How do you calculate the arithmetic mean return?

Add the periodic returns and divide by the number of periods: RA = (R1 + R2 + … + Rn) ÷ n.

When should I use arithmetic instead of geometric mean?

Use the arithmetic mean to estimate the expected return for a single future period; use the geometric mean to describe past compound growth.

What is volatility drag?

The gap between the arithmetic and geometric means, roughly half the variance of returns (σ²/2).

Which standard deviation is shown?

The sample standard deviation, dividing by n − 1, as used by Excel's STDEV.S.

Arithmetic Mean Return Formula

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Arithmetic Mean Return Calculator

The arithmetic mean return is the simple average of a series of periodic returns: add them up and divide by how many there are. It is the best single estimate of what to expect in any one future period, which is why expected returns in portfolio theory and the CAPM are arithmetic.

Formula

R_A = R₁ + R₂ + ⋯ + R_nn R_G ≈ R_A − σ²2

Where

R_A: arithmetic mean (simple average) return per period
R_i: return in period i
n: number of periods
σ: standard deviation of the returns
R_G: geometric mean return

Calculator

Returns per period (%)

One return per period, in percent. Losses are negative.

Result and step-by-step solution

Arithmetic mean return

4.2%

Standard deviation 12.6965%; geometric (compound) mean 3.5716%.

Add the returns
10% − 5% + 20% + 8% − 12% = 21%
Divide by n = 5
R_A = 4.2%
Spread of the returns (sample standard deviation)
σ = 12.6965%
Volatility drag
R_A − σ²/2 = 4.2% − 0.806% ≈ 3.394% (the exact geometric mean is 3.5716%)

How to use the formula

It is not a good description of what an investor actually earned over several periods, because returns compound. The calculator therefore also reports the sample standard deviation of the returns and the geometric mean, and shows the well-known approximation R_G ≈ R_A − σ²/2. The σ²/2 term is called volatility drag: the more returns swing around, the more the compound result falls short of the simple average.

For returns of 10%, −5%, 20%, 8% and −12%, the arithmetic mean is 4.20% and the standard deviation 12.70%. The drag estimate of the geometric mean is 3.39%, close to the exact value of 3.57%. The standard deviation printed here is the volatility input for the Sharpe ratio. For the compound figure on its own, see the geometric mean return.

Frequently asked questions

How do you calculate the arithmetic mean return?: Add the periodic returns and divide by the number of periods: R_A = (R₁ + R₂ + … + R_n) ÷ n.
When should I use arithmetic instead of geometric mean?: Use the arithmetic mean to estimate the expected return for a single future period; use the geometric mean to describe past compound growth.
What is volatility drag?: The gap between the arithmetic and geometric means, roughly half the variance of returns (σ²/2).
Which standard deviation is shown?: The sample standard deviation, dividing by n − 1, as used by Excel’s STDEV.S.

Last reviewed: September 26, 2026. Calculations run in your browser and were checked against numpy-financial, SciPy and published spreadsheet examples.