CAGR & XIRR Return Calculator (2025/2026)

1. Compound Annual Growth Rate (CAGR) Formula:

where $V_{\text{initial}}$ is beginning investment capital, $V_{\text{final}}$ is terminal portfolio valuation, and $t = \frac{\text{Days}}{365.25}$ is holding duration in years. CAGR smooths out interim volatility to provide the constant annual compounding rate.

2. Extended Internal Rate of Return (XIRR) Formulation:

For multiple irregular investments and redemptions $(C_0, d_0), (C_1, d_1), \dots, (C_n, d_n)$, XIRR is the exact discount rate $r$ that equates the net present value (NPV) to zero:

Solved numerically via the Newton-Raphson algorithm: $r_{k+1} = r_k - \frac{f(r_k)}{f'(r_k)}$ until convergence within $10^{-6}$ error tolerance. XIRR is the mandatory standard for mutual fund SIPs and irregular stock portfolios.

3. Volatility Drag & Arithmetic vs Geometric Mean:

Due to mathematical compounding asymmetry, geometric CAGR is always strictly less than the simple arithmetic average return. The relationship is governed by the volatility drag approximation: $\text{CAGR} \approx \bar{R} - \frac{\sigma^2}{2}$, where $\sigma^2$ is portfolio return variance. Portfolios with lower volatility achieve superior terminal wealth compounding over long horizons.

4. Inflation-Adjusted Real CAGR:

where $\pi$ represents average annual inflation. If an equity portfolio generates 12% nominal CAGR in an economy with 6% CPI inflation, the real purchasing power expansion rate is 5.66% per annum.

5. Point-to-Point CAGR vs Rolling Returns Methodology:

Point-to-point CAGR is highly sensitive to the arbitrary selection of start and end dates (end-point bias). A market crash immediately prior to the valuation date can artificially depress multi-year CAGR, while a speculative rally can exaggerate long-term performance. Professional asset managers and SEBI mutual fund performance disclosures utilize rolling returns (e.g., 3-year or 5-year daily rolling CAGR) to evaluate true managerial alpha and eliminate cyclic timing distortions.