Time-Weighted and Money-Weighted Return Calculator

Read the calculator result

An account that grows from $10,000 to $15,000 hasn’t necessarily earned a 50% investment return. Some of that increase may be money you deposited. This calculator separates contributions from observed portfolio values over exactly three annual periods. It reports annual subperiod returns, cumulative and annualized time-weighted performance, an annual money-weighted return, and the net dollar gain.

The two return measures answer different questions. Time-weighted return links investment performance between the defined cash-flow dates. Money-weighted return reflects the amount of money committed and how long each contribution was invested. Neither is automatically the “real” return while the other is wrong. Their usefulness depends on whether you’re assessing the investment path or the experience of the actual dollars contributed.

The GIPS Standards Handbook for Firms explains geometric linking of subperiod returns and describes money-weighted return as reflecting the timing and size of external cash flows. This educational tool uses those mathematical distinctions in a restricted three-year schedule. It doesn’t produce a GIPS-compliant performance report or assess a manager’s compliance.

Investment return: the valuation date must come before the contribution

Enter the opening account value at the beginning of year one. Enter the ending value of year one before any new contribution, then the contribution made immediately after that valuation. Repeat that pattern at the end of year two. Finally, enter the year-three ending value with no new contribution at that final date.

The first added contribution therefore participates in years two and three. The second participates only in year three. There are no additional cash flows within a year, and no withdrawals are supported. If actual deposits arrived monthly, or a withdrawal occurred midway through a year, the dates don’t fit this form. Don’t combine those transactions into a convenient year-end amount and assume the return is unchanged.

Use values on a consistent basis. Include the cash and securities that belong to the account being measured. If expenses are deducted inside the account, their effect is already reflected in the observed value. A fee paid from another account is outside these values unless you separately incorporate it in a suitable broader cash-flow analysis. Keep the scope consistent across every year.

How the calculator works

For year one, divide the ending value before its contribution by the opening value, then subtract one. For year two, divide its ending value by year one’s ending value plus the first contribution, then subtract one. For year three, divide the final value by year two’s ending value plus the second contribution, then subtract one.

Cumulative time-weighted return = (1 + year-one return) × (1 + year-two return) × (1 + year-three return) − 1. Annualized time-weighted return = (1 + cumulative return)^1/3 − 1.

The multiplication links growth factors. Simply adding annual percentages would ignore compounding. Dividing the cumulative percentage by three would also produce a different figure from the constant annual compounded rate. Each period must begin with a positive value after any preceding contribution; otherwise a percentage return for that period has no valid positive capital base.

Solve one rate for the contribution timeline

Let V be the opening value, C1 the contribution after year one, C2 the contribution after year two, E the final value, and r the annual money-weighted return. The tool solves:

V × (1 + r)³ + C1 × (1 + r)² + C2 × (1 + r) = E.

The opening money has three years to grow, the first added contribution has two, and the second has one. With a positive opening value and nonnegative contributions, the equation has one nonnegative solution for the growth factor 1 + r. The annual rate itself can be negative. If the final account value is zero, that rate is −100%.

The intermediate year-end valuations affect time-weighted performance but don’t enter this money-weighted equation directly. The latter needs the contribution amounts, their dates, and the final value. That distinction explains how two paths can have the same dollar-weighted experience yet different sequences of annual investment performance.

Investment return calculator example: $13,000 contributed and $15,000 ending value

Start with $10,000. The account reaches $11,000 at the end of year one, and you immediately add $2,000. It ends year two at $13,000 before another $1,000 contribution. At the end of year three, the account is worth $15,000.

The linked growth factor is 1.10 × 1.00 × 1.07142857, giving a cumulative time-weighted return of 17.8571%. Its annualized value is 5.6295%. The annual money-weighted return solving the contribution equation is approximately 5.4392%. The difference arises from the amount invested during the particular years, not from a rounding error.

Total cash invested is $13,000, and the net dollar gain is $2,000. Dividing that gain by $13,000 gives approximately 15.38%, but this simple ratio treats contributions made at different times as if they had equal investment exposure. It is neither the linked time-weighted return nor the annual money-weighted return reported by the investment return calculator.

See how final value and contributions change the measures

Change only the final value to $17,000. Year-three return becomes 21.4286%, cumulative time-weighted return becomes 33.5714%, and annualized time-weighted return becomes 10.1297%. The annual money-weighted return is approximately 10.4063%. This time the money-weighted figure is higher because more dollars participate in the stronger final year.

As a different experiment, restore the $15,000 ending value and set both added contributions to zero, while keeping the observed $11,000 and $13,000 intermediate values. The period returns now change because each later year begins with less contributed capital. Cumulative return is 50%, and both annualized measures equal approximately 14.4714%.

That zero-contribution case isn’t a claim that removing deposits would cause the same market values in real life. It’s a mathematical comparison using a different entered history. If you want to simulate a counterfactual account, you must also choose internally consistent ending values rather than keeping observed values that depended on the original deposits.

If the final value is zero, the net loss equals all $13,000 invested in the original contribution scenario. Year-three, cumulative, annualized time-weighted, and money-weighted returns become −100% under the model. Negative ending account values and borrowing are outside this long-only, nonnegative-value framework.

Read account value beside cumulative money invested

The original chart and table show the entered annual values and contributions using the stated before-and-after timing. A contribution can increase account value without creating investment profit. The cumulative-invested reference helps reveal that distinction. It’s a cash ledger, not the path a hypothetical benchmark would necessarily have followed.

Check the table’s year-one and year-two rows carefully. The value before contribution belongs to the completed year’s return; the value after contribution becomes the next year’s starting capital. At year zero, the opening amount is the initial investment. This consistent timing prevents the same deposit from being treated both as a return and as new capital.

Use statements to build a reliable input history

When recording a valuation at the same time as a contribution, retain both figures rather than relying on a single closing balance. A statement showing $13,000 after a $2,000 deposit corresponds to an $11,000 pre-deposit valuation in the first-year example. Entering $13,000 as the pre-deposit value and also entering the $2,000 contribution would count that deposit twice, inflate the first year’s return, and distort the capital base for the next year.

Choose three exact annual periods and collect the beginning value, end valuations, and transaction history. Confirm that the only external cash flows are the two permitted year-boundary contributions. Distinguish a new deposit from a dividend or interest payment retained inside the account; the latter is already part of investment value and shouldn’t be added again as outside money.

Check transfers between accounts, stock splits, reinvestments, fees, and missing positions before comparing the result with a statement. A different statement convention, a different date, or a different account perimeter can explain a difference without either calculation being arithmetically wrong. A dated transaction-level method is needed when the actual cash-flow history doesn’t fit these annual boundaries.

The compound interest calculator projects a constant assumed return instead of measuring observed results. The investment fee calculator isolates modeled charges. The portfolio rebalancing calculator examines target allocations and trades rather than historical performance.

Investment return calculator questions

Which return should I compare with a benchmark?

Use a measure, period, currency, and fee basis comparable with the benchmark. This calculator doesn’t load benchmark data or determine an appropriate comparison. An annualized three-year result shouldn’t be compared casually with a single-year figure or an unadjusted account-balance change.

Can I enter withdrawals as negative contributions?

No. Contributions are restricted to nonnegative amounts. Withdrawals can create different cash-flow patterns and potentially more complicated rate-solving behavior. Use a tool that accepts the actual dated deposits and withdrawals instead of forcing them into this restricted schedule.

Does the dollar gain include taxes?

Only if their effect is already reflected in the entered account values within the chosen scope. The calculator doesn’t compute capital-gains tax, tax basis, distributions owed outside the account, or after-tax purchasing power. Label the input values consistently and keep any separate tax estimate separate.