Money Weighted Rate of Return
Also written MWRR · Money-weighted rate of return (MWRR) · Money weighted return
The 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.
In plain language
An investor rarely puts in one lump sum and leaves it. Money goes in over several years, and sometimes comes out. The money-weighted rate of return asks: given exactly when this investor put money in and took it out, what single annual rate did their money earn?
It is the internal rate of return (IRR) of those cash flows. Because larger sums get more weight, a good year that happens to fall when the investor had the most money invested lifts the MWRR a lot; the same good year with little money in barely moves it.
That makes MWRR the right answer to "how did my money do?" and the wrong answer to "how good is the manager?"
How it works
The workbook's illustration uses one set of five annual returns — −5.00%, −15.20%, 8.10%, 30.75%, 17.65% — and a total of ₹75,000 contributed at the start of each year.
| Contribution pattern | Ending value | MWRR |
|---|---|---|
| ₹5,000 → ₹10,000 → ₹15,000 → ₹20,000 → ₹25,000 | ₹1,05,920.31 | 15.15% |
| ₹25,000 → ₹20,000 → ₹15,000 → ₹10,000 → ₹5,000 | ₹1,07,900.97 | 10.21% |
Same returns, same total contributed, and yet the MWRR differs by almost five percentage points — purely because of when the money arrived. In the first pattern most of the money was invested for the two strong final years.
The time-weighted rate of return on those same returns is 6.021% in both cases, because TWRR strips out the effect of cash flows.
The formula
MWRR is the rate r that makes the present value of all contributions equal the present value of the ending value (and any withdrawals):
C₀ + C₁/(1+r) + C₂/(1+r)² + … = V_n/(1+r)^n
It has no closed-form solution; solve it with a financial calculator or the spreadsheet IRR function. For irregular dates, the spreadsheet XIRR function is used.
A worked example
The workbook's Chapter 20 caselet, in lakh rupees. An investor puts ₹50 lakh into a PMS, then ₹45 lakh, ₹35 lakh, ₹60 lakh and ₹50 lakh at the start of years 2 to 5. Net returns after all charges are 15%, 12%, −10%, −8%, 25%.
| Year | Opening + new money | Return | Closing value |
|---|---|---|---|
| 1 | 50.00 | +15% | 57.50 |
| 2 | 57.50 + 45 = 102.50 | +12% | 114.80 |
| 3 | 114.80 + 35 = 149.80 | −10% | 134.82 |
| 4 | 134.82 + 60 = 194.82 | −8% | 179.23 |
| 5 | 179.23 + 50 = 229.23 | +25% | 286.54 |
Solve the IRR of −50, −45, −35, −60, −50 and +286.54: MWRR = 6.09%.
For comparison, on the same data the workbook gives TWRR = 5.92% and a simple arithmetic average = 6.80%. The investor's MWRR is higher than TWRR here because the largest balance of the whole period — ₹229.23 lakh — happened to be invested in the best year, the final +25%.
Why NISM asks about it
Chapter 20 (Performance Measurement and Evaluation of Portfolio Managers), section 20.2.2, contrasts MWRR with TWRR using the two contribution patterns above, and the Chapter 20 caselets ask for MWRR, TWRR and the arithmetic mean on one data set. Section 20.7 adds the regulatory angle: when reporting to an investor, a portfolio manager presents the XIRR for each investment approach the investor is in, alongside the approach's TWRR and the benchmark's trailing return.
Common exam traps
- MWRR depends on cash-flow timing; TWRR does not. Reversing the contribution order changed MWRR from 15.15% to 10.21% while TWRR stayed at 6.021%.
- MWRR is the IRR — the workbook uses the two terms interchangeably.
- Use TWRR to judge the manager, because the manager does not control when the client adds or withdraws money. GIPS and the SEBI regulations both require TWRR for presenting a manager's performance.
- Use MWRR (XIRR) to tell an investor what their own money earned. The two numbers differing is not an error.
- In a spreadsheet, contributions go in as negative cash flows and the final value as positive; getting the signs wrong makes IRR fail or return nonsense.
Check yourself
1.Which return measure removes the effect of external cash flows made by the client and best reflects the portfolio manager's ability?
- a)Money-weighted rate of return
- b)Time-weighted rate of return
- c)Arithmetic mean return
- d)Holding period return
Show the answer
Answer: (b) Time-weighted rate of return
The GIPS glossary defines TWRR as a calculation that computes period-by-period returns and removes the effects of external cash flows, which "best reflects the portfolio manager's ability".
MWRR is the IRR and depends on the timing of cash flows — the workbook shows it moving from 15.15% to 10.21% just by reversing the order of contributions. The arithmetic mean ignores compounding. HPR is a single-period measure that assumes income at year end.
2.An investor puts ₹50 lakh into a PMS, then adds ₹45 lakh, ₹35 lakh, ₹60 lakh and ₹50 lakh at the start of the following years. Net annual returns are 15%, 12%, −10%, −8% and 25%. What is the annualised time-weighted rate of return?
- a)5.92%
- b)6.09%
- c)6.80%
- d)13.84%
Show the answer
Answer: (a) 5.92%
TWRR ignores the contributions and chain-links the returns:
[(1.15 × 1.12 × 0.90 × 0.92 × 1.25)^(1/5)] − 1 = (1.3331)^(0.2) − 1 = 5.92%.
6.09% is the MWRR (IRR) on the same data — it differs because it weights each year by the money invested at the time. 6.80% is the arithmetic average (34 ÷ 5). Three different "averages" from one set of numbers — the exam loves this.
Where this is taught
Free preparation for NISM Series XXI-BRelated terms
- 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.
- Arithmetic Mean ReturnThe simple average of a series of period returns. It is the best single guess for next year, but it overstates what a multi-year investment actually grew at.
- 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.
- Time Weighted Rate of ReturnA 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.
- GIPSGlobal Investment Performance Standards — voluntary ethical standards, owned by CFA Institute, for calculating and presenting investment performance on the principles of fair representation and full disclosure.
- Gross IRRAn AIF's IRR computed on fund-level cash flows before management fees, incentive fees, fund expenses and taxes — the return the portfolio earned, not the return investors kept.
- 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.