📈 Average Return Calculator
Average Return Calculator — CAGR & Returns
Calculate your investment's CAGR, cumulative return, arithmetic mean, geometric mean, and volatility. Enter start/end values or year-by-year annual returns.
📊 CAGR Calculator
📐 Arithmetic vs Geometric
📉 Volatility & Std Dev
📈 Growth of $10,000
Average Return Calculator
CAGR · Arithmetic & Geometric Mean · Volatility
📊 Simple Return (Start/End)
📅 Annual Returns
Investment Values
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Enter Annual Returns
Enter the annual return for each year as a percentage (e.g., 12 for 12%, -5 for -5%). Green = positive, red = negative.
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CAGR
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Arithmetic Mean
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Geometric Mean
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Volatility (σ)
⚖️ Arithmetic vs Geometric Mean — Why It Matters
Arithmetic Mean (Simple Average)
FormulaSum of returns ÷ n
Result0%
$10K grows to$0
Geometric Mean (Compound Average)
Formula(∏(1+r))^(1/n) − 1
Result0%
$10K grows to$0
The geometric mean always equals or is less than the arithmetic mean. The difference increases with higher volatility. Use the geometric mean (CAGR) to measure actual compounded investment performance.
📈 Growth of $10,000
📋 Year-by-Year Breakdown
| Period | Annual Return | Opening Value | Gain/Loss | Closing Value |
|---|
CAGR vs Arithmetic vs Geometric Mean
These three measures of return tell different stories about the same investment. Knowing which to use is essential for accurate performance evaluation:
| Measure | Formula | Best Used For | Limitation |
|---|---|---|---|
| CAGR | (End/Start)^(1/years) − 1 | Overall multi-year performance | Masks year-to-year volatility |
| Arithmetic Mean | Sum of returns ÷ n | Expected return in one future year | Overstates actual compound growth |
| Geometric Mean | (∏(1+rᵢ))^(1/n) − 1 | Actual compound growth rate | More complex to calculate |
| Total Return | (End − Start) / Start | Simple gain over the period | Not annualized |
Why Geometric Mean is Always Less Than Arithmetic Mean
The classic example: an investment that gains 50% in year 1 and loses 50% in year 2. Arithmetic mean = (50% − 50%) / 2 = 0%. But geometric mean = √(1.5 × 0.5) − 1 = √0.75 − 1 = −13.4%. A $1,000 investment → $1,500 → $750. You've actually lost money, not broken even.
This gap — called the variance drag — gets larger with higher volatility. It's why high-volatility investments need higher average returns just to maintain the same geometric (compounded) return as low-volatility alternatives.
Historical Average Returns by Asset Class
| Asset Class | Arithmetic Mean | Geometric Mean (CAGR) | Volatility (σ) |
|---|---|---|---|
| US Stocks (S&P 500) | ~11.5% | ~10.0% | ~15–20% |
| US Bonds (10-yr Treasury) | ~5.0% | ~4.8% | ~8% |
| 60/40 Portfolio | ~8.5% | ~7.9% | ~10–12% |
| International Stocks | ~9.5% | ~8.0% | ~17–20% |
| Real Estate (REITs) | ~10% | ~8.8% | ~14–18% |
| Cash (T-Bills) | ~3.3% | ~3.3% | ~3% |
Frequently Asked Questions
CAGR (Compound Annual Growth Rate) is the annualized rate at which an investment grows from its starting value to its ending value, assuming it grew at a smooth rate each year. Formula: CAGR = (Ending Value / Starting Value)^(1/Years) − 1. For example, $10,000 growing to $18,500 in 7 years = (18,500/10,000)^(1/7) − 1 = 9.19% CAGR. It's the most useful single metric for comparing investment performance.
Arithmetic mean is a simple average: add all annual returns and divide by n. Geometric mean accounts for compounding: multiply (1+r) for each year, take the nth root, subtract 1. Example: returns of +100% and -50% give arithmetic mean 25% but geometric mean 0% (because $100 → $200 → $100). The geometric mean equals actual realized compound growth. The arithmetic mean is useful for estimating expected returns in a single future year.
Volatility is the standard deviation of annual returns — it measures how much returns vary around the average. Higher volatility means more unpredictable year-to-year returns. The S&P 500 has annual volatility of about 15-20%, meaning returns typically fall within ±15-20% of the average in any given year (approximately 68% of the time). Higher volatility also reduces the geometric mean relative to the arithmetic mean (variance drag).
A good CAGR depends on the investment type and risk level. Benchmarks: US stocks (S&P 500) historically CAGR ~10%; bonds ~4-5%; real estate ~8-9%; savings accounts ~0.5-5%. A 7% real (inflation-adjusted) CAGR is a widely used long-term planning benchmark for diversified stock portfolios. Compare your investment's CAGR to the relevant benchmark (not to unrelated investments with different risk profiles).
Variance drag is the gap between arithmetic and geometric mean returns, caused by volatility. Formula: Geometric Mean ≈ Arithmetic Mean − (Variance/2). An investment with 12% arithmetic mean and 20% annual volatility has an effective geometric mean of about 12% − (0.04/2) = 10%. Higher volatility investments need higher arithmetic returns to deliver the same compounded result as lower-volatility alternatives. This is why risk management matters as much as raw return maximization.