Time Weighted Rate of Return
Also written TWRR · Time-Weighted Rate of Return (TWRR) · Time weighted return · Time-weighted return
A compounded return that neutralises client deposits and withdrawals by linking sub-period returns, so it measures the manager’s decisions. Mandatory for PMS investment approach performance.
In plain language
Imagine a portfolio manager who does brilliantly for eleven months — and then a client adds a large sum just before a market fall. The client's rupee loss is large, but was the manager bad?
Time-Weighted Rate of Return answers that question fairly. It breaks the period into pieces at every external cash flow (a deposit or withdrawal), measures the return of each piece on its own, and then chains the pieces together. The size and timing of the client's money stop mattering; what is left is the return produced by investment decisions and the market.
That is why SEBI requires portfolio managers to use it when presenting the performance of an investment approach.
How it works
Formula (Chapter 10, section 10.1.3).
TWRR = [(1 + R1) × (1 + R2) × … × (1 + Rn)] − 1
Each sub-period return, per the Step 1 formula and the worked table:
Rn = (Ending value − Beginning value − Contribution + Withdrawal) / (Beginning value + Contribution − Withdrawal)
Annualised: (1 + TWRR)^(1/n) − 1, where n is the number of years.
The workbook's example — ₹1,00,000 invested on 01/01/2020:
| Sub-period ends | Begin | Contribution | Withdrawal | End | Return |
|---|---|---|---|---|---|
| 20/02/20 | 1,00,000 | — | — | 1,10,000 | 10.00% |
| 04/04/20 | 1,10,000 | 20,000 | — | 1,45,000 | 11.54% |
| 30/09/20 | 1,45,000 | — | 15,000 | 1,25,000 | −3.85% |
| 30/09/20 | 1,25,000 | 30,000 | — | 1,80,000 | 16.13% |
| 31/12/21 | 1,80,000 | — | 10,000 | 1,85,000 | 8.82% |
Linked: 1.10 × 1.1154 × 0.9615 × 1.1613 × 1.0882 = 1.4909 → 49.09% over two years; (1.4909)^(1/2) − 1 = 22.10% a year.
Regulatory use (Chapter 8).
- The disclosure document's dynamic section (item 14) requires a discretionary portfolio manager to disclose performance indicators calculated using TWRR.
- When communicating, advertising or publishing an investment approach's performance, the portfolio manager presents its TWRR with the trailing return of the selected benchmark.
- In reports to an investor, the approach's TWRR and the benchmark's trailing return are presented separately from the investor's own XIRR.
The formula
TWRR = [(1 + R1) × (1 + R2) × … × (1 + Rn)] − 1
Rn = (EV − BV − Contribution + Withdrawal) / (BV + Contribution − Withdrawal)
Annual TWRR = (1 + TWRR)^(1/n) − 1
A worked example
Check one sub-period of the workbook's table to see the mechanism.
Second sub-period, to 04/04/20.
- Beginning value ₹1,10,000; client adds ₹20,000; ending value ₹1,45,000.
- Gain due to the manager: 1,45,000 − 1,10,000 − 20,000 = ₹15,000
- Money actually at work: 1,10,000 + 20,000 = ₹1,30,000
- Return: 15,000 ÷ 1,30,000 = 11.54%
Without the adjustment, the portfolio would appear to have risen from ₹1,10,000 to ₹1,45,000, a "return" of 31.8% — most of which was simply the client's own ₹20,000.
Third sub-period, to 30/09/20. Beginning ₹1,45,000; client withdraws ₹15,000; ending ₹1,25,000. Manager's result: 1,25,000 − 1,45,000 + 15,000 = −₹5,000 on ₹1,30,000 = −3.85%. A naive reading would call the ₹20,000 drop a 13.8% loss.
All five linked: 49.09% over two years, 22.10% a year. A second client with entirely different deposit timing in the same investment approach would see a different XIRR but the same TWRR, because TWRR describes the approach, not the client.
Why NISM asks about it
Chapter 10 (Performance Measurement and Evaluation of Portfolio Managers, 10%), section 10.1.3, carries the calculation. Chapter 8 (Operational Aspects of Portfolio Managers, 13%), sections 8.2 and 8.8, carries the regulation — TWRR in the disclosure document for discretionary portfolio managers and in all communication of an investment approach's performance. Expect a "which measure neutralises client cash flows" question and one on which measure is used for the approach versus the investor.
Common exam traps
- TWRR is for the investment approach; XIRR is for the individual investor. Chapter 8 requires both, presented separately.
- TWRR removes the effect of external cash flows; XIRR includes them.
- The workbook prints two versions of the sub-period denominator. The formula on page 147 reads "(BV − Contribution + Withdrawal)", but Step 1 and every row of the worked table use (BV + Contribution − Withdrawal). The table's numbers only reconcile with the second — use it.
- The table also shows two rows dated 30/09/20 and a final row dated 31/12/21, which is why the period is two years (01/01/2020 to 31/12/2021).
- Annualise with the nth root, not by dividing 49.09% by two (that would give 24.55%, not 22.10%).
- The limitation the workbook names is complexity of calculation — splitting into sub-periods and linking geometrically.
Check yourself
1.The main reason TWRR is preferred for evaluating portfolio managers is that it:
- a)Is the easiest return measure to calculate
- b)Neutralises the effect of investor deposits and withdrawals
- c)Includes the effect of taxes
- d)Ignores compounding
Show the answer
Answer: (b) Neutralises the effect of investor deposits and withdrawals
TWRR neutralises external cash flows, so the manager is judged purely on investment decisions — not on the timing of the investor's own flows, which it does not control.
It is actually complex to calculate — that is its stated limitation. It does not bring in taxes, and it compounds sub-period returns geometrically.
2.A portfolio's TWRR over 2 years is 49.09%. The annualised TWRR is approximately:
- a)24.55%
- b)22.10%
- c)49.09%
- d)20.00%
Show the answer
Answer: (b) 22.10%
Annual TWRR = (1 + TWRR)^(1/n) − 1 = (1.4909)^(1/2) − 1 ≈ 22.10%.
24.55% is simple division by 2 — it ignores compounding. 49.09% is the whole-period figure, not per annum.
3.Which statement about the holding period return (HPR) is correct as per the workbook?
- a)It is also called the time-weighted return and removes the effect of cash flows
- b)It assumes income distributions are received evenly through the year
- c)It is popularly known as total return or point-to-point return, and is considered the starting point of performance measurement
- d)It is rarely used because it ignores income
Show the answer
Answer: (c) It is popularly known as total return or point-to-point return, and is considered the starting point of performance measurement
The workbook calls HPR “the most straightforward rate of return … popularly known as total return or point-to-point return.” Although it “assumes that all income distributions are made at the end of the year”, it “is widely used and generally accepted” and “considered as the starting point of performance measurement exercise.”
- TWRR is the measure that neutralises external cash flows, not HPR.
- HPR assumes income arrives at the end of the year, not evenly through it.
- HPR does include income: HPR = (I + (E − B)) ÷ B.
Where this is taught
Free preparation for NISM Series XXI-BRelated terms
- CAGRThe single smoothed annual rate at which a starting value would have to grow, compounding each year, to reach the ending value over a given period.
- Holding period returnThe total of coupons, income earned on reinvesting them and any capital gain, expressed as a percentage of the purchase price — a crude return for the period actually held, with no compounding in it.
- XIRRExtended Internal Rate of Return: the annualised return on an investment with irregular cash flows, found by assigning a date to each flow. PMS reports it for each investor’s own experience.
- ReturnThe reward for postponing consumption — the difference between what an investor gives up today and the larger amount received later, measured in several ways depending on the purpose.
- BenchmarkThe independently published index a scheme's performance is measured against, chosen to match its investment objective, asset allocation and strategy, and disclosed in the Scheme Information Document.
- Investment approachA broad outlay of the securities and permissible instruments a portfolio manager will invest in for a client, set out in the PMS agreement and tagged to exactly one strategy.
- Money Weighted Rate of ReturnThe internal rate of return on an investor's actual cash flows into and out of a portfolio — so it rewards or punishes the timing of those flows, not just the manager's skill.
- Geometric Mean ReturnThe single constant yearly rate that would turn the starting value into the ending value — found by chain-linking period returns and taking the nth root.
- Wealth relativeThe ending value of one unit of money over a period — 1 plus the period's return in decimals. Multiplying wealth relatives chain-links sub-period returns into TWRR or geometric return.
- Managers universe analysisEvaluating a portfolio manager's performance by ranking it against the median portfolio of other managers running a similar investment approach, rather than only against a market index.
- Customised benchmarkA benchmark built from a portfolio manager's own investment universe, used when no market index fits the manager's strategy or style. Valid, but costly to build and maintain.
- Disclosure DocumentThe document a portfolio manager must give every prospective client with the account opening form, before the agreement is signed, and keep on its website — setting out the manager, services, risks, fees and performance.