The time‑weighted rate of return (TWR) is a method for measuring the compounded growth rate of an investment portfolio over time while removing the distorting effects of investor cash flows (deposits and withdrawals). By breaking the total measurement period into subperiods defined by external cash flows, calculating the return for each subperiod, and then chaining (geometrically linking) those subperiod returns, TWR isolates the portfolio’s investment performance — the effect of the manager’s decisions — from the timing and size of cash flows.
Key takeaways
– TWR measures the compound rate of return of a portfolio net of the effect of external cash flows.
– It is the industry standard for evaluating and benchmarking investment managers because it shows performance independent of client cash flows.
– TWR requires a valuation at each external cash flow (or whenever you split subperiods).
– TWR does not represent an investor’s actual dollar experience; for that, use a money‑weighted return (e.g., IRR or XIRR).
How TWR works (conceptual)
1. Split the full measurement period into subperiods so that no external cash flows occur inside a subperiod. Typically you create a new subperiod each time there is a deposit or withdrawal.
2. For each subperiod, compute the subperiod return based only on the portfolio values immediately before and immediately after the subperiod’s market performance (i.e., excluding flows).
3. Chain all subperiod returns multiplicatively (geometrically): the compounded growth for the whole period equals the product of (1 + each subperiod return), minus 1.
Formula for TWR
Let HPi be the return for subperiod i (i = 1..n). Then
TWR = (1 + HP1) × (1 + HP2) × … × (1 + HPn) − 1
where a subperiod return HPi is calculated using values that exclude the external cash flow at the subperiod boundary. In practice, when cash flows occur at the end of a subperiod, compute
HPi = (Value_before_next_flow − Value_at_start_of_subperiod) / Value_at_start_of_subperiod
Put another way, measure portfolio performance during the interval ignoring the deposit/withdrawal that starts or ends that interval.
Practical steps (step‑by‑step)
1. Identify all external cash flows (dates and amounts) and the portfolio valuations immediately before and after each cash flow.
2. Define subperiods so that each subperiod begins immediately after a cash flow (or at the beginning of the measurement period) and ends immediately before the next cash flow (or at the end of the measurement period).
3. For each subperiod i, compute the subperiod return HPi = (Value_end_of_subperiod_before_flow − Value_start_of_subperiod) / Value_start_of_subperiod. (If flows occur at start or end, make sure you exclude them from the end/start values appropriately.)
4. Compute the cumulative TWR = Product over i of (1 + HPi) − 1.
5. Report the result as a percentage (e.g., 0.4306 = 43.06% for the whole period). If desired, convert to an annualized TWR if the period is not one year: Annualized TWR = (1 + TWR)^(1/years) − 1.
Worked example — two portfolios (cleaned and consistent numbers)
We evaluate two portfolios that both begin with $1,000,000. External cash flows occur only at quarter ends. We compute subperiod returns for each quarter, then chain them.
Portfolio A (quarterly sequence)
– Start Q1: $1,000,000
– Q1 market: grows to $1,200,000 → Subperiod return r1 = 20.000% (1.2000)
– Q1 cash flow (end of Q1): +$400,000 → AUM becomes $1,600,000 (this flow is excluded from r1)
– Q2 market: grows 1,600,000 → $1,650,000 → r2 = (1,650,000 − 1,600,000)/1,600,000 = 3.125% (1.03125)
– Q2 cash flow: −$200,000 → AUM becomes $1,450,000
– Q3 market: grows to $1,500,000 → r3 = (1,500,000 − 1,450,000)/1,450,000 ≈ 3.4483% (1.0344827586)
– Q3 cash flow: +$200,000 → AUM becomes $1,700,000
– Q4 market: grows to $1,900,000 → r4 = (1,900,000 − 1,700,000)/1,700,000 ≈ 11.7647% (1.1176470588)
– No cash flow after Q4 → final AUM = $1,900,000
Compute TWR for Portfolio A:
TWR_A = (1.20) × (1.03125) × (1.0344827586) × (1.1176470588) − 1 ≈ 1.4305882353 − 1 = 0.4305882353 → 43.06%
Portfolio B (quarterly sequence)
– Start Q1: $1,000,000
– Q1 market: grows to $1,150,000 → r1 = 15.000% (1.15)
– Q1 cash flow: +$50,000 → AUM becomes $1,200,000
– Q2 market: grows to $1,400,000 → r2 = (1,400,000 − 1,200,000)/1,200,000 = 16.6667% (1.166666667)
– Q2 cash flow: +$50,000 → AUM becomes $1,450,000
– Q3 market: grows to $1,600,000 → r3 = (1,600,000 − 1,450,000)/1,450,000 ≈ 10.3448% (1.103448276)
– Q3 cash flow: −$100,000 → AUM becomes $1,500,000
– Q4 market: grows to $1,800,000 → r4 = 20.000% (1.20)
– Q4 cash flow: +$50,000 → final AUM = $1,850,000
Compute TWR for Portfolio B:
TWR_B = (1.15) × (1.166666667) × (1.103448276) × (1.20) − 1 ≈ 1.776066667 − 1 = 0.776066667 → 77.61%
Interpretation of the example
– Portfolio B’s TWR (≈77.6%) is materially higher than Portfolio A’s (≈43.1%), showing that B’s underlying investment performance was better over the year despite ending with slightly less AUM ($1.85M vs $1.9M).
– The difference exists because TWR removes the effect of when and how much investors added or withdrew money, and therefore isolates manager/investment returns.
How to compute TWR in Excel (practical)
– Arrange rows for each subperiod with columns: StartValue, EndValueBeforeFlow (i.e., the portfolio value after market movement but before any cash flow at the period end), CashFlow (at period end), EndValueAfterFlow = EndValueBeforeFlow + CashFlow (if you track it).
– Subperiod return formula (assuming flows at period end): SubReturn = (EndValueBeforeFlow − StartValue) / StartValue
– Then overall TWR = PRODUCT(1 + SubReturnRange) − 1
Example formulas:
– If subreturns are in cells D2:D5, use =PRODUCT(1 + D2:D5) – 1 (in older Excel you may need to enter as array or use =PRODUCT(OFFSET(…)) style; in modern Excel PRODUCT(1 + D2:D5) works as a dynamic array if you wrap with proper constructs). Or do =PRODUCT(E2:E5)-1 where E2:E5 already contain 1+subreturns.
Dealing with flows inside a day or valuation issues
– Best practice: obtain a market valuation immediately before or after each external cash flow so subperiod returns exclude flows. If a valuation exactly at the flow time is not available, use a trusted proxy or price at the nearest available time — but be consistent and disclose methodology.
– If multiple cash flows occur on the same day, treat that day as one boundary; you don’t need separate subperiods for flows that happen simultaneously.
When to use TWR vs Money‑Weighted Return (MWRR / IRR / XIRR)
– Use TWR when you want to evaluate the investment manager’s skill or to benchmark performance against indices: it removes client cash flow effects.
– Use money‑weighted return (internal rate of return, XIRR in Excel) when you want to know the investor’s actual experience (dollar-weighted), because MWRR accounts for the timing and size of cash flows.
– Both metrics complement each other: TWR for performance attribution and manager evaluation; MWRR for investor-level return reporting.
Limitations of TWR
– Requires accurate and frequent valuations around every external cash flow (data intensive).
– Does not reflect the actual dollars gained or lost by an investor (it ignores the effect of the timing of contributions/withdrawals on realized investor return).
– Can be sensitive to valuation timing and mis-recorded flows; inconsistent treatment of flows can materially affect results.
The bottom line
TWR is the standard way to measure portfolio performance independently of investor cash flows. By partitioning the measurement interval at cash flows and chaining subperiod returns, TWR gives a pure view of investment performance that is appropriate for evaluating managers and benchmarking. For an investor’s real-dollar experience, calculate a money‑weighted return (IRR/XIRR). Always document how and when valuations and cash flows are recorded, because the accuracy of TWR depends on consistent and correct timing.
Sources and further reading
– Investopedia, “Time‑Weighted Rate of Return (TWR)”
– J.P. Morgan Wealth Management, “What is Time‑weighted Rate of Return?”
– Dynamic Funds, “Time‑weighted vs. Money‑weighted Returns.”
Editor’s note: The following topics are reserved for upcoming updates and will be expanded with detailed examples and datasets.