Average Return Calculator Calculate arithmetic vs. geometric (CAGR) returns, model money-weighted performance (IRR), and ...
Average Return Calculator
Calculate arithmetic vs. geometric (CAGR) returns, model money-weighted performance (IRR), and adjust for inflation — with visual analytics and benchmarks.
Arithmetic Average** = Sum of annual returns ÷ number of years
→ Useful for estimating *expected* next-year return, but overstates multi-year growth.
Geometric Average (CAGR)** = $$\left( \frac{\text{Ending}}{\text{Beginning}} \right)^{\frac{1}{n}} - 1$$
→ Reflects *actual* compounded growth. Always ≤ arithmetic (unless all returns equal).
Money-Weighted (IRR)** = Discount rate where NPV of cash flows = 0
→ Best for accounts with deposits/withdrawals (e.g., 401(k), brokerage).
Example** (3 years: +20%, −10%, +15%): • Arithmetic = (20 − 10 + 15)/3 = **8.33%** • Geometric = $(1.2 × 0.9 × 1.15)^{1/3} - 1$ = **7.43%** • → Volatility drag = 0.90%
⚠️ Avoid these errors:
- Using arithmetic for multi-year performance** — inflates results (e.g., 10% avg ≠ 10% CAGR)
- Ignoring inflation** — 6% nominal return = 2.6% real if inflation = 3.4%
- Cherry-picking timeframes** — “S&P up 20% last year” (but down 15% the year before)
- Not adjusting for cash flows** — CAGR fails if you add $10K mid-investment
✅ Pro Tips**:
- Report **CAGR + standard deviation** for full picture
- Use **XIRR in Excel/Google Sheets** for irregular cash flows
- Compare to **benchmarks** (S&P 500: 9.8% nominal long-term)
| Asset Class | Nominal | Real (3% Infl.) | Std Dev |
|---|---|---|---|
| S&P 500 (Long-Term) | 9.8% | 6.8% | 15% |
| 10-Yr Treasury | 4.2% | 1.2% | 8% |
| Aggregate Bonds | 4.5% | 1.5% | 6% |
| 60/40 Portfolio | 7.5% | 4.5% | 10% |
📉 Volatility Drag Formula**:
$$\text{CAGR} \approx \text{Arithmetic} - \frac{\sigma^2}{2}$$
→ 15% std dev = 1.125% annual drag → 10% std dev = 0.5% drag
➡️ Simple Average
Enter yearly returns (comma-separated) → see arithmetic vs. geometric.
➡️ CAGR
“$10K → $18K in 7 years” → what’s the annualized return?
➡️ Money-Weighted (IRR)
“I put in $5K, $100/mo for 10 yrs, now have $21K” → true annual return.
You’ll get:
- Arithmetic & geometric (CAGR) returns
- Real (inflation-adjusted) return
- Volatility drag estimate
- SVG return timeline
Note: IRR uses Newton-Raphson for accuracy. Inflation adjustment uses Fisher equation: $(1 + r_{\text{nom}}) / (1 + \pi) - 1$.