Performance measurement - Money- and time-weighted returns

Learning Outcomes

This article explains money-weighted and time-weighted portfolio returns within performance measurement, including:

• Clearly defining money-weighted return (MWR) and time-weighted return (TWR) and linking them to IRR and compounded growth rates in an exam context
• Calculating MWR as an internal rate of return for portfolios with multiple external cash flows, using calculator or spreadsheet functions and interpreting the solution
• Calculating TWR by segmenting the total horizon into valuation sub-periods, computing each sub-period return, and geometrically linking them to obtain an annualized rate
• Distinguishing internal versus external cash flows, classifying typical transaction types correctly, and understanding how each affects MWR and TWR
• Interpreting why MWR reflects the investor’s actual dollar-weighted experience, while TWR isolates manager skill and facilitates fair comparison with benchmarks and peer managers
• Choosing the appropriate metric (MWR versus TWR) in common CFA Level 3 private-wealth and institutional scenarios, and clearly justifying that choice in written responses
• Reconciling situations where MWR and TWR diverge materially, explaining the role of large, poorly timed cash flows, and identifying common pitfalls such as misclassifying flows or averaging sub-period returns incorrectly

CFA Level 3 Syllabus

For the CFA Level 3 exam, you are required to understand performance measurement techniques essential for manager evaluation, with a focus on the following syllabus points:

• Comparing and contrasting money-weighted return and time-weighted return
• Calculating MWR (IRR) and TWR with multiple cash flows and valuation dates
• Judging when each measure is appropriate for evaluating portfolio managers versus investor decisions
• Explaining the limitations and strengths of each metric in portfolio and manager evaluation contexts
• Applying MWR and TWR within broader performance appraisal, attribution, and benchmarking discussions

Test Your Knowledge

Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision.

1. A private client directs all contributions and withdrawals, while the manager only selects securities. Which performance measure best isolates the manager’s skill?
   1. Money-weighted return, because it incorporates the investor’s timing decisions
   2. Time-weighted return, because it neutralizes the investor’s timing decisions
   3. Money-weighted return, because it is easier to compute from account statements
   4. Arithmetic average return, because it is not distorted by compounding

2. A portfolio has the following annual data (all cash flows at year-end):
   Year 0: Beginning value $1,000 (no cash flow)
   Year 1: Ending value $1,080 and contribution $500
   Year 2: Ending value $1,900 (no cash flow)
   Which approach correctly computes the time-weighted return over the two-year period?
   a) Compute IRR on all cash flows over two years
   b) Treat the contribution as return and calculate one two-year holding-period return
   c) Compute a sub-period return for Year 1 excluding the $500, then another for Year 2, and link them
   d) Average the two annual money-weighted returns arithmetically

3. An investor contributes a very large sum just before an equity market crash. The manager’s security selection is in line with the benchmark. Which statement is most accurate?
   1. MWR will likely understate manager skill because it reflects the poorly timed contribution
   2. TWR will likely understate manager skill because it reflects the poorly timed contribution
   3. MWR and TWR will both be unaffected by the contribution timing
   4. TWR will equal MWR because the benchmark performed similarly
4. A consultant is comparing three global equity managers who all run open-ended funds with frequent investor cash flows that they do not control. Which performance measure is most appropriate for ranking these managers?
   1. Money-weighted returns over the last three years
   2. Time-weighted returns over the last three years
   3. Total dollar profit over the last three years
   4. Average account balances over the last three years

Introduction

Performance measurement is a core skill in portfolio management. For the CFA Level 3 exam and in real-world analysis, it is essential to distinguish between money-weighted returns (MWR) and time-weighted returns (TWR). Selecting the wrong metric can lead to incorrect conclusions about investor experience and, more critically for Level 3, about manager skill.

Two viewpoints are intertwined:

• The investor viewpoint: “How did my wealth actually grow, taking into account when I added or withdrew money?”
• The manager viewpoint: “How well did the assets I controlled perform, irrespective of when the client chose to contribute or withdraw?”

MWR is aligned with the investor viewpoint, while TWR is aligned with the manager viewpoint. Level 3 exam questions frequently ask you to justify which return should be used in a given scenario, not just to perform the calculation.

Key Term: money-weighted return (MWR)
The internal rate of return (IRR) for a series of portfolio cash flows, equating the present value of all external cash flows and the terminal value to zero. It reflects both investment performance and the timing and amount of external cash flows.

Key Term: time-weighted return (TWR)
A measure of portfolio performance that removes the effect of external cash flows by breaking the total period into sub-periods between cash flows, computing each sub-period return, and geometrically linking them. It measures compounded growth of the portfolio as if the manager controlled all cash flows.

Key Term: external cash flow
Any deposit into or withdrawal from the portfolio that is not generated by the investment process itself (for example, contributions, withdrawals, transfers). These flows are usually controlled by the investor rather than the manager.

Key Term: internal rate of return (IRR)
The discount rate that sets the net present value of all cash flows (including the terminal value) equal to zero. In portfolio performance, IRR is used synonymously with money-weighted return.

The remainder of this article deepens each concept, walks through worked examples, and then focuses on how to select and justify the appropriate measure in exam-style situations.

MONEY-WEIGHTED RETURN (MWR): DEFINITION AND USES

The money-weighted rate of return, also called the IRR, evaluates total portfolio performance, reflecting the size and timing of all external cash flows. It is especially relevant when the investor decides when to add or withdraw funds, because it captures the compounded growth of the investor’s actual money in the portfolio.

The MWR is the rate $r$ that satisfies:

where:

• $CF_t$ = net cash flow at time $t$ (defined from the investor’s viewpoint)
  • Cash invested into the portfolio: negative
  • Cash received from the portfolio at the end (including ending market value if liquidated): positive

Time $t$ can be measured in years, months, or fractions of a year; the resulting $r$ is then an annual, monthly, or appropriately scaled rate, which you may need to annualize.

Interpretation and intuition

Conceptually, MWR answers: “What single rate of return applied to my actual cash flows would reproduce my final wealth?” It combines:

• Asset performance, and
• The effect of when and how much the investor chose to invest or withdraw.

If the investor increases exposure just before a strong market, MWR will be higher than TWR. If the investor adds a lot right before a downturn, MWR will be punished, even if the manager’s security selection was sound.

Calculation approach

In practice, MWR is found using:

• Financial calculator IRR functions, or
• Spreadsheet IRR or XIRR functions (for irregular timing), or
• Algebraic solution if there are only one or two unknowns and simple structure.

For exam purposes, you may be given sufficient information to solve directly or to approximate using trial-and-error.

Worked Example 1.1

An investor deposits $100,000 at the start of Year 1. At the start of Year 2, she deposits another $20,000. At the end of Year 2, the account is worth $130,000. What is the money-weighted return?

Answer:
Set up the IRR equation treating cash invested as negative and the final value as positive. At $t = 0$, $CF_0 = -100{,}000$; at $t = 1$, $CF_1 = -20{,}000$; at $t = 2$, $CF_2 = +130{,}000$. Solve:

$$-100{,}000 + \frac{-20{,}000}{(1+r)} + \frac{130{,}000}{(1+r)^2} = 0$$

Rearranging:

$$130{,}000 = 100{,}000(1+r)^2 + 20{,}000(1+r)$$

This is a quadratic in $(1+r)$. Solving yields $r \approx 4.6\%$ per annum. This is the investor’s money-weighted return over the two-year horizon.

Notice that the investor added capital after the first year; the return is therefore an outcome of both the portfolio performance and this contribution timing.

Strengths and limitations of MWR

• Strengths:

  • Directly reflects the investor’s actual experience with the account.
  • Appropriate when the investor controls external cash flows and wishes to evaluate whether their combined decisions (manager plus timing) met their objectives.
  • Required for asset classes where cash flows are a key part of the investment decision, such as private equity, real estate, or infrastructure, where managers also influence the timing of capital calls and distributions.

• Limitations:

  • Highly sensitive to timing and size of external cash flows. Large, poorly timed contributions or withdrawals can dominate the result.
  • Not suitable for comparing managers, because two managers with the same asset performance but different client cash-flow patterns will show different MWRs.
  • When there are multiple sign changes in the cash-flow series (e.g., multiple switches between net inflows and outflows), the IRR equation can have multiple solutions or no economically meaningful solution. This is rarely examined explicitly but is a fundamental conceptual limitation.

When is MWR appropriate

In CFA Level 3 contexts, MWR is generally appropriate for:

• Measuring the performance of a single investor’s strategy, including their timing decisions
• Evaluating illiquid investments where the manager controls capital calls and distributions (private equity, certain real estate mandates)
• Situations where the objective is to assess whether the investment met required return targets for the investor’s plan (e.g., did the portfolio meet a 5% required return including the investor’s additions and withdrawals?)

By contrast, it is not the primary measure for comparing external managers on a like-for-like basis.

Worked Example 1.2

A client invests $1,000,000 on 1 January. The manager earns +10% during the first year. On 1 January of Year 2, impressed by the performance, the client adds $4,000,000. During Year 2, the market falls and the portfolio loses 20%. At the end of Year 2, what is the MWR over the full two-year period? Comment on manager evaluation.

Answer:
At $t=0$: $CF_0 = -1{,}000{,}000$.
After Year 1, portfolio value = $1,000,000 × 1.10 = $1,100,000.
At $t=1$: client contributes $4,000,000, so $CF_1 = -4{,}000{,}000$, and the new invested amount is $5,100,000.
Year 2 return is −20%, so ending value at $t=2$ is $5,100,000 × 0.80 = $4,080,000.
The IRR equation is:

$$-1{,}000{,}000 + \frac{-4{,}000{,}000}{(1+r)} + \frac{4{,}080{,}000}{(1+r)^2} = 0$$

Solving this quadratic yields $r \approx -9.9\%$ per year over the two-year period.

Despite the manager delivering +10% then −20% (similar to the market), the MWR is strongly negative because most of the client’s capital was invested just before the downturn. MWR therefore penalizes the timing of the client’s own decision, not the manager’s asset selection. For evaluating manager skill, this result would be misleading; TWR is more appropriate.

This kind of example is typical of exam questions where you must explain why a low MWR does not necessarily imply poor manager performance.

TIME-WEIGHTED RETURN (TWR): DEFINITION AND USES

The time-weighted rate of return eliminates the effect of the timing and size of external cash flows. The idea is to evaluate the manager as if they had full discretion over the portfolio at all times and did not receive or pay out client cash during sub-periods.

To compute TWR:

• Break the total investment period into sub-periods whenever significant external cash flows occur or whenever the portfolio is valued.
• Compute the return $r_i$ for each sub-period using beginning market value and ending market value before the external cash flow.
• Geometrically link (compound) the sub-period returns.

If the sub-period returns are $r_1, r_2, \ldots, r_n$, then:

In the continuous compounding language, TWR is essentially the geometric mean of the sequence of sub-period returns.

Sub-period returns and cash flow treatment

For each sub-period:

• Sub-period return: $$r_i = \frac{V_{\text{end, pre-flow}} - V_{\text{begin}}}{V_{\text{begin}}}$$
• External cash flows at the end of the sub-period do not affect that sub-period’s return; they simply change the starting value of the next sub-period.

In practice, for daily valued portfolios, TWR is often computed using daily returns and then linked over the month, quarter, or year.

Why TWR is preferred for manager evaluation

Because TWR removes the effect of when the client sends or withdraws money, it aligns with the question: “How did the assets perform under the manager’s control?” That is why TWR is the standard measure for:

• Comparing managers
• Comparing a manager to a benchmark
• Assessing value added in performance attribution

Even if a client made poor timing decisions, TWR shows what would have happened to any dollar invested continuously with the manager.

Worked Example 1.3

A portfolio is worth $50,000 at the start of the year. At the end of 6 months, after earning $3,000 in investment gains, the owner adds $10,000. By the year’s end, the account is worth $66,000. Calculate the time-weighted and money-weighted returns.

Answer:
First compute the time-weighted return.

At the 6‑month point, before the contribution, the value is $50,000 + $3,000 = $53,000.

• Sub-period 1 (Jan–Jun): $$r_1 = \frac{53{,}000 - 50{,}000}{50{,}000} = 0.06 \text{ or } 6\%$$ The investor then contributes $10,000, so the value immediately after the contribution is $53,000 + $10,000 = $63,000.
• Sub-period 2 (Jul–Dec): $$r_2 = \frac{66{,}000 - 63{,}000}{63{,}000} \approx 0.0476 \text{ or } 4.76\%$$

Now link the sub-period returns:

$$TWR = (1.06)(1.0476) - 1 \approx 0.115 \text{ or } 11.5\%$$

For the money-weighted return, treat cash flows from the investor’s viewpoint. At $t=0$, $CF_0 = -50{,}000$; at $t=0.5$, $CF_{0.5} = -10{,}000$; at $t=1$, $CF_1 = +66{,}000$. Solve:

$$-50{,}000 + \frac{-10{,}000}{(1+r)^{0.5}} + \frac{66{,}000}{(1+r)} = 0$$

Using a financial calculator or spreadsheet, the IRR is approximately $r \approx 10.7\%$ over the year.

The difference between 11.5% (TWR) and 10.7% (MWR) reflects the fact that the additional $10,000 earned only the second-period return, not the first-period return.

This example illustrates a key idea: when contributions are made after strong performance, MWR will often be lower than TWR because the new money misses the earlier gains.

Worked Example 1.4

A portfolio is valued quarterly. The following data are available (all contributions occur at quarter-end):

• Beginning of Q1: $200,000
• End of Q1 before contribution: $210,000; contribution $40,000
• End of Q2 before contribution: $250,000; withdrawal $30,000
• End of Q3 before contribution: $210,000; no cash flow
• End of Q4 (year-end): $230,000; no cash flow

Compute the annual TWR.

Answer:
First compute each quarter’s return before the external cash flow at quarter-end.

• Q1: $$r_1 = \frac{210{,}000 - 200{,}000}{200{,}000} = 0.05 \text{ or } 5\%$$ After a $40,000 contribution, starting value for Q2 is $250,000.
• Q2: $$r_2 = \frac{250{,}000 - 250{,}000}{250{,}000} = 0$$ The portfolio did not change before the $30,000 withdrawal; starting value for Q3 is $220,000.
• Q3: $$r_3 = \frac{210{,}000 - 220{,}000}{220{,}000} \approx -0.0455 \text{ or } -4.55\%$$ There is no cash flow at quarter-end; starting value for Q4 is $210,000.
• Q4: $$r_4 = \frac{230{,}000 - 210{,}000}{210{,}000} \approx 0.0952 \text{ or } 9.52\%$$

Link the four quarterly returns:

$$TWR = (1.05)(1.00)(0.9545)(1.0952) - 1 \approx 0.097 \text{ or } 9.7\%$$

This 9.7% is the manager’s time-weighted annual performance, independent of the investor’s quarterly contribution and withdrawal decisions.

Note that the size and timing of the $40,000 contribution and $30,000 withdrawal do not affect the TWR; only the path of market values between those flows matters.

COMPARISON AND APPROPRIATE APPLICATIONS

MWR and TWR are both valid return measures, but they answer different questions. Level 3 questions often require you not only to compute them, but also to evaluate which is appropriate, explain discrepancies, or criticize an evaluation that used the wrong metric.

Conceptual comparison

• Sensitivity to cash flows:

  • MWR: Explicitly incorporates external cash flows and their timing.
  • TWR: Neutralizes external cash flows by design.

• Viewpoint:

  • MWR: Investor-centric; reflects actual dollar-weighted experience.
  • TWR: Manager-centric; reflects performance of assets under management.

• Use in manager comparison:

  • MWR: Poor for comparing different managers or accounts with different cash-flow patterns.
  • TWR: Suitable for comparing managers, strategies, and benchmarks.

• Data requirements:

  • MWR: Requires cash-flow amounts and dates; does not require frequent portfolio valuations.
  • TWR: Requires portfolio values at every cash-flow date (or at least at regular intervals to approximate). This can be difficult for illiquid or infrequently priced assets.

Exam-relevant guidance on application

• When the investor controls cash flows (typical private wealth account):

  • Use TWR to assess manager skill.
  • Use MWR to describe the client’s experience and evaluate progress toward their required return.

• When the manager controls cash flows (e.g., private equity fund with capital calls and distributions):

  • MWR becomes more appropriate for evaluating the manager, because timing decisions are part of the strategy.
  • TWR may be impractical due to infrequent, subjective valuations.

• When comparing managers or strategies in an institutional setting:

  • TWR is the standard. Using MWR can unfairly penalize or reward managers based on client-driven flows.

• When regulatory or professional standards apply:

  • Global performance standards (such as those referenced in the curriculum) generally require time-weighted returns for composite reporting where the manager does not control external flows, reinforcing the principle that TWR is the fair measure of manager skill.

Impact of large, poorly timed cash flows

Exam Warning

If the investor controls the timing and size of cash flows, large deposits made just before a market decline can produce a poor MWR—even if the manager performed well on constituent assets. In such cases, MWR is not an appropriate basis for comparing the manager to a benchmark or to other managers. Always use TWR to fairly compare manager skill.

From a Level 3 exam standpoint, you might be asked to:

• Explain why a manager’s underperformance judged by MWR is misleading relative to TWR
• Recommend TWR for manager evaluation and MWR for planning discussions with the client
• Diagnose whether poor performance was due to manager choices or client timing based on the two metrics

Practical pitfalls and exam traps

• Misclassifying cash flows:
  Dividends, interest, and realized gains reinvested in the portfolio are internal cash flows and should not be treated as external contributions. Only deposits and withdrawals initiated by the investor (or transfers between accounts) are external.

• Incorrect sub-period breakpoints:
  For TWR, you must break the period at each external cash flow. Failing to do so effectively mixes contributions with investment return and biases the result.

• Averaging returns incorrectly:
  Annualizing returns by taking an arithmetic average of sub-period returns is incorrect for TWR; you must use geometric linking. The same caution applies when linking multi-year TWRs.

• Interpreting small differences:
  When external cash flows are small or evenly spread, MWR and TWR will be very close. On exams, large differences usually signal material timing effects that you should discuss.

Revision Tip

TWR is always required when manager performance is being compared across accounts or time periods in CFA exam questions, unless the problem explicitly states that the manager controls the timing of all external cash flows.

Summary

Money-weighted returns (IRR) reflect the actual investor experience, including the impact of external contributions and withdrawals and their timing. Time-weighted returns measure the performance of the portfolio assets by neutralizing these cash flows and are therefore the appropriate basis for evaluating and comparing managers and strategies when the investor controls cash flows.

For Level 3, strong answers go beyond calculation:

• Justify why TWR is preferred for manager evaluation in most liquid public-market mandates
• Recognize when MWR is the relevant measure (illiquid strategies, investor-experience discussions)
• Explain discrepancies between MWR and TWR in terms of cash-flow timing and investor behavior

Correctly choosing and interpreting MWR versus TWR is frequently integrated into broader portfolio evaluation, attribution, and recommendation questions.

Key Point Checklist

This article has covered the following key knowledge points:

• Define and interpret money-weighted return (MWR) and time-weighted return (TWR)
• Understand MWR as an internal rate of return on the portfolio’s external cash flows
• Calculate MWR by setting up and solving the IRR equation for multiple cash flows
• Calculate TWR by subdividing the overall horizon at each external cash flow and geometrically linking sub-period returns
• Interpret why MWR is investor-specific and sensitive to the timing and size of external cash flows
• Interpret why TWR better isolates manager skill and is appropriate for comparing managers and benchmarks
• Recognize situations where MWR and TWR yield materially different results and explain why
• Select and justify the appropriate return measure for performance evaluation scenarios in CFA Level 3 exam questions

Key Terms and Concepts

• money-weighted return (MWR)
• time-weighted return (TWR)
• external cash flow
• internal rate of return (IRR)