Average Annual Return Calculation

Average Annual Return Formula:

\[ AAR = \left( \left( \frac{End}{Start} \right)^{\frac{1}{n}} - 1 \right) \times 100 \]

Average Annual Return (AAR):

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1. What is Average Annual Return?

Average Annual Return (AAR) is the geometric mean amount of money earned by an investment each year over a given time period. It shows the average rate of return per year over multiple years, accounting for compounding effects.

2. How Does the Calculator Work?

The calculator uses the AAR formula:

\[ AAR = \left( \left( \frac{End}{Start} \right)^{\frac{1}{n}} - 1 \right) \times 100 \]

Where:

$ End $ — Ending value of investment ($)
$ Start $ — Starting value of investment ($)
$ n $ — Number of years

Explanation: This formula calculates the geometric mean return, which accounts for compounding and provides a more accurate representation of investment performance than simple average returns.

3. Importance of AAR Calculation

Details: AAR is crucial for comparing investment performance over different time periods, evaluating portfolio returns, and making informed investment decisions. It helps investors understand the compounded growth rate of their investments.

4. Using the Calculator

Tips: Enter the starting value and ending value in dollars, and the number of years. All values must be positive (start value > 0, end value > 0, years ≥ 1).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between AAR and CAGR?
A: AAR (Average Annual Return) and CAGR (Compound Annual Growth Rate) are essentially the same concept - both represent the geometric mean annual return that smooths out investment returns over time.

Q2: Why use geometric mean instead of arithmetic mean?
A: Geometric mean accounts for compounding effects and volatility, providing a more accurate representation of actual investment performance over multiple periods.

Q3: What is a good AAR?
A: A good AAR depends on the asset class and risk level. Generally, 7-10% is considered good for stock investments, while 2-4% might be typical for bonds over the long term.

Q4: Does AAR account for inflation?
A: No, AAR typically shows nominal returns. To get real returns, you would need to adjust for inflation separately.

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