Calculate Average Yearly Return

Average Annual Return Formula:

\[ AAR = \left( \frac{\text{Ending Value}}{\text{Beginning Value}} \right)^{\frac{1}{\text{years}}} - 1 \]

AAR (decimal):

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1. What is Average Annual Return?

Average Annual Return (AAR) is the average amount of money earned by an investment each year over a given time period. It represents the geometric average return an investor earns over multiple years.

2. How Does the Calculator Work?

The calculator uses the AAR formula:

\[ AAR = \left( \frac{\text{Ending Value}}{\text{Beginning Value}} \right)^{\frac{1}{\text{years}}} - 1 \]

Where:

\( \text{Ending Value} \) — Final value of the investment
\( \text{Beginning Value} \) — Initial value of the investment
\( \text{years} \) — Number of years the investment was held

Explanation: This formula calculates the compound annual growth rate (CAGR) that would take the beginning value to the ending value over the specified number of years.

3. Importance of AAR Calculation

Details: AAR is crucial for comparing investment performance across different time periods and asset classes. It helps investors evaluate the effectiveness of their investment strategies and make informed decisions about portfolio allocation.

4. Using the Calculator

Tips: Enter the beginning value and ending value in the same currency units. The years must be a positive integer greater than zero. All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between AAR and CAGR?
A: AAR typically refers to the arithmetic mean of annual returns, while this calculator actually computes CAGR (Compound Annual Growth Rate), which is the geometric mean and more accurate for multi-year periods.

Q2: How do I convert AAR to percentage?
A: Multiply the decimal result by 100. For example, an AAR of 0.08 equals 8% annual return.

Q3: Does AAR account for volatility?
A: No, AAR/CAGR shows the smoothed annual return and doesn't reflect the year-to-year volatility or risk of the investment.

Q4: What is a good AAR?
A: This depends on the asset class and risk tolerance. Generally, 7-10% is considered good for stock investments over the long term, but this varies by market conditions.

Q5: Can AAR be negative?
A: Yes, if the ending value is less than the beginning value, AAR will be negative, indicating an overall loss on the investment.