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Performance & Return Analytics

CAGR & Multi-Cashflow XIRR Calculator

Evaluate annualized geometric performance across point-to-point holdings and irregular multiple cashflow deposit schedules.

Point-to-Point Investment Parameters

Initial capital, terminal portfolio valuation, and elapsed tenure

$
$
Yrs

Multi-Cashflow Schedule (XIRR Simulation)

Irregular deposit and withdrawal cashflows resolved via Newton-Raphson

Transaction DateCashflow EventCash Amount
2019-01-01Initial Deposit-$100,000
2021-06-01Follow-on Injection-$30,000
2023-01-01Interim Distribution+$20,000
2026-01-01Current Portfolio NAV+$320,000

Compound Annual Growth (CAGR)

18.08% / yr

Point-to-point over 7 years

Extended IRR (XIRR)

16.48% / yr

Money-weighted cashflow yield

Total Absolute Net Profit

+$220,000

+220% absolute return

Wealth Multiplier

3.20x

Capital multiple of original principal

Compounding Speed Diagnostic

18.08% Annual Geometric Growth

At this pace, your invested capital doubles every 4.0 years (Rule of 72).

CAGR vs. Absolute Return vs. XIRR

Absolute Return (220%):Measures total raw growth from start to finish with zero consideration of time or duration.
CAGR (18.08%/yr):Smooths out annual volatility to give the exact geometric constant rate of return required to reach terminal value.
XIRR (16.48%/yr):Accounts for the exact calendar dates of multiple deposits and withdrawals (Money-Weighted Return).
Quantitative Performance Measurement11 min readToro Quantitative Analytics Desk

The Mathematical Mechanics of Investment Returns: Point-to-Point CAGR vs. Multi-Period Newton-Raphson XIRR

In portfolio analytics, measuring return is not a trivial arithmetic exercise. A simple average return fails due to volatility drag; point-to-point CAGR fails when additional capital is deposited mid-tenure; and internal rate of return requires numerical root-finding algorithms. Below is the full mathematical foundation of return metrics.

1. The Compound Annual Growth Rate (CAGR) Formula

CAGR represents the geometric mean growth rate that dampens annual volatility spikes, answering the question: "What constant annual rate would yield this ending balance from this initial investment?"

Formula 1: Geometric Compound Annual Growth RateGeometric Return
CAGR = [ ( Vfinal / Vinitial ) ]( 1 / t ) − 1

Vfinal = Terminal asset value at horizon end.

Vinitial = Beginning investment principal.

t = Holding period in years.

2. The Newton-Raphson Numerical Root-Finding for XIRR

When an investor makes multiple SIP deposits, dividend withdrawals, or lump-sum top-ups at irregular calendar dates, CAGR cannot be computed directly. Instead, we solve for the rate r where the Net Present Value (NPV) of all cash flows equals zero:

Formula 2: Net Present Value Equation for XIRRInternal Rate of Return
Σ [ Ci / ( 1 + r )( di − d0 ) / 365 ] = 0

Ci = Cash flow amount at transaction index i.

di − d0 = Number of elapsed days since initial transaction date.

r = The annualized internal rate of return solved via iterative derivatives.

Frequently Asked Questions & Quantitative Reference

Average annual return ignores volatility drag. If a $100 portfolio gains +50% in Year 1 ($150) and loses -50% in Year 2 ($75), the average return is 0%, but the investor actually lost 25% of their money. CAGR accurately reflects the negative geometric compounding (-13.4% CAGR).
Performance Calculation Disclaimer

Educational & Mathematical Tool Only: Historical CAGR and XIRR figures represent past performance and do not guarantee future investment returns. Tax liabilities, management expense ratios, and brokerage fees can reduce net realized investor returns.