To calculate the average annual return on an investment, you can use one of two formulas: the arithmetic average, which is the simple mean of each year’s percentage return, or the geometric average, better known as the compound annual growth rate (CAGR), which reflects how your money actually compounded from start to finish. The arithmetic version adds each year’s return and divides by the number of years. The CAGR version takes the ending value divided by the beginning value, raises the result to the power of one over the number of years, and subtracts one. Both use the same underlying data, but they answer slightly different questions, and for anything involving a multi-year holding period, CAGR is the number that matches your account balance.
What You Need Before You Calculate
For the arithmetic average, collect each year’s return as a percentage from your brokerage statements or fund fact sheets. Every period must cover the same length of time; mixing a six-month return with a full-year return will distort the result.
For CAGR, you need three numbers: the beginning value of the investment, the ending value, and the number of years in between. If dividends were reinvested, they should already be in the ending balance. If you took money out during the period, add those withdrawals back to the ending value so you’re measuring market performance rather than the effect of your spending. Subtract any deposits you made for the same reason, so new money doesn’t get counted as investment growth.
Arithmetic Average Return
Add each year’s return, then divide by the number of years.
Formula: Arithmetic Average Return = (Return₁ + Return₂ + … + Returnₙ) / n
Say you held a fund for five years and it returned +20%, −15%, +25%, +10%, and −5%. Adding them gives 35. Dividing by 5 gives 7%. That is your arithmetic average annual return.
The figure is quick to compute and gives you a rough sense of typical year-to-year behavior. Financial firms often quote it in marketing materials because it tends to be the highest average they can truthfully state. Its blind spot is that it ignores compounding and the order of returns, so it overstates what you actually earned. A 7% arithmetic average would only match reality if you earned exactly 7% every year with no variation.
Geometric Average Return (CAGR)
The geometric average shows the single steady rate that would have taken your starting balance to your ending balance. It accounts for compounding.
Formula: CAGR = (Ending Value / Beginning Value)^(1 / n) − 1
Using the same five-year returns above, start with $10,000 and track the dollars:
- Year 1 (+20%): $10,000 × 1.20 = $12,000
- Year 2 (−15%): $12,000 × 0.85 = $10,200
- Year 3 (+25%): $10,200 × 1.25 = $12,750
- Year 4 (+10%): $12,750 × 1.10 = $14,025
- Year 5 (−5%): $14,025 × 0.95 = $13,323.75
Now apply the formula: ($13,323.75 / $10,000)^(1/5) − 1 = 1.3324^0.2 − 1 ≈ 0.059, or about 5.9%. That is meaningfully lower than the 7% arithmetic average from the same returns, and it is the rate your money actually compounded at.
The formula still works if the holding period isn’t a clean number of years. For an investment held 3.5 years, use 3.5 in the denominator of the exponent: (Ending Value / Beginning Value)^(1/3.5) − 1.
Why the Two Numbers Differ
The gap between the arithmetic and geometric averages comes from volatility. Every time an investment drops and then recovers, it needs a larger percentage gain to get back to where it started. Lose 50% and you need a 100% gain just to break even. Because of that asymmetry, a volatile investment always has a geometric average below its arithmetic average, and the rougher the ride, the bigger the gap.
A useful approximation: the geometric return is roughly the arithmetic return minus half the variance of returns. If two funds have the same arithmetic average but one swings wildly while the other is steady, the steady fund leaves you with more money. This effect is sometimes called volatility drag.
Use the arithmetic average when you want to estimate what a single future year might look like, since each year is independent. Use CAGR when you want to know what an investment actually delivered over a multi-year stretch. For fund comparisons, retirement projections, or any performance evaluation, CAGR is the right tool.
When You Added or Withdrew Money
The basic CAGR formula assumes a lump sum left alone. Most real portfolios don’t work that way, and when cash moves in and out, two additional methods apply.
Time-Weighted Return
The time-weighted return removes the effect of your deposits and withdrawals. Break the overall period into sub-periods at each cash flow, calculate the return for each sub-period, and link them together: [(1 + HPR₁) × (1 + HPR₂) × … × (1 + HPRₙ)] − 1, where HPR is the holding period return for each sub-period.
This method answers how the underlying investment performed regardless of when you added or removed money. It is the standard for evaluating a fund manager’s skill, because the manager doesn’t control when clients deposit or withdraw.
Money-Weighted Return
The money-weighted return, also called the internal rate of return, factors in the timing and size of every cash flow. It gives more weight to periods when your balance was larger. If you added a large deposit right before a rally, your money-weighted return will exceed the time-weighted return. If you added it right before a downturn, the opposite happens.
This is the better measure for evaluating your own decisions and timing. Most brokerage platforms calculate it automatically, sometimes labeled “personal rate of return.”
If you made no additional contributions or withdrawals during the period, both methods produce the same result as a simple CAGR calculation. The distinction only matters when cash moved in or out.
Adjusting for Fees, Taxes, and Inflation
The raw return isn’t the whole picture. Three things reduce what you keep.
Management Fees
Every fund charges an expense ratio as an annual percentage of invested assets. Passively managed index funds typically charge around 0.05% to 0.15%, while actively managed funds commonly charge 0.40% to 0.65% or more. Subtract the expense ratio from your gross annual return to get the net figure. A fund returning 8% with a 0.60% expense ratio delivered roughly 7.4% net.
Taxes
Investment gains are taxed at different rates depending on holding period. For 2026, long-term capital gains on assets held longer than one year are taxed at 0%, 15%, or 20% depending on taxable income and filing status. Short-term gains are taxed as ordinary income at your marginal rate. To estimate an after-tax return, multiply the pre-tax return by (1 − your applicable tax rate). An 8% return taxed at 15% becomes roughly 6.8%. Tax-advantaged accounts like 401(k)s and IRAs defer or eliminate this drag.
Inflation
Inflation erodes the purchasing power of your gains. The Fisher equation gives the precise adjustment: Real Return = [(1 + Nominal Return) / (1 + Inflation Rate)] − 1. For quick math, subtract the inflation rate from the nominal return. An 8% nominal return during a year with 3% inflation gives roughly a 5% real return. Over long periods, the S&P 500 has returned about 10% annually in nominal terms and roughly 6% to 7% after inflation.
Comparing Your Number to a Benchmark
A return figure in isolation doesn’t tell you much. Earning 6% sounds fine until you learn the broad market returned 12% that year. The most common benchmark is the S&P 500, which has averaged roughly 10% per year in nominal terms over its long-term history.
When you compare your calculated return to a benchmark, make sure both numbers use the same method. Compare CAGR to CAGR, not an arithmetic average to a compound return. Confirm both figures are either gross or net of fees, and either nominal or inflation-adjusted. Mixing those will produce misleading comparisons. If your returns consistently trail an appropriate benchmark after fees, that is the signal a lower-cost index fund might have served you better, and running the calculation yourself is how you find out.