Money-Weighted Return Calculator

The money-weighted return (MWR) is a measure of investment performance that accounts for both the size and the timing of every cash flow you contribute or withdraw during a holding period. Unlike the time-weighted return, which strips out the effect of investor behavior, the MWR rewards or penalizes you for the exact moments you put money to work. If you invested a large lump sum just before a strong rally, your MWR will be higher than an investor who held back; if you piled in right before a drawdown, it will be lower.

Mathematically, the MWR is identical to the Internal Rate of Return (IRR) — the annualized discount rate that sets the net present value (NPV) of all your cash flows to zero. Because it anchors every contribution and withdrawal to the calendar, the MWR is frequently called the dollar-weighted return in the mutual-fund and pension-fund industries. It is the rate that best reflects the actual experience of the individual investor rather than the theoretical performance of the portfolio strategy.

Financial analysts use MWR when evaluating portfolios where the investor controls the timing of contributions — personal brokerage accounts, real estate investments, private equity funds, and retirement accounts funded with irregular contributions all fall into this category. The CFA Institute recognizes MWR as the appropriate metric for evaluating individual investor performance, while reserving time-weighted return for comparing fund managers who do not control client cash-flow timing.

Because MWR incorporates the real dollars you put at risk on specific dates, it gives a complete and honest picture of what your money actually earned. A simple return calculation ignores the compounding difference between an early deposit and a late deposit; the money-weighted return corrects for that gap, making it indispensable for personal finance planning and portfolio analysis alike.

Finding the money-weighted return requires solving a polynomial equation that has no closed-form solution when more than one cash flow is present. This calculator uses the Newton-Raphson method, an iterative numerical technique that converges rapidly to the exact answer. Starting from an initial guess of 10% (r = 0.10), the algorithm repeatedly refines the estimate until the NPV is within a tolerance of 1 × 10⁻⁸ — far more precision than any real-world investment decision requires.

Each iteration computes the NPV at the current rate guess and divides it by the NPV's first derivative with respect to r. The next guess is the current guess minus that quotient:

r_next = r − NPV(r) / NPV′(r)

The derivative of the NPV formula above is:

NPV′(r) = Σ [ CFₜ × (tₘ/12) ÷ (1 + r)^(tₘ/12 + 1) ] − V_T × (T/12) ÷ (1 + r)^(T/12 + 1)

The process stops when consecutive guesses differ by less than 1 × 10⁻⁸ or after 100 iterations, whichever comes first. The result is clamped to a range of −99% to +1,000% to prevent numerical overflow for extreme inputs. Once the annual rate r is found, the monthly MWR is derived using the standard compounding formula: Monthly MWR = ((1 + r)^(1/12) − 1) × 100.

The calculator also reports a simple return for comparison: (Final Value − Total Invested) / Total Invested × 100. This figure ignores timing entirely and tends to overstate performance when deposits are made early in a down market or understate it when deposits are made late in a bull market.

The two dominant performance metrics in professional investing are the money-weighted return and the time-weighted return (TWR). Understanding when each applies prevents a common and costly analytical mistake.

The practical takeaway: use the money-weighted return calculator when you want to know how your investment decisions actually performed — accounting for every dollar you added at every point in time. Use the time-weighted return when comparing two fund managers who manage money on behalf of clients who control deposits and withdrawals independently.

The gap between MWR and TWR can be dramatic. A fund might post a 20% TWR for the year, but if the majority of investor money flowed in just before a correction, the average MWR experienced by investors could be negative. This is sometimes called the investor return gap and is a well-documented phenomenon in behavioral finance research.

Once the calculator returns your annual money-weighted return, several related figures help you place that number in context.

Annual MWR: The headline result, expressed as a percentage per year. A positive MWR means your portfolio grew in dollar-weighted terms; a negative MWR means you lost purchasing power after accounting for all contributions. Benchmark this figure against appropriate indices — for a diversified equity portfolio, comparing against the S&P 500's time-weighted return is common, though note that the benchmark uses TWR while you are measuring MWR.

Monthly MWR: Derived by converting the annual rate to a monthly equivalent using compounding: ((1 + r)^(1/12) − 1). This figure is useful for comparing to monthly savings-account or CD rates, and for projecting forward how quickly a portfolio might compound at this pace.

Simple Return: The calculator also shows a simple (unweighted) return: (Final Value − Total Invested) / Total Invested. When additional cash flows are small relative to the initial investment and the holding period is exactly one year, the simple return and MWR will be close. Larger and earlier deposits cause the MWR to diverge from the simple return — upward if the portfolio performed well after each deposit, downward if it did not.

Net Gain/Loss: The raw dollar profit (Final Value minus Total Invested across all periods). This is the absolute return — it complements the percentage MWR by showing the actual dollar impact on your wealth. Two portfolios could have the same MWR but very different dollar gains simply because of scale.

The money-weighted return calculator applies across a wide range of real investment scenarios. Understanding each helps you use the right input values and interpret results correctly.

Retirement Account Contributions

401(k) and IRA investors add money at irregular intervals — often biweekly with payroll contributions plus year-end lump sums. Enter each contribution as a cash flow with its corresponding month number to see how your timing decisions affected the overall IRR of your retirement savings.

Real Estate Investment Analysis

Property investors can model the initial purchase price as the initial investment, renovation costs and carrying charges as positive cash flows at the appropriate months, and the net sale proceeds as the final value. The resulting MWR is the true annualized return on capital deployed — directly comparable across properties of different sizes and holding periods.

Private Equity and Venture Capital

PE and VC funds are evaluated almost exclusively on IRR, which is the MWR for the fund's cash flows. Capital calls (drawdowns) are the positive cash flows; distributions back to limited partners are negative cash flows. The fund's terminal NAV is the final value. The money-weighted return calculator replicates this exact IRR calculation.

Dollar-Cost Averaging Evaluation

If you invest a fixed dollar amount every month, enter each monthly purchase as a cash flow and the current portfolio value as the final value. The MWR will show whether your consistent buying plan outperformed, matched, or lagged a lump-sum investment made at the start.

Freelancer and Business Owner Portfolios

Irregular income earners often invest large amounts when business is good and small amounts — or nothing — during slow periods. The money-weighted return captures this uneven cadence and gives a realistic return figure that simple return formulas would misrepresent.