annualized_return [CapiPedia]

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======Annualized Return======
Annualized Return (also known as the '[[Compound Annual Growth Rate]]' or '[[CAGR]]') is the geometric average rate of return an [[asset]] generates per year over a specific period longer than one year. Think of it as the steady, smooth rate at which your money would have had to grow each year to reach its final value, assuming all profits were reinvested. This is a cornerstone concept for any serious investor, especially in [[Value Investing]], because it provides a much more accurate picture of performance than a simple average. For instance, a stock that jumps 50% in year one and then drops 50% in year two has a simple average return of 0%. However, an initial investment of $100 would be worth only $75 at the end, a significant loss! The annualized return correctly captures this reality, showing a negative return and demonstrating the powerful, and sometimes deceptive, effects of [[compounding]]. It's the true measure of your investment's journey, not just a snapshot of its ups and downs.
===== Why Is It Important? =====
The annualized return is your universal translator for investment performance. It allows you to make fair, apples-to-apples comparisons between different investments held for different lengths of time.
Imagine you're comparing two funds. Fund A returned 40% over three years, while Fund B returned 50% over five years. Which did better? At a glance, it's tough to say. The annualized return cuts through the confusion. It smooths out an investment's [[volatility]] and presents a single, comparable number that represents its long-term growth rate. It’s like calculating the average speed of a car on a long road trip; you don't care about the moments you were stuck in traffic or speeding on the open highway, you just want to know the average pace that got you from your starting point to your destination.
===== The Math Behind the Magic (Don't Worry, It's Easy!) =====
While it sounds complex, the formula is quite straightforward. It measures the growth from a beginning value to an ending value and then standardizes it to a one-year period.
The formula is: **Annualized Return = ((Ending Value / Beginning Value) ^ (1 / Number of Years)) - 1**
Let's walk through an example. Say you invested $10,000 in a stock. Five years later, you sold it for $16,105.
  - **1. Divide the Ending Value by the Beginning Value:**
    * $16,105 / $10,000 = 1.6105
  - **2. Calculate the Exponent:**
    * The investment period is 5 years, so the exponent is 1 / 5, which is 0.2.
  - **3. Apply the Exponent:**
    * 1.6105 ^ 0.2 = 1.10 (You can use a calculator for this part!)
  - **4. Subtract 1:**
    * 1.10 - 1 = 0.10
  - **5. Convert to a Percentage:**
    * 0.10 x 100 = 10%
Your annualized return was 10%. This means your investment performed //as if// it had grown by exactly 10% every single year for five years.
===== Annualized Return vs. Other Metrics =====
It's crucial not to confuse annualized return with other, less accurate performance measures.
==== Average Annual Return (AAR) ====
The [[Average Annual Return (AAR)]] is a simple arithmetic average of yearly returns. It can be dangerously misleading because it ignores the effect of compounding.
Let's revisit our famous example: an investment that gains 50% in Year 1 ($100 becomes $150) and loses 50% in Year 2 ($150 becomes $75).
  * **AAR:** (+50% + (-50%)) / 2 = 0% return. This suggests you broke even.
  * **Annualized Return:** (($75 / $100) ^ (1/2)) - 1 = -13.4% return. This reveals the truth: you actually lost money!
Always trust the annualized return. It accounts for the changing base value of your investment each year.
==== Cumulative Return ====
[[Cumulative Return]] is simply the total profit or loss over the entire investment period, expressed as a percentage. For our 5-year, $10,000 investment that grew to $16,105, the cumulative return is 61.05%.
While useful, this figure lacks context. A 61% return is fantastic over five years (10% annualized) but mediocre over 20 years (2.4% annualized). The cumulative return tells you //what// happened, but the annualized return tells you //how fast// it happened, which is essential for understanding the [[Time Value of Money]].
===== A Value Investor's Perspective =====
For a value investor, the annualized return is more than just a metric; it's a tool for discipline. Legends like [[Benjamin Graham]] and [[Warren Buffett]] built their fortunes not on wild, speculative bets, but on achieving consistent, respectable annualized returns over very long periods.
Value investors use annualized return to:
  * **Set expectations:** It helps in evaluating whether a potential investment can realistically meet a personal performance target, or [[hurdle rate]].
  * **Compare with a [[benchmark]]:** Is your stock pick outperforming the [[S&P 500]] on an annualized basis? If not, you might be better off just buying an index fund.
  * **Maintain a long-term focus:** By focusing on the smooth, annualized growth rate, you're less likely to be swayed by short-term market noise and panic during downturns. It helps you focus on what truly matters: the long-term compounding power of your well-chosen investments.