Average Return Calculator Calculate Simple Average, CAGR, or Geometric Mean Return to evaluate investment performance ove...
Average Return Calculator
Calculate Simple Average, CAGR, or Geometric Mean Return to evaluate investment performance over time.
Average return is a measure of investment performance over time. It helps investors compare assets, assess risk-adjusted performance, and project future growth. However, not all averages are equal:
- Simple Average (Arithmetic Mean) = (R₁ + R₂ + ... + Rₙ) / n
Good for estimating expected return in a single future period, but ignores compounding. - Compound Annual Growth Rate (CAGR) = (FV / PV)^(1/n) − 1
Represents the steady annual return needed to grow an initial investment to its final value. Accounts for compounding — ideal for comparing investments over time. - Geometric Mean = [(1+R₁) × (1+R₂) × ... × (1+Rₙ)]^(1/n) − 1
The mathematically correct way to average multi-period returns. Always ≤ simple average (by the AM-GM inequality), especially when volatility is high.
Example: Returns of +50%, −50% over 2 years:
• Simple average = 0%
• Geometric mean = √(1.5 × 0.5) − 1 = −13.4%
• Real outcome: $10,000 → $15,000 → $7,500 ⇒ **−25% total**, or −13.4% CAGR.
**Simple average overstates performance when returns are volatile.** Always prefer geometric/CAGR for long-term analysis.
- Performance Benchmarking — Compare your portfolio’s return to benchmarks like the S&P 500 (historical avg ~10% CAGR).
- Retirement Planning — Forecast 401(k) growth using realistic return assumptions (e.g., 6–7% net of fees for a balanced portfolio).
- Risk Assessment — High volatility (standard deviation) lowers geometric return, even if simple average is high.
- Fee Impact Analysis — A 1% annual fee reduces CAGR by ~1%, which compounds dramatically over decades (e.g., 7% → 6% CAGR turns $100K into $574K vs. $761K over 30 years).
Historical Averages (U.S. Markets, 1926–2023, Source: Morningstar):
- Large-Cap Stocks (S&P 500): ~10.0% CAGR
- Small-Cap Stocks: ~12.0% CAGR
- Long-Term Gov’t Bonds: ~5.5% CAGR
- Inflation: ~3.0% CAGR
→ **Real (inflation-adjusted) stock return: ~7% CAGR** — the number most retirement planners use for projections.
1. Simple Average
Use when you have a list of annual returns and want a quick estimate. Caution: does not reflect actual compounded growth.
2. CAGR (Recommended for most cases)
Best for: - Comparing investments with different time horizons - Estimating growth for retirement projections - Evaluating mutual funds or ETFs over 3+ years Enter initial/final value and years — the calculator does the rest.
3. Geometric Mean
Use when you have year-by-year returns and want the true compounded average. Essential for academic or precise financial analysis.
Pro Tip: After calculating, look at **Volatility** (standard deviation). If it’s high, the simple average is misleading — trust the geometric/CAGR instead.
- “Average return = what I’ll earn next year” — No. Markets are random; past performance ≠ future results.
- “10% average = double in 7 years” — Only if it’s *CAGR*. Simple average of +20%, −10% gives 5% simple mean but only ~3.9% CAGR.
- “Funds advertise simple average returns” — Some do (misleadingly). SEC requires mutual funds to report annualized (geometric) returns.
- “More data = more accurate” — Not necessarily. A 10-year bull market skews upward. Use rolling averages or long-term (30+ year) data when possible.
→ Always ask: “Is this arithmetic or geometric?” before drawing conclusions.