Time-Weighted vs. Dollar-Weighted Return Calculator

Two investors can hold the exact same fund, over the exact same period, and walk away with genuinely different personal returns, not because the fund manager did anything different for either of them, but because of when each investor happened to add or withdraw money. This is the central fact that time-weighted return (TWR) and dollar-weighted return (DWR, also called money-weighted return) are each designed to handle differently, and confusing the two, or not realizing a single number cannot answer both questions at once, is one of the most common sources of confusion in performance reporting.

Time-weighted return measures the compound growth rate of one dollar invested for the entire period, completely removing the distorting effect of when cash flows happened or how large they were. It is calculated by breaking the period into subperiods bounded by each cash flow, calculating the return for each subperiod on its own, and chain-linking (compounding) those subperiod returns together. Because it strips out cash-flow timing entirely, TWR is the industry-standard way to judge a portfolio manager's skill: a manager has no control over when a client decides to add or withdraw money, so it would be unfair to let those decisions affect the number used to evaluate the manager's investment decisions.

Dollar-weighted return measures the actual annualized return an individual investor experienced, given the specific size and timing of every dollar they personally put in or took out, and what the portfolio was worth at the end. It is calculated as the internal rate of return (IRR) on the investor's full stream of dated cash flows. Because it is directly sensitive to an investor's own timing decisions, DWR is the right number for answering "what did I personally earn on my money," even though it is the wrong number for evaluating whether the manager's investment decisions were skillful.

Time-Weighted Return chain-links each subperiod return:

$$\text{TWR} = \left[\prod_{t=1}^{n}(1 + r_t)\right] - 1$$

Where $r_t$ is the manager's return for subperiod $t$, calculated independently for each subperiod between cash flows. This calculator computes TWR using the platform's shared chain-linking function, applied directly to the subperiod returns you enter.

Dollar-Weighted Return solves for the single discount rate that makes the net present value of the investor's entire dated cash flow stream equal to zero:

$$0 = \sum_{t=0}^{n} \frac{CF_t}{(1 + \text{DWR})^{t}}$$

Where $CF_t$ is each cash flow (initial investment and any contribution as a negative outflow, any withdrawal and the final ending value as a positive inflow), discounted back to Day 0 using the actual number of days between each cash flow date. This calculator computes DWR using the platform's shared IRR solver applied to the exact dated series: the initial investment, up to two interim contributions or withdrawals, and the final ending value treated as if liquidated on the last day.

A portfolio starts with a $10,000 investment. In the first subperiod it returns 10%. Right after that period ends, the investor contributes an additional $5,000. In the second subperiod, the portfolio returns 5%.

Time-Weighted Return (ignores the contribution entirely): $$\text{TWR} = (1.10 \times 1.05) - 1 = 15.5\%$$

Tracking the actual dollars: $10,000 grows to $11,000 after the first period (10%). The $5,000 contribution brings the balance to $16,000. That grows 5% to a final $16,800.

Dollar-Weighted Return solves the IRR on the cash flow series: −$10,000 on Day 0, −$5,000 at the contribution date, and +$16,800 at the end. That works out to approximately 14.49%, noticeably below the 15.5% TWR.

Why the gap exists: the $5,000 contribution added more money right before the weaker 5% subperiod, meaning a larger share of the investor's total capital was exposed to the lower-return period than the higher-return period. The manager's skill (15.5% chain-linked) didn't change; the investor's personal timing simply happened to work against them, pulling their actual dollar-weighted result below the manager's time-weighted result. Had the investor instead withdrawn $5,000 at that same point (reducing exposure to the weaker period), the dollar-weighted return would have come in above 15.5% instead, purely from the opposite timing effect.

If a fund reported dollar-weighted returns as its headline performance figure, that number would be at the mercy of whatever the fund's largest investors happened to do with their money, entirely outside the manager's control. A large client who happened to add a big contribution right before a strong quarter would flatter the fund's dollar-weighted number; a large client who added money right before a weak quarter would drag it down, regardless of anything the manager actually did. This is precisely why the CFA Institute's Global Investment Performance Standards (GIPS), the widely recognized standard for reporting investment performance, require time-weighted returns for composite performance reporting: TWR isolates the manager's actual investment decisions from client-driven cash-flow timing, making it possible to fairly compare one manager against another or against a benchmark.

Dollar-weighted return has not become less useful for its own purpose; it remains the correct number for an individual investor asking "what did I personally earn." A retirement account statement showing an investor's personal annualized return is typically closer to a dollar-weighted calculation, since it reflects that specific person's actual contribution and withdrawal history, not an idealized single-dollar benchmark.

This calculator requires the subperiod returns to be entered directly, since deriving true chain-linked subperiod returns from raw cash flows alone requires knowing the portfolio's exact value immediately before and after each cash flow, information typically produced by a fund administrator's official valuation process rather than something this calculator can infer. It supports up to three subperiods and two interim cash flows; portfolios with many more contribution and withdrawal events over a long history would need those returns pre-aggregated into subperiods before use. It does not account for the difference between pre-tax and after-tax returns, fees charged at different points in the period, or currency effects for portfolios holding foreign-denominated assets. The dollar-weighted calculation solves numerically for the internal rate of return and, like any IRR calculation, can in rare cash-flow patterns with multiple sign changes produce more than one mathematically valid solution; this calculator's underlying cash-flow patterns (one initial outlay, optional interim flows, one final positive value) are structured to avoid that ambiguity in ordinary use.

• Reporting DWR as if it measured manager skill. A manager who made excellent investment decisions can still show a mediocre dollar-weighted return if a large client happened to add money right before a downturn; that is a statement about the client's timing, not the manager's judgment.
• Reporting TWR as if it measured an individual investor's actual personal return. TWR intentionally ignores what the investor actually put in and took out; it answers "how did the strategy perform," not "how did my money do."
• Assuming a large gap between TWR and DWR means something is wrong. A gap is expected and normal whenever an investor's contributions or withdrawals are meaningfully concentrated around strong or weak performance periods; it is a description of timing, not an error.
• Forgetting that the direction of the gap depends on whether cash moved in or out. Contributing before a weak period drags DWR below TWR; withdrawing before a weak period pushes DWR above TWR; the same logic reverses around strong periods.
• Comparing your personal DWR-style account statement directly against a fund's published TWR-style performance figure. These are frequently different calculation methods measuring different things, and comparing them directly without adjusting for that is a common source of "why doesn't my return match the fund's advertised performance" confusion.

• CFA Institute, Global Investment Performance Standards (GIPS).
• CFA Institute, Portfolio Risk and Return: Time-Weighted and Money-Weighted Rate of Return, CFA Program Curriculum.
• U.S. Securities and Exchange Commission, Investor.gov, Internal Rate of Return (IRR).