======Compound Annual Growth Rate (CAGR)======
Compound Annual Growth Rate (CAGR) is a financial metric that provides a smoothed, annualized rate of return for an investment over a specific time period. Think of it as the average speed on a long road trip. You might have sped up, slowed down, and even stopped for coffee, but your average speed gives you a single, understandable number for the entire journey. Similarly, CAGR takes the starting and ending value of your investment and calculates the hypothetical, steady growth rate it would have needed to achieve each year to get from point A to point B. It elegantly cuts through the noise of market `[[Volatility]]` and provides a clear, comparable figure that is far more insightful than a simple arithmetic average. For long-term investors, this is a crucial tool for understanding the true performance of an asset, as it incorporates the power of `[[Compound Interest]]`.
===== The Magic of Smoothing: Why CAGR? =====
The beauty of CAGR lies in its honesty. A simple average of annual returns can be dangerously misleading.
Imagine you invest €100 in a hot tech stock.
  * **Year 1:** The stock soars by 50%! Your investment is now worth €150.
  * **Year 2:** The market turns, and the stock crashes by 50%. Your investment is now worth €75.
If you calculate the simple average of your annual returns, you get (+50% - 50%) / 2 = 0%. It looks like you broke even. But did you? You started with €100 and ended with €75. You actually lost 25% of your capital!
This is where CAGR tells the true story. It shows that your investment's compound annual growth rate was -13.4%. It’s a sobering figure, but it’s the //real// figure. For a value investor focused on the long-term preservation and growth of capital, this kind of honest feedback is priceless.
===== How to Calculate CAGR (Without the Headache) =====
While the name sounds complex, the concept is straightforward. You only need three pieces of information: the investment's beginning value, its ending value, and the number of years in between.
==== The Formula ====
The formula looks like this:
**CAGR = (Ending Value / Beginning Value)^(1 / Number of Years) - 1**
Let's break that down:
  * **Ending Value:** What the investment is worth at the end of the period.
  * **Beginning Value:** What the investment was worth at the start.
  * **Number of Years:** The duration of the investment.
==== A Practical Example ====
Let's say you bought shares in a solid, dividend-paying company for €10,000. Five years later, your holding is valued at €15,000.
  - Beginning Value = €10,000
  - Ending Value = €15,000
  - Number of Years = 5
Plugging these into the formula:
**CAGR = (€15,000 / €10,000)^(1 / 5) - 1**
**CAGR = (1.5)^(0.2) - 1**
**CAGR = 1.08447 - 1 = 0.08447**
To express this as a percentage, you multiply by 100. So, your CAGR is **8.45%**. This means your investment performed //as if// it had grown by a steady 8.45% every single year for five years.
===== CAGR in the Wild: Uses and Limitations =====
CAGR is a versatile tool, but like any tool, you need to know when and how to use it.
==== How Value Investors Use CAGR ====
Value investors love CAGR because it helps them make objective comparisons and cut through market hype.
  * **Comparing Investments:** Is Fund A with its 12% CAGR over 10 years a better choice than Fund B with its 15% CAGR over 5 years? CAGR provides a standardized yardstick to compare the performance of different stocks, funds, and assets over similar timeframes.
  * **Analyzing a Business:** You can use CAGR to measure a company's historical growth in key metrics like revenue, profit, or `[[Earnings Per Share (EPS)]]`. Consistent, strong EPS growth is often a hallmark of a high-quality business.
  * **Performance Review:** You can use CAGR to see if your own portfolio is meeting your personal `[[Hurdle Rate]]` or outperforming a `[[Benchmark]]` index like the `[[S&P 500]]`.
==== The Fine Print: What CAGR Doesn't Tell You ====
CAGR is a summary, and summaries always leave details out. Be aware of its limitations.
  * **It Hides Volatility:** An investment with a smooth 8% CAGR is far less stressful than a rollercoaster investment that also averages 8% after wild swings. CAGR won't show you the journey's bumps, which is a key component of `[[Risk]]`.
  * **It's a Historical Measure:** This is the big one. CAGR tells you about the past. It offers no guarantee of future performance. A company that grew at 20% per year for the last decade may not do so for the next.
  * **It Assumes a Closed System:** The basic formula works perfectly for a single lump-sum investment. It doesn't account for additional deposits or withdrawals. For portfolios with ongoing cash flows, a metric like `[[Internal Rate of Return (IRR)]]` might be more appropriate.