Money weighted return

What Is Money Weighted Return?

Money weighted return (MWR) is a measure of an investment's performance that takes into account the timing and size of all cash flows into and out of a portfolio. It is equivalent to the internal rate of return (IRR) for a series of investment cash flows. This metric falls under the broader category of portfolio theory, which encompasses various methods for evaluating investment outcomes. Unlike other return measures, the money weighted return gives greater weight to periods when a larger amount of capital is invested.²⁹ This makes it particularly useful for assessing an individual investor's actual experience, as it reflects the impact of their decisions to contribute or withdraw funds.²⁸

History and Origin

The concept of measuring investment returns, particularly considering the impact of varying cash flows, gained prominence with the development of discounted cash flow techniques. The money weighted return, being synonymous with the internal rate of return (IRR), has its roots in capital budgeting and project evaluation. IRR emerged as a key metric for evaluating the profitability of potential investments by identifying the discount rate that makes the net present value of all cash flows equal to zero. Over time, this methodology was adapted to assess the performance of investment portfolios, especially when the investor has control over the timing and magnitude of cash movements. The widespread adoption of formal performance measurement standards, such as the Global Investment Performance Standards (GIPS), has further refined the application and reporting of money weighted returns in professional investment management. The 2020 GIPS standards, for instance, expanded the flexibility for firms to present money weighted returns under specific conditions, particularly for portfolios where the firm controls external cash flows, or for illiquid and closed-end funds.²⁷ More information on GIPS standards can be found on the CFA Institute's website.²⁶

Key Takeaways

• Money weighted return (MWR) is a performance measure that considers the timing and size of all cash flows.
• It is mathematically equivalent to the internal rate of return (IRR) for a series of investment cash flows.
• MWR is highly influenced by investor behavior, making it suitable for evaluating an individual's personal portfolio performance.
• Periods with larger invested capital have a greater impact on the calculated money weighted return.
• It is less suitable for comparing the skill of an investment manager who does not control the timing of client contributions or withdrawals.

Formula and Calculation

The money weighted return (MWR) is calculated by finding the discount rate that equates the present value of all cash inflows with the present value of all cash outflows associated with an investment. This is the same principle used to calculate the internal rate of return. There is no simple explicit formula for MWR; instead, it is found iteratively or using financial calculators and software, as it requires solving for 'r' in the following equation:

Where:

• (CF_t) = Net cash flow at time (t) (positive for inflows, negative for outflows)
• (r) = Money weighted return (the discount rate to be solved for)
• (n) = Total number of periods
• (t) = The specific time period

The initial investment at (t=0) is typically represented as a negative cash flow ((-CF_0)), and subsequent deposits are negative, while withdrawals and the final portfolio value are positive. The goal is to find the rate (r) that makes the sum of the present values of all these cash flows equal to zero.

Interpreting the Money Weighted Return

Interpreting the money weighted return involves understanding that it provides a personalized view of an investor's actual return experience. Because it factors in the size and timing of deposits and withdrawals, a high money weighted return suggests that the investor made well-timed contributions during periods of strong performance or avoided significant withdrawals during downturns. Conversely, a lower money weighted return might indicate that large sums were invested just before market declines or withdrawn before significant gains.²⁵

For instance, an investor's money weighted return could be positive even if the underlying investments performed poorly, if large deposits were made right before a rebound.²⁴ This highlights its utility in personal financial planning and assessing the impact of one's own investment decisions. However, it also means that the money weighted return can be significantly influenced by factors external to the investment's inherent performance, such as an investor's personal liquidity needs or their ability to time the market.²³ Therefore, when evaluating a portfolio using money weighted return, it's crucial to consider the context of the investor's cash flow activity.²²

Hypothetical Example

Consider an investor, Alex, who starts with an initial investment in a diversified mutual fund.

• Day 0: Alex invests $10,000.
• End of Year 1: The portfolio value is $11,000. Alex adds an additional $5,000. The portfolio value immediately after the contribution becomes $16,000.
• End of Year 2: The portfolio value is $17,500. Alex withdraws $2,000. The portfolio value immediately after withdrawal becomes $15,500.
• End of Year 3: The portfolio is liquidated, and Alex receives $19,000.

To calculate the money weighted return, we set up the cash flows and solve for the discount rate (r) that makes the net present value zero:

Note that the $11,000 at the end of Year 1 and $17,500 at the end of Year 2 are intermediate portfolio values, not cash flows. The relevant cash flows are the initial investment, the additional deposit, the withdrawal, and the final liquidation value. Using a financial calculator or spreadsheet software with an IRR function, the money weighted return for Alex's investment would be approximately 7.2%. This rate reflects the effective annual compounded return on the capital Alex had invested, taking into account the specific timing and amounts of his deposits and withdrawals.

Practical Applications

Money weighted return is particularly valuable in situations where the investor has control over the timing and magnitude of cash flows. This makes it a highly relevant metric for:

• Individual Investors: For personal portfolios, money weighted return accurately reflects the investor's actual experience, showing how their contributions and withdrawals influenced their overall return. It answers the question, "What was my personal return?"²¹ Many financial institutions, such as Fidelity, use a money-weighted calculation (often called "Personal Rate of Return") for client performance reporting, as it factors in the client's deposits and withdrawals.¹⁹, ²⁰
• Private Equity and Venture Capital: These investment vehicles often involve irregular capital calls and distributions. The money weighted return, frequently referred to as IRR in this context, is crucial for assessing the performance of such funds because it accounts for the uneven nature of capital deployment and retrieval over the fund's lifecycle.¹⁸
• Real Estate Investments: Similar to private equity, real estate projects typically have intermittent cash inflows and outflows, making money weighted return a suitable measure for evaluating project-specific performance.
• Capital Budgeting Decisions: In corporate finance, the internal rate of return (which is a money weighted return) is a primary tool for evaluating the viability of new projects or investments by a company. It helps determine if a project's expected return meets or exceeds a company's hurdle rate.

Limitations and Criticisms

Despite its utility, the money weighted return has several limitations that warrant careful consideration:

• Sensitivity to Cash Flow Timing: The primary criticism of money weighted return is its sensitivity to the timing and size of external cash flows.¹⁶, ¹⁷ A large deposit made just before a period of strong market performance can significantly boost the money weighted return, even if the underlying investment strategy wasn't particularly skillful. Conversely, ill-timed large withdrawals can depress the return.¹⁵ This makes it less ideal for evaluating the performance of an investment manager, as their skill might be obscured by client-driven cash movements.¹⁴
• Not Ideal for Manager Evaluation: Because it reflects the investor's behavior, money weighted return is generally not preferred for assessing the skill of an investment management firm or fund manager. Investment managers typically do not control client deposits or withdrawals, and thus, a metric that accounts for these external flows might unfairly penalize or reward them.¹³ The Global Investment Performance Standards (GIPS) generally mandate the use of time-weighted returns for external performance reporting by firms, precisely because it removes the effects of external cash flows.¹²
• Multiple IRRs: For projects with unusual cash flow patterns (e.g., alternating positive and negative cash flows), there can be multiple internal rates of return, making interpretation ambiguous. This mathematical peculiarity, known as the "multiple IRR problem," can complicate the use of money weighted return in certain scenarios.¹¹
• Reinvestment Rate Assumption: The calculation implicitly assumes that all intermediate cash flows are reinvested at the money weighted return itself.¹⁰ This assumption can be unrealistic, especially for projects with very high or very low rates, as it might not be feasible to continuously reinvest at that specific rate in the real world.

Money Weighted Return vs. Time Weighted Return

The distinction between money weighted return and time weighted return is crucial in investment performance measurement.

While money weighted return reflects "my" return (the investor's actual experience), time weighted return reflects "the portfolio's" return (how the underlying assets performed, independent of investor behavior).⁶ Understanding this difference is key to appropriate financial analysis and performance evaluation.

FAQs

1. When should I use money weighted return?

You should use money weighted return when you want to understand the actual rate of return on your personal investment portfolio, taking into account all the deposits you've made and withdrawals you've taken over time. It's particularly useful if your cash flows are significant or frequent, as it gives more weight to periods when more money was invested.⁴, ⁵

2. Is money weighted return the same as IRR?

Yes, money weighted return (MWR) is mathematically equivalent to the internal rate of return (IRR). Both calculations seek to find the discount rate that makes the net present value of all cash flows equal to zero.

3. Why don't investment managers typically report money weighted returns?

Investment managers typically do not report money weighted returns because these returns are heavily influenced by the timing and size of client contributions and withdrawals, which the manager usually does not control. To accurately assess the manager's skill in selecting investments, a time weighted return is generally preferred, as it seeks to remove the impact of these external cash flows.³ Professional standards, such as GIPS, largely require time-weighted returns for public reporting.²

4. Can money weighted return be negative?

Yes, the money weighted return can be negative. If the total value of your investment, considering all inflows and outflows, results in a loss over the investment period, then your money weighted return will be negative. This indicates that your investment, factoring in your specific cash flow decisions, did not generate a positive return.¹