When investing, your capital is at risk and you may get back less than invested. Past performance doesn’t guarantee future results.
Money-Weighted Rate of Return (MWRR) vs Time-Weighted Rate of Return (TWRR)
Not all investment returns are created equal, especially when money moving in and out over time is involved. Imagine you invest £10,000 in a fund, you add another £5,000 six months later, then withdraw £1,000 a year after that.
How do you measure your true return, considering the impact of these cash flows? Enter the Money-Weighted Rate of Return (MWRR).
Alternatively, how would you ignore such cash flows? That would be Time-Weighted Return (TWRR).
How do you measure your true return, considering the impact of these cash flows? Enter the Money-Weighted Rate of Return (MWRR).
Alternatively, how would you ignore such cash flows? That would be Time-Weighted Return (TWRR).
MWRR DEFINITION
MWRR measures investment performance by taking into account both the timing and amount of cash flows into and out of the investment. It reflects the actual return experienced by the investor, based on when money was contributed or withdrawn.
TWRR DEFINITION
TWRR measures investment performance by eliminating the impact of cash flows. It calculates the return for each sub-period between cash flows and then compounds them, providing a clear view of how the investment itself performed, regardless of investor behaviour.
Big ideas
- There are many formulas that calculate investment performance. MWRR is differentiated by its inclusion of cash flow size and timings, such as dividends, withdrawals, deposits, sale proceeds, etc. TWRR isolates such things to de-emphasize them.
- The MWRR figure is the Present Value (PV) of all cash flows of the initial investment. It is equivalent to the Internal Rate of Return (IRR) in the sense that they both measure the compounded rate of return that equates all cash inflows and outflows to a final value.
- The calculation is useful in the determination of the required investment to get started, taking into account all cash flow changes. It is highly applicable to any portfolio with irregular cash flows, particularly investor portfolios.
What is the Money-Weighted Rate of Return?
The MWRR assesses the performance of a portfolio in instances where cash flows are irregular. It can be used by investors who frequently change their contributions and withdrawals. It can also account for fluctuations in dividend-paying stocks and bonds with variable interest rates.
It is the discount rate where the PV is equal to 0. The PV of inflows must balance the PV of outflows.
Of course, all of this depends on an accurate analysis of portfolio inflows and outflows, and it can be time-consuming to collect the data and run the analysis. This is a drawback of the MWRR.
The formula is closely related to the IRR concept found in project finance, which identifies the discount rate that represents the PV of future cash flows. If the IRR is more than the required rate of return, it is considered a solid investment. The XIRR function in Excel can be used to calculate the MWRR.
Of course, all of this depends on an accurate analysis of portfolio inflows and outflows, and it can be time-consuming to collect the data and run the analysis. This is a drawback of the MWRR.
The formula is closely related to the IRR concept found in project finance, which identifies the discount rate that represents the PV of future cash flows. If the IRR is more than the required rate of return, it is considered a solid investment. The XIRR function in Excel can be used to calculate the MWRR.
What is the difference between TWRR and MWRR?
The TWRR and the MWRR measure investment performance differently.
TWRR eliminates the impact of external cash flows, making it ideal for comparing fund managers. It breaks the investment period into sub-periods, calculates returns for each, and links them. This ensures deposits and withdrawals do not distort performance.
MWRR assigns more weight to periods when larger amounts of capital are invested. It measures the actual return an investor experiences, factoring in when money was added or withdrawn.
📈 If an investor increases capital before strong returns, MWRR will be higher.
📉 If money is added into an investment before a decline, MWRR will be lower.
TWRR is best for evaluating fund managers since it isolates investment decisions. MWRR is more relevant for investors managing their own capital, as it reflects real gains or losses based on cash flow timing.
When cash flows are small, both measures give similar results. If cash flows are large, the difference can be significant.
TWRR eliminates the impact of external cash flows, making it ideal for comparing fund managers. It breaks the investment period into sub-periods, calculates returns for each, and links them. This ensures deposits and withdrawals do not distort performance.
MWRR assigns more weight to periods when larger amounts of capital are invested. It measures the actual return an investor experiences, factoring in when money was added or withdrawn.
📈 If an investor increases capital before strong returns, MWRR will be higher.
📉 If money is added into an investment before a decline, MWRR will be lower.
TWRR is best for evaluating fund managers since it isolates investment decisions. MWRR is more relevant for investors managing their own capital, as it reflects real gains or losses based on cash flow timing.
When cash flows are small, both measures give similar results. If cash flows are large, the difference can be significant.
Exploring the MWRR formula
The MWRR formula is the same one used to calculate the IRR. The MWRR measures investment performance while accounting for the timing and size of cash flows. It finds the discount rate that equates the present value of all inflows and outflows to zero.
FORMULA
Σ [Cₜ ÷ (1 + r)⁽ᵗ⁾] = 0
Where:
• C represents cash flows (negative for investments, positive for the final value).
• t represents the time in years (fractional for mid-year deposits).
• r is the unknown return.
Where:
• C represents cash flows (negative for investments, positive for the final value).
• t represents the time in years (fractional for mid-year deposits).
• r is the unknown return.
This method gives more weight to periods with larger capital, making it sensitive to deposits and withdrawals.
MWRR is widely used for portfolios with irregular cash flows, private equity, and personal investments. Again, it reflects the investor’s real return based on actual money invested and withdrawn.
MWRR is widely used for portfolios with irregular cash flows, private equity, and personal investments. Again, it reflects the investor’s real return based on actual money invested and withdrawn.
MWRR example
The following is a simple MWRR example with a single investment after a 6 month period, with time expressed as a fraction for mid-year deposits, quarterly deposits, etc.
Since there is no direct algebraic solution for r, it must be solved numerically (by using Excel’s XIRR function, a financial calculator or by trial-and-error).
Using numerical methods, we find:
Since there is no direct algebraic solution for r, it must be solved numerically (by using Excel’s XIRR function, a financial calculator or by trial-and-error).
Using numerical methods, we find:
FORMULA
John invests £1,000 at the start of the year. After six months, he adds £500.
By year-end, his portfolio grows to £1,700.
The MWRR is found by solving for r using:
1000 × (1 + r)ᵗ + 500 × (1 + r)⁰⋅⁵ = 1700
Solving numerically, r ≈ 13.43%, meaning John’s investments earned an annualized return of 13.43%.
Past performance is no guarantee of future results. This information is not investment advice. Do your own research. The calculations are hypothetical and intended solely for educational use.
By year-end, his portfolio grows to £1,700.
The MWRR is found by solving for r using:
1000 × (1 + r)ᵗ + 500 × (1 + r)⁰⋅⁵ = 1700
Solving numerically, r ≈ 13.43%, meaning John’s investments earned an annualized return of 13.43%.
Past performance is no guarantee of future results. This information is not investment advice. Do your own research. The calculations are hypothetical and intended solely for educational use.
TWRR example
In most cases, the TWRR is easier to compute than the MWRR, as it does not account for cash flows in the same way. It takes investor actions out of the equation, which simplifies matters.
FORMULA
An investor tracks the TWRR of a UK equity fund.
The fund starts with £100,000. After one year, it gains 10%, reaching £110,000.
The investor then adds £20,000, making the total £130,000.
In the second year, the fund drops 5%, ending at £123,500.
TWRR calculates the return for each period separately and links them:
TWRR = ((1 + R₁) × (1 + R₂) × ⋯ × (1 + Rₙ))¹⁄ⁿ − 1 = (1 + 0.10) × (1 − 0.05) − 1 = 4.5%
The final return is 4.5%, showing the fund’s performance without the effect of additional capital. Note that the investor deposit of £20,000 made no difference to the TWRR.
Past performance is no guarantee of future results. This information is not investment advice. Do your own research. The calculations are hypothetical and intended solely for educational use.
The fund starts with £100,000. After one year, it gains 10%, reaching £110,000.
The investor then adds £20,000, making the total £130,000.
In the second year, the fund drops 5%, ending at £123,500.
TWRR calculates the return for each period separately and links them:
TWRR = ((1 + R₁) × (1 + R₂) × ⋯ × (1 + Rₙ))¹⁄ⁿ − 1 = (1 + 0.10) × (1 − 0.05) − 1 = 4.5%
The final return is 4.5%, showing the fund’s performance without the effect of additional capital. Note that the investor deposit of £20,000 made no difference to the TWRR.
Past performance is no guarantee of future results. This information is not investment advice. Do your own research. The calculations are hypothetical and intended solely for educational use.
How cash flows affect fund performance
The MWRR depends on both investment performance and cash flow timing. Large contributions during strong growth periods increase MWRR, while withdrawals in good years can reduce it. The opposite is true during downturns — investing more before losses will drag the return down, while pulling money out early can improve it. Think about this:
EXAMPLE
If an investor puts £50,000 into a fund, it grows by 20%, and then they add another £50,000, the return on the second half benefits less from past gains. If the market then drops 10%, the overall MWRR could be much lower than the fund’s time-weighted return.
Past performance is no guarantee of future results. This information is not investment advice. Do your own research. The calculations are hypothetical and intended solely for educational use.
Past performance is no guarantee of future results. This information is not investment advice. Do your own research. The calculations are hypothetical and intended solely for educational use.
Since MWRR reflects personal investment choices, it varies from investor to investor, even within the same fund. This makes it useful for assessing individual portfolio performance but less ideal for comparing fund managers or benchmarks.
Because it gives more weight to periods with larger capital, investors with different cash flow timing can report very different MWRRs, even with the same underlying asset performance.
Because it gives more weight to periods with larger capital, investors with different cash flow timing can report very different MWRRs, even with the same underlying asset performance.
Pros of using the MWRR
- Reflects actual investor experience – MWRR accounts for the impact of deposits and withdrawals, showing the real return an investor earns. It captures how timing decisions affect overall performance, making it useful for personal portfolios.
- Considers cash flow timing – since MWRR includes the effect of when money is added or withdrawn, it provides a better picture of how capital allocation decisions impact returns. This is important for investors managing their own funds.
- Useful for private portfolios – investors who control their own contributions and withdrawals benefit from MWRR because it tells them whether their decisions helped or hurt overall performance. It measures the real growth of invested capital.
- Easier to relate to performance – unlike TWRR, which isolates investment returns from cash flows, MWRR shows the return based on actual money invested. This makes it easier to connect the result with financial outcomes.
Cons of using the MWRR
- Sensitive to large cash flows – MWRR can change significantly if an investor adds or withdraws money at the wrong time. If a large deposit is made before a market drop, it will lower the return even if the investment performs well later.
- Not Ideal for comparing fund managers – Since MWRR is influenced by investor cash flows, it does not reflect the skill of a portfolio manager. It may show different returns for the same strategy depending on when deposits and withdrawals occur.
- Difficult to use for benchmarking – MWRR is harder to compare across funds or portfolios because each investor has different cash flow timing. This makes it less useful for evaluating funds with multiple investors.
- More complex to calculate – Unlike TWRR, which follows a simple formula, MWRR requires solving for the IRR. This can be challenging without software or financial tools.
Recap
The MWRR is an excellent way to capture fund performance where cash flows are irregular, making it useful for dividend-paying stocks, variable-rate bonds, and investor portfolio returns. It is equivalent to the IRR, handy for those adept at using that formula already. A major consideration before using it is that cash flows need to be accurate for the formula to work.
Generally, though not always, an investment with a higher MWRR is a better option than one with a smaller MWRR. It is especially useful for personal portfolios, but applies to all investments that are subject to cash flows.
TWRR is a better way to measure fund manager performance because the main objective is to judge how well the FM is choosing investments, not any one investor’s decisions (in the form of inflows/outflows). While the TWRR is a clearer assessment of investment performance, MWRR represents the actual investor experience.
Generally, though not always, an investment with a higher MWRR is a better option than one with a smaller MWRR. It is especially useful for personal portfolios, but applies to all investments that are subject to cash flows.
TWRR is a better way to measure fund manager performance because the main objective is to judge how well the FM is choosing investments, not any one investor’s decisions (in the form of inflows/outflows). While the TWRR is a clearer assessment of investment performance, MWRR represents the actual investor experience.
FAQ
Q: What is the money-weighted interest rate?
The money-weighted interest rate is the rate of return that accounts for the timing and amount of cash flows in an investment. It is the Internal Rate of Return (IRR) of all cash flows, including contributions and withdrawals. This measure gives more weight to periods when more money is invested. If an investor adds capital before a strong performance, the return will be higher than if they invest before a decline.
Q: Is IRR money-weighted?
Yes, IRR is a money-weighted measure of return. It reflects the impact of cash flow timing and size on overall performance. Since IRR accounts for when money enters or exits an investment, it differs from time-weighted returns, which ignore external cash flows. This makes IRR useful for evaluating portfolios where an investor has control over contributions and withdrawals.
Q: Is time-weighted return the same as CAGR?
No, time-weighted return and CAGR are different. Time-weighted return removes the effect of cash flows by breaking returns into sub-periods and linking them. CAGR assumes a constant annual growth rate over time. CAGR is simpler but can be misleading if cash flows vary. Time-weighted return is more useful for comparing portfolio managers since it reflects their actual investment skills.
Q: What is the cumulative time-weighted return?
Cumulative time-weighted return is the total return of an investment over a given period, ignoring the effect of cash flows. It is calculated by multiplying the returns of each sub-period together. This method ensures that periods with larger investments do not disproportionately affect the final result. It is commonly used to assess long-term performance without distortions from external cash movements.
Q: What is the difference between Time-Weighted and Money-Weighted Rate of Return?
The key difference is how they handle cash flows. TWRR ignores deposits and withdrawals, isolating the investment manager’s performance. MWRR, or IRR, includes cash flow timing and size, showing the investor’s actual experience. If cash flows are significant and poorly timed, money-weighted return can differ sharply from time-weighted return.
Q: Is there any difference between IRR and MWRR?
No, there is no difference in the underlying calculation method. MWRR (Money-Weighted Rate of Return) is simply another name for IRR (Internal Rate of Return) when applied to investment portfolios. Both represent the discount rate that sets the NPV (Net Present Value) of all cash flows, including deposits, withdrawals, and the final value, to zero.
Since they account for both the timing and size of cash flows, the IRR/MWRR reflects the actual return experienced by the investor. This means that:
• A high return during periods when the portfolio holds more capital will have a greater impact on the overall IRR/MWRR.
• Similarly, losses during high-capital periods can significantly lower the return.
Since they account for both the timing and size of cash flows, the IRR/MWRR reflects the actual return experienced by the investor. This means that:
• A high return during periods when the portfolio holds more capital will have a greater impact on the overall IRR/MWRR.
• Similarly, losses during high-capital periods can significantly lower the return.
