Average Return Calculator Using Percentages

Geometric Average Return Formula:

\[ \text{Avg Return} = \left( \prod_{i=1}^{n} (1 + \text{Return}_i) \right)^{\frac{1}{n}} - 1 \]

Geometric Average Return:

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1. What is Geometric Average Return?

The geometric average return (also known as the compound average return) calculates the average rate of return per period for investments that compound over multiple periods. It accounts for the volatility and compounding effect of returns.

2. How Does the Calculator Work?

The calculator uses the geometric average return formula:

\[ \text{Avg Return} = \left( \prod_{i=1}^{n} (1 + \text{Return}_i) \right)^{\frac{1}{n}} - 1 \]

Where:

\( \text{Return}_i \) — Return for period i (in decimal form)
\( n \) — Number of periods
\( \prod \) — Product of all terms

Explanation: The formula multiplies together all the (1 + return) terms, takes the nth root, and subtracts 1 to get the average return per period.

3. Importance of Geometric Average

Details: The geometric mean gives the most accurate measurement of portfolio performance when returns are volatile and compound over time. It's always less than or equal to the arithmetic average return.

4. Using the Calculator

Tips: Enter percentage returns separated by commas (e.g., "5, -3, 10, 2"). The calculator will convert these to decimals, compute the product of (1 + return) terms, take the nth root, and convert back to percentage.

5. Frequently Asked Questions (FAQ)

Q1: Why use geometric average instead of arithmetic average?
A: Geometric average accounts for compounding and volatility drag, giving the true annualized return. Arithmetic average overestimates performance.

Q2: When should I use geometric average return?
A: Use for compounded returns over multiple periods, especially when analyzing investment performance or comparing different investments.

Q3: What's the difference between CAGR and geometric average?
A: They are essentially the same concept - both measure compound growth rates. CAGR typically refers to multi-year periods.

Q4: Can geometric average be negative?
A: Yes, if the overall product of returns is negative. This would mean the investment lost value over the period.

Q5: How does volatility affect geometric average?
A: Higher volatility decreases geometric average return compared to arithmetic average, due to the compounding of losses.