your portfolio.
• The Upward Buoyant Force: The value you receive. This is the “weight” of all the future cash flows the business will generate for you as an owner, discounted back to today's dollars.

For an investment to be successful—to “float”—the upward buoyant force of its future earnings (its value) must be greater than the cash it displaces (its price). The bigger the difference, the more buoyant the investment, and the higher it will float. This crucial difference is what value investors call the margin_of_safety.

“Price is what you pay. Value is what you get.” - Warren Buffett

Buffett's famous quote is the perfect summary of the Archimedes' Principle for investors. The speculator is obsessed with the splashing and the ripples on the surface of the water—the daily price fluctuations. The value investor is focused entirely on the object itself: its density, its composition, and the buoyant force it generates.

Adopting the Archimedes' Principle as a mental model fundamentally changes how you view the market. It's not just a clever analogy; it's a guiding philosophy that reinforces the core tenets of value investing.

• It Forces a Focus on Business Fundamentals: The stock market is a chaotic sea of flashing prices, news headlines, and expert predictions. This model encourages you to ignore that surface noise. The only things that truly matter are the two variables in our equation: the cash you're displacing (price) and the buoyant force you're receiving (value). The “value” is generated by the underlying business—its sales, profits, and competitive position—not by market sentiment.
• It Makes Intrinsic Value Tangible: The concept of “intrinsic value” can feel abstract. Thinking of it as a “buoyant force” makes it concrete. Your job as an analyst is to calculate the weight of that future stream of cash. Is this business a solid gold bar that will create a powerful upward force, or is it a hollow piece of plastic that just looks good on the surface? This calculation, often done through a Discounted Cash Flow (DCF) analysis, becomes the central task.
• It Beautifully Illustrates the Margin of Safety: Benjamin Graham's foundational concept of a margin of safety is built directly into this model.
  • If you pay a price equal to the value (displaced water = buoyant force), the investment just barely floats. There is no room for error. A slight miscalculation or a bit of bad luck, and it sinks.
  • If you pay a price higher than the value (displaced water > buoyant force), the investment is guaranteed to sink. You have overpaid.
  • If you pay a price significantly lower than the value (displaced water < buoyant force), the investment doesn't just float; it surges upwards. This gap is your protection against unforeseen problems, analytical errors, or just plain bad luck.
• It Inoculates Against Speculation: Speculators buy assets hoping someone else—a “greater fool”—will pay more for them later. They aren't concerned with the object's density or its buoyant force. They are merely betting on the direction of the water's ripples. A value investor using the Archimedes model simply doesn't care about the ripples. They buy a business for the cash it produces, confident that its buoyant force will eventually be recognized.

Turning this powerful metaphor into a practical investment process involves a clear, rational methodology.

You can think of it as a four-step inspection process for any potential investment “crown.”

1. Step 1: Measure the Displaced Water (Determine the Price).

This is the easiest step. The price is the total cost of the investment. For a stock, it's the company's market capitalization (share price multiplied by the number of shares outstanding). This is the amount of cash your portfolio must “displace” to acquire the entire business.

1. Step 2: Calculate the Buoyant Force (Estimate the Value).

This is the most challenging and most important step. It requires you to act as a business analyst, not a stock picker. You must estimate the total amount of “owner earnings” or free cash flow the business is likely to generate from now until judgment day. Because a dollar tomorrow is worth less than a dollar today, you must then discount those future cash flows back to their present value. The primary tool for this is a discounted_cash_flow (DCF) model. This requires a deep understanding of the business, its industry, and its competitive advantages, a concept known as your circle_of_competence.

1. Step 3: Compare the Force to the Displacement (Look for a Margin of Safety).

Now, you compare your two figures. Is your calculated intrinsic value (the buoyant force) significantly higher than the current market price (the displaced water)? A value investor typically looks for a substantial discount—for example, buying a business for $0.50 when you believe it's worth $1.00. This 50% discount is your margin of safety.

1. Step 4: Analyze the “Density” of the Object (Assess Business Quality).

Not all objects that float are created equal. A giant, hollow log might float, but a small, solid gold ingot is far more valuable. “Density” in our analogy represents business quality. A high-quality, “dense” business is one that has a durable economic moat, high returns on invested capital, a strong balance sheet, and honest, capable management. It generates a powerful buoyant force relative to its size. A low-quality business might be large and displace a lot of water, but its weak profitability means it generates very little upward force—it's “hollow.” Always prefer a dense, high-quality business at a fair price over a low-quality one at a bargain price.

Let's examine two hypothetical companies through the lens of Archimedes' Principle: “Steady Brew Coffee Co.” and “Flashy Fusion Inc.”

As you can see, mr_market is offering you both “crowns.” The shiny, exciting Flashy Fusion crown displaces a huge amount of your cash but offers little to no real buoyant force to support it. The “boring” Steady Brew crown, however, offers a powerful upward force of predictable earnings, more than enough to justify the cash you displace to acquire it. The value investor chooses Steady Brew every time.

• Powerful Simplification: It transforms the complex, and often intimidating, process of valuation into an intuitive physical principle that is easy to remember and apply.
• Encourages Discipline: The framework forces a disciplined comparison between price and value, which is the cornerstone of rational investing and the antidote to emotional decision-making.
• Inherent Risk Management: By focusing on the gap between the buoyant force and the displaced water, it automatically prioritizes the margin_of_safety, which is the investor's single best defense against risk.

• Value is an Estimate, Not a Fact: The greatest weakness is that while the price (displaced water) is precise and known, the value (buoyant force) is always an estimate about an uncertain future. The “Garbage In, Garbage Out” rule applies; a DCF model is only as good as the assumptions you feed into it.
• The Quality (Density) Problem: The analogy can sometimes break down when comparing business quality. A small, exceptionally profitable “dense” company can be a much better investment than a massive, marginally profitable “hollow” one. The metaphor must be paired with a rigorous analysis of business quality metrics like return on capital.
• Risk of False Precision: An investor might become so enamored with their “buoyant force” calculation that they forget it's a blurry estimate, not a number carved in stone. The principle is a mental model to guide thinking, not a substitute for deep, critical analysis and humility about the future.

• intrinsic_value
• margin_of_safety
• price_vs_value
• discounted_cash_flow
• mr_market
• circle_of_competence
• economic_moat