Money-weighted return measures investment performance while accounting for both the size and timing of cash flows into and out of a portfolio.
It is effectively the internal rate of return, or IRR, of the investor’s cash flows.
That makes money-weighted return especially useful when an investor contributes or withdraws substantial amounts during the measurement period.
If a large contribution occurs immediately before strong performance, the resulting money-weighted return can be higher than a return measure that gives each time period equal importance. If a large contribution occurs immediately before a decline, the investor’s money-weighted result can be worse.
What Is Money-Weighted Return?
Money-weighted return asks:
What discount rate makes the present value of all investor cash flows, including the ending portfolio value, equal to zero?
The method gives more economic weight to periods during which more investor capital was at work.
That distinguishes it from performance methods designed to neutralize the timing of external cash flows.
Money-Weighted Return Formula
For equally spaced annual cash flows:
0 = CF₀ + CF₁ ÷ (1 + r) + CF₂ ÷ (1 + r)² + … + CFₙ ÷ (1 + r)ⁿ
Where:
- CF₀ = initial cash flow;
- CF₁, CF₂, … = later contributions, withdrawals, or final value;
- r = money-weighted return;
- n = number of periods.
The return r is the IRR.
Cash-Flow Sign Convention
A consistent sign convention is essential.
From the investor’s perspective:
- money invested into the portfolio = negative cash flow;
- money received from the portfolio = positive cash flow.
For example:
Initial $10,000 Investment = −$10,000
Additional $2,000 Contribution = −$2,000
Final $13,500 Portfolio Proceeds = +$13,500
Using the opposite convention produces the same return if every sign is reversed consistently.
Money-Weighted Return Example
Suppose:
Beginning of Year 1
Investor contributes:
−$10,000
End of Year 1
Investor contributes another:
−$2,000
End of Year 2
The portfolio is liquidated for:
+$13,500
The IRR equation is:
0 = −$10,000 − $2,000 ÷ (1 + r) + $13,500 ÷ (1 + r)²
The goal is to solve for r.
Solve the Example
Let:
x = 1 + r
Then:
0 = −10,000 − 2,000 ÷ x + 13,500 ÷ x²
Multiply by x²:
0 = −10,000x² − 2,000x + 13,500
Rearrange:
10,000x² + 2,000x − 13,500 = 0
Solving the quadratic gives the economically meaningful positive root:
x ≈ 1.0661904
Therefore:
r = 1.0661904 − 1
r ≈ 0.0661904
Money-Weighted Return ≈ 6.62% per year
The investor’s money-weighted return is approximately 6.62% annually.
Verify the Result
Discount the year-one $2,000 contribution:
$2,000 ÷ 1.0661904 ≈ $1,875.84
Discount the $13,500 ending value for two years:
$13,500 ÷ 1.0661904² ≈ $11,875.84
Then:
−$10,000 − $1,875.84 + $11,875.84 ≈ $0
The cash flows balance at approximately 6.62%, confirming the IRR.
Why Cash-Flow Timing Matters
Suppose a portfolio performs very well before a large contribution and poorly afterward.
A return measure that evaluates investment periods independently might still show respectable portfolio performance.
But the investor had relatively little money invested during the strong period and much more invested during the weak period.
Money-weighted return reflects that reality.
It measures the experience of the actual dollars invested.
Example: Contribution Before a Loss
Suppose:
- initial investment = $10,000;
- portfolio rises 20% to $12,000;
- investor then adds $50,000;
- total becomes $62,000;
- portfolio subsequently falls 10%.
Ending value:
$62,000 × 0.90 = $55,800
The investor had much more capital exposed during the losing period than during the winning period.
A money-weighted return therefore gives substantial influence to that later decline.
Example: Contribution Before a Gain
Reverse the sequence.
Suppose:
- $10,000 initially loses 10%;
- value becomes $9,000;
- investor adds $50,000;
- portfolio becomes $59,000;
- portfolio then gains 20%.
Ending value:
$59,000 × 1.20 = $70,800
Now the investor had much more capital exposed during the strong period.
The money-weighted result improves substantially.
Money-Weighted Return vs Simple Total Gain
Suppose:
- total contributions = $12,000;
- ending value = $13,500.
A simple gain calculation is:
$13,500 − $12,000 = $1,500
Relative to total contributions:
$1,500 ÷ $12,000 = 12.5%
But that 12.5% ignores timing.
The $12,000 was not invested for the same length of time.
Money-weighted return accounts for the fact that $10,000 was invested for two years while the later $2,000 was invested for only one.
Money-Weighted Return With Withdrawals
Withdrawals are generally treated as positive cash flows to the investor.
Suppose:
- initial investment = −$20,000;
- year-one withdrawal = +$2,000;
- year-two ending value = +$21,500.
The MWR equation is:
0 = −$20,000 + $2,000 ÷ (1 + r) + $21,500 ÷ (1 + r)²
The return that solves the equation incorporates the benefit of receiving the $2,000 before the final date.
Irregularly Timed Cash Flows
When cash flows occur on irregular dates rather than exact annual intervals, each cash flow should be discounted according to its actual time from the starting date.
A general relationship is:
0 = Σ[CFᵢ ÷ (1 + r)^tᵢ]
Where tᵢ represents the fraction of a year associated with each cash-flow date.
Spreadsheet functions commonly designed for irregular-date IRR calculations can be useful when many cash flows are involved.
Multiple IRRs Can Occur
Money-weighted return has an important mathematical limitation.
When the sequence of cash flows changes sign more than once, the IRR equation can sometimes produce:
- multiple valid mathematical solutions;
- no economically meaningful solution.
For example, a project with contributions, large withdrawals, another contribution, and final proceeds can create a complicated polynomial.
The resulting IRR should therefore be checked rather than accepted mechanically.
Money-Weighted Return and Modified Duration
Modified duration measures fixed-income price sensitivity to yield changes.
Money-weighted return measures investor performance across cash flows.
A bond portfolio can have modified duration of 4 while generating a money-weighted return of 8%, −2%, or another value.
One measures risk sensitivity; the other measures cash-flow-weighted performance.
Money-Weighted Return and Maximum Drawdown
Maximum drawdown measures the largest peak-to-trough decline.
Money-weighted return can still be positive even when a portfolio experiences a severe drawdown.
Likewise, an investor can experience a disappointing money-weighted return in a portfolio whose maximum drawdown was relatively modest if cash flows occurred at unfavorable times.
Return and downside path should be evaluated separately.
Money-Weighted Return and Lump-Sum Investing
With lump-sum investing, most or all capital enters at the beginning.
If there are no later external cash flows, the money-weighted return becomes much easier to interpret because the investor’s capital is exposed throughout the measurement period.
Frequent contributions and withdrawals create the cash-flow timing effects that make MWR especially useful.
Money-Weighted Return and Monthly Interest
A portfolio can contain cash or fixed-income components that generate monthly interest.
If interest is distributed to the investor rather than retained in the portfolio, those payments can become positive cash flows in a money-weighted return calculation.
If income remains inside the portfolio and is already reflected in ending value, it should not also be added separately unless the methodology specifically requires it.
Money-Weighted Return and Net Worth
Net worth measures assets minus liabilities at a point in time.
Money-weighted return measures performance through time.
A person’s net worth can increase because of:
- investment returns;
- salary savings;
- debt repayment;
- business changes;
- property values.
MWR should not be applied to total net-worth growth without carefully separating these external financial flows.
Money-Weighted Return vs Portfolio Manager Skill
Money-weighted return can be influenced by decisions made by the investor rather than the portfolio manager.
Suppose an investor adds a large amount immediately before a market decline.
The manager may have had no control over the contribution timing.
The investor’s MWR will reflect the poor timing because that is the result experienced by the investor’s dollars.
For evaluating manager performance independently of investor cash-flow decisions, another methodology may be preferable.
Contributions at Market Peaks
Suppose an investor makes a very large contribution near a market peak.
If prices subsequently fall, MWR can deteriorate sharply because a large amount of money participated in the loss.
This makes the measure particularly useful for answering:
How did my actual capital perform?
rather than only:
How did the underlying strategy perform per period?
Withdrawals Before Gains
The same concept works in reverse.
If an investor withdraws a large amount immediately before strong future returns, less capital remains to benefit from the rally.
The portfolio strategy may later report strong performance, while the investor’s accumulated wealth benefits less because money was removed earlier.
Money-Weighted Return Does Not Equal Dollar Profit
Two portfolios can earn the same MWR but generate very different dollar profits.
Suppose:
- Investor A invests $10,000;
- Investor B invests $1 million.
An identical 8% money-weighted return does not imply identical dollar gains.
Percentage performance and capital scale remain separate.
MWR Can Be Negative
If the IRR solving the cash-flow equation is negative, the investor experienced a negative money-weighted return.
For example, if investments consistently lose value after major contributions, the return can fall below zero.
The formula does not assume profitability.
MWR and Fees
If ending portfolio values and distributions are already reported after investment fees, those costs are naturally incorporated in the investor’s cash-flow result.
If fees are paid separately outside the portfolio, the methodology should specify whether they are included as additional investor cash flows.
Consistency matters when comparing returns.
Common Money-Weighted Return Mistakes
One common mistake is using inconsistent positive and negative cash-flow signs.
Another is treating deposits as investment gains.
People can also use equally spaced IRR calculations when cash flows occurred on irregular dates.
Finally, an IRR result should be examined carefully when cash flows change sign several times because multiple mathematical solutions can occur.
Frequently Asked Questions
What is money-weighted return?
Money-weighted return is the internal rate of return generated by an investor’s actual contributions, withdrawals, and ending portfolio value.
What is the money-weighted return formula?
0 = Σ[CFₜ ÷ (1 + r)^t]
The value of r that solves the equation is the money-weighted return.
Is money-weighted return the same as IRR?
Yes, money-weighted return is generally an IRR calculation applied to investment cash flows.
Why does contribution timing affect MWR?
Because periods in which more investor capital is present have a larger impact on the result.
How are contributions entered?
From the investor’s perspective, contributions are typically negative cash flows.
How are withdrawals entered?
They are typically positive cash flows to the investor.
Does MWR include the ending portfolio value?
Yes. Ending portfolio value is normally treated as a final positive cash flow when calculating the return through that date.
Can money-weighted return be negative?
Yes.
Can there be more than one IRR?
Yes. Certain cash-flow patterns with multiple sign changes can produce multiple mathematical solutions.
Is MWR good for measuring my personal investment experience?
Yes. It is particularly useful when the timing and size of your contributions and withdrawals materially affect your outcome.
Is MWR a risk measure?
No. It does not measure volatility, drawdown, or other dimensions of risk.
Why use money-weighted return?
It connects actual investor cash flows with investment performance within a broader Savings & Investing analysis.
