Period Returns

Enter the return for each period. Add or remove periods as needed.

Ryan O'Connell, CFA
Calculator by Ryan O'Connell, CFA

Historical Context

  • S&P 500 (1926-2023): ~10.5% geometric mean
  • US Bonds (1926-2023): ~5.5% geometric mean
  • Inflation (1926-2023): ~3.0% geometric mean
  • Real stock returns: ~7.5% after inflation

Geometric Mean Return

Geometric Mean (Compounded Average) +6.82% Moderate

Reasonable compounded return - in line with market expectations

Arithmetic Mean +7.00%
Cumulative Return +30.18%
Volatility Drag 0.18%
Calculated over 4 periods

Formula Breakdown

G = [(1+R1)(1+R2)...(1+Rn)]1/n - 1

Understanding the Results

Geometric vs Arithmetic

The geometric mean is your true compounded return. The arithmetic mean overstates performance when returns vary. The difference is the "volatility drag."

Volatility Drag

Higher volatility creates a larger gap between arithmetic and geometric mean. This is why reducing portfolio risk can improve long-term wealth.

Geometric Mean Return Interpretation

Return Rating Interpretation
> 15% Excellent Outstanding compound growth
10% - 15% Good Above market performance
5% - 10% Moderate Market-level returns
0% - 5% Low Below market average
< 0% Negative Capital erosion

Understanding Geometric Mean Return

What is Geometric Mean Return?

The geometric mean return is the true average rate at which an investment grows over multiple periods. Unlike the simple arithmetic average, it accounts for the compounding effect of returns.

If you invest $100 and earn +50% in year one (ending at $150) then lose -50% in year two (ending at $75), your arithmetic average return is 0%. But you've actually lost money! The geometric mean correctly shows -13.4%, reflecting your true compounded result.

Key Insight: The geometric mean is always less than or equal to the arithmetic mean. They're only equal when all returns are identical (zero volatility).

The Volatility Drag Effect

Volatility drag is the reduction in compound returns caused by fluctuating returns. It's approximately equal to half the variance of returns:

Volatility Drag ≈ σ²/2

This means a portfolio with 20% volatility suffers about 2% annual drag compared to a perfectly stable portfolio with the same average return. This is why risk management matters for long-term wealth accumulation.

When to Use Geometric Mean

  • Performance evaluation: Always use geometric mean when evaluating historical investment performance
  • Comparing investments: Especially important when comparing investments with different volatilities
  • Long-term projections: The geometric mean provides realistic expectations for compound growth
  • Fund reporting: Mutual funds and ETFs report annualized returns using geometric mean
Important: A return of -100% (total loss) makes the geometric mean undefined because you cannot recover from losing everything. Returns worse than -100% (possible with leverage) are similarly problematic.

Practical Example

Consider two investment options over 4 years:

  • Investment A: Returns of +10%, +10%, +10%, +10%
    Arithmetic Mean: 10% | Geometric Mean: 10% (no volatility drag)
  • Investment B: Returns of +30%, -10%, +30%, -10%
    Arithmetic Mean: 10% | Geometric Mean: 8.17% (significant volatility drag)

Both have the same arithmetic mean, but Investment A actually delivers better compound returns because of lower volatility.

Frequently Asked Questions

The geometric mean return is the true compounded average return of an investment over multiple periods. Unlike the arithmetic mean, it accounts for compounding and gives the actual annualized rate at which your investment grew. It's calculated by multiplying all the (1 + return) values together, taking the nth root, and subtracting 1.

The arithmetic mean simply adds returns and divides by the number of periods, while the geometric mean multiplies (1 + return) values and takes the nth root. The geometric mean is always less than or equal to the arithmetic mean and better represents actual investment performance because it accounts for compounding.

The geometric mean is lower due to volatility drag. When returns fluctuate, the compounding effect reduces the effective average return. This happens because losses have a larger impact than equal-sized gains - a 50% loss requires a 100% gain to break even. The more volatile the returns, the greater the gap between arithmetic and geometric mean.

Use geometric mean when evaluating investment performance over time, comparing investments with different volatilities, or calculating true annualized returns. It's the standard for reporting mutual fund and portfolio performance. The arithmetic mean is only appropriate for single-period expected returns, not multi-period performance.

Higher volatility increases the gap between arithmetic and geometric mean. This is called volatility drag. Two investments with the same arithmetic mean but different volatilities will have different geometric means - the less volatile one will be higher. The drag is approximately equal to half the variance (σ²/2).

Volatility drag is the reduction in compound returns caused by fluctuating returns. It equals approximately half the variance of returns (variance drag formula). This explains why reducing portfolio volatility can improve long-term wealth accumulation, even if expected single-period returns stay the same.
Disclaimer

This calculator is for educational purposes only and does not constitute financial advice. Past returns do not guarantee future results. Always consult with a qualified financial advisor before making investment decisions.

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