Understand Money-Weighted Rate of Return (MWRR) With Simple Examples

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The money-weighted rate of return (MWRR) is the single, constant rate of return that makes the present value of all the money you put into an investment equal to the present value of all the money you take out, plus its ending value. Because it accounts for both the size and the timing of every deposit, withdrawal, dividend and sale, the MWRR measures the return you earned, not only the return the investment produced. Mathematically it is the internal rate of return (IRR) applied to a portfolio’s cash flows. It is also called the dollar-weighted return.

How MWRR Works

A simple return compares an ending value with a starting value. That breaks down as soon as money moves in or out. If you start with $10,000, add $5,000 later and end with $16,000, the $6,000 gain is mostly your own deposit, not investment growth.

The MWRR solves that by treating every cash flow as a dated event. It asks what steady rate, compounded over the whole period, turns the exact sequence of money you invested into the exact sequence you got back, including the ending value. That rate is the money-weighted return.

Periods when more money is invested count for more, because a 10% gain on $50,000 adds more dollars than a 10% gain on $5,000. The MWRR therefore leans toward performance when the portfolio was largest.

The Money-Weighted Return Formula

The MWRR is the rate r that satisfies:

0 = CF₀ + CF₁ / (1 + r) + CF₂ / (1 + r)² + … + CFₙ / (1 + r)ⁿ

where:

• CF₀ is the initial investment (entered as a negative number from the investor’s point of view)
• CF₁ to CFₙ are the cash flows in each later period: additional contributions (negative), withdrawals, dividends and interest received, and sale proceeds (positive)
• CFₙ includes the ending market value if the position is still held
• n is the number of periods
• r is the money-weighted rate of return per period

Equivalently, the present value of outflows equals the present value of inflows. With more than two periods there is no algebraic shortcut, so r is found by iteration: guess a rate, check whether the equation balances, and adjust.

Which Cash Flows Count and How to Sign Them

The direction of each flow depends on perspective. Measure from the investor’s side and stay consistent.

Money leaving your pocket (negative):

• The purchase price of any investment you buy
• New contributions to the account
• Dividends or interest that you reinvest by buying more of the holding, if you are tracking the security on its own

Money coming back to you (positive):

• Proceeds from any investment you sell
• Dividends or interest paid out to you in cash
• Withdrawals from the account
• The ending market value of whatever you still hold

When you calculate MWRR for a whole account rather than a single security, dividends paid and reinvested inside the account are not external cash flows. They show up only in the ending value. Only money crossing the boundary of whatever you are measuring belongs in the formula.

Example: Calculating MWRR for a Single Stock

Hypothetical example for illustration.

You buy one share for $50. It pays a $2 dividend at the end of year 1 and another $2 at the end of year 2, and you sell it for $65 right after the second dividend.

The equation to solve is:

0 = -50 + 2 / (1 + r) + 67 / (1 + r)²

With two periods this happens to be a quadratic, and the solution is r ≈ 17.78% per year. Checking it: $2 discounted one year at 17.78% is about $1.70, and $67 discounted two years is about $48.30. Together they equal the $50 you paid.

In a spreadsheet, enter -50, 2 and 67 in three cells and use =IRR(A1:A3), which returns about 17.78%.

Getting the Periods Right

The IRR function assumes the cash flows are equally spaced, one per row. Two common mistakes come from this:

• Splitting simultaneous flows into separate rows. If the dividend and the sale happen on the same date, combine them. Putting the sale in its own row tells the spreadsheet it happened one full period later, which changes the answer.
• Irregular dates. Real accounts have deposits on random days. Excel and Google Sheets offer XIRR, which takes a column of cash flows and a matching column of dates and returns an annualized rate.

Annualized Money-Weighted Rate of Return

The rate you get is per period. If you used yearly cash flows, it is already an annual rate. If you used monthly flows, IRR returns a monthly rate, and the annualized MWRR is (1 + monthly rate)¹² - 1. XIRR handles this automatically by working in days.

For periods shorter than a year, many practitioners report the cumulative return instead of annualizing, because stretching a few weeks of performance into a yearly figure can produce misleading numbers.

MWRR vs. TWRR

The time-weighted rate of return breaks the measurement period into sub-periods at every external cash flow, calculates the return for each sub-period, and links them together by multiplying (1 + return) for each piece. Because each sub-period stands on its own, the size of the account during that sub-period does not matter. TWRR shows how the investments performed. MWRR shows how the investor fared, given when they added or removed money.

Hypothetical example for illustration. Two investors hold the same fund for two years. Each starts with $10,000 and adds $10,000 at the end of year 1. Only the order of the fund’s returns differs.

The fund delivered the same compound growth in both cases: 1.20 × 0.90 = 1.08, or 8% over two years, which is 3.92% a year. That is the TWRR, and it is identical for both investors because it ignores the deposit.

The money-weighted returns differ sharply. Investor A put the larger amount to work just before the loss, contributed $20,000 in total and ended with $19,800. Investor B added money before the gain and ended with $22,800. MWRR captures exactly that difference in outcomes.

Compound annual growth rate (CAGR) measures growth from a starting value to an ending value with no interim flows, so without deposits or withdrawals CAGR, TWRR and MWRR agree. Return on investment (ROI) is different again: a total percentage gain that ignores both timing and the length of the holding period.

When to Use Money-Weighted vs. Time-Weighted Returns

Use MWRR when you control the cash flows and want to know how your own decisions played out, as in a personal brokerage or retirement account where you choose when to contribute and withdraw.

Use TWRR when someone else controls the cash flows and you want to judge the person or strategy managing the money. A mutual fund manager cannot stop shareholders from buying in at a peak or redeeming at a bottom, so judging the manager on MWRR would credit or blame them for investor behavior. The GIPS standards, the industry’s performance-reporting framework, therefore generally call for time-weighted returns, while permitting money-weighted returns where the manager controls the timing of external cash flows. Venture capital and private equity funds call and return capital on the manager’s schedule, so their performance is commonly reported as an IRR.

Looking at both numbers together is often most informative: the gap between them measures how much the timing of contributions and withdrawals helped or hurt. Investor A’s timing cost about 4.6 percentage points a year relative to the fund itself.

The same IRR logic underlies yield to maturity, which is the money-weighted return a bondholder earns if they buy at today’s price, collect every coupon and hold to maturity.

Advantages of MWRR

• It reflects your actual experience. It is the only standard return measure that responds to how much money you had invested and when.
• It connects directly to goals. It tells you whether your real contributions grew at the rate your plan assumes.
• It handles messy cash flows. Regular contributions, irregular withdrawals and dividends all fit into the same equation.

Limitations of MWRR

• It mixes investment performance with investor behavior. A low MWRR alone could reflect poor investments or poor timing, and comparing it with TWRR separates the two. That also makes it unsuitable for comparing managers or funds.
• Results are dominated by large balances. Performance while the account was small barely moves the figure, even if that period lasted years.
• Unusual cash flow patterns can break the math. If the cash flow signs change more than once (for example, invest, withdraw, invest heavily again, then withdraw), the equation can have more than one valid solution or none at all. Spreadsheet functions may return just one of several answers or an error.
• It is a smoothed average. A single constant rate hides the volatility along the way. Risk-adjusted measures such as the Sharpe ratio address that.

FAQs

The Bottom Line

MWRR matters most to people running their own brokerage or retirement accounts, because it shows how their contribution and withdrawal decisions affected results. Fund managers should be judged on time-weighted returns, since they do not control investor cash flows. Comparing both figures shows how much timing helped or hurt, and XIRR gives an annualized MWRR when deposits fall on irregular dates.