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What are the advantages of using the money-weighted rate of return for investment portfolios?

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If you are an investment banker, you probably deal with various types of investment portfolios, such as stocks, bonds, funds, and derivatives. How do you measure the performance of these portfolios over time and compare them with benchmarks or peers? One common method is to use the money-weighted rate of return (MWRR), which takes into account the timing and amount of cash flows in and out of the portfolio. In this article, we will explain what MWRR is, how to calculate it, and what are the advantages of using it for investment portfolios.

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Jeremy Goldberg, CFA, CFP?

Portfolio Manager and Research Analyst | M.S. in Finance

1 What is MWRR?

MWRR is a measure of the compound annual growth rate of an investment portfolio, based on the net present value of its cash flows. It assumes that all cash flows are reinvested at the same rate as the portfolio. To calculate MWRR, you need to find the internal rate of return (IRR) that equates the present value of the cash flows to the initial value of the portfolio. For example, if you invest $100,000 in a portfolio and receive $10,000 in dividends after one year, and then sell the portfolio for $120,000 after another year, your MWRR is the IRR that satisfies the equation: $100,000 = $10,000/(1+IRR) + $120,000/(1+IRR)^2.

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2 Why use MWRR?

MWRR has several advantages over other methods of measuring portfolio performance, such as the time-weighted rate of return (TWRR) or the arithmetic or geometric mean return. For instance, MWRR reflects the impact of investment decisions on portfolio performance, and it is easy to understand and communicate. Additionally, MWRR is consistent with the net present value (NPV) criterion, which is widely used in investment banking to evaluate projects or deals. If you add or withdraw money from the portfolio at opportune times, MWRR will capture the effect of these cash flows on the portfolio growth. As a result, your MWRR will be higher than your TWRR, which ignores the timing of cash flows. Furthermore, MWRR is a single number that represents the annualized return of the portfolio and can be used to calculate the future value of the portfolio by applying the compound interest formula. Additionally, MWRR indicates the minimum required return for an investment to be acceptable and thus is aligned with using NPV for investment decision making.

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Jeremy Goldberg, CFA, CFP?

Portfolio Manager and Research Analyst | M.S. in Finance
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The comparison between MWRR and TWRR is not straightforward; MWRR can be higher or lower than TWRR, dependent on how the timing of contributions and withdrawals aligns with the portfolio’s performance. TWRR is often preferred for evaluating investment managers since it measures performance without the distorting effects of cash flows, which are typically beyond a manager’s control. Furthermore, MWRR does not inherently signify the minimum required return; rather, it calculates the actual return based on cash flows. The minimum required return is predetermined, serving as a benchmark for future investments and is distinct from MWRR’s retrospective analysis.

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3 How to calculate MWRR?

MWRR can be calculated using a spreadsheet software, such as Excel, or a financial calculator. To do this, you must first identify the initial value of the portfolio and the dates and amounts of all cash flows in and out of the portfolio. Cash flows can be positive or negative, such as dividends, interest, purchases or fees. Then, enter the data into a spreadsheet or a calculator using the appropriate functions or keys. In Excel, you can use the XIRR function to return the IRR for a series of cash flows that occur at irregular intervals. In a financial calculator, you can use the cash flow keys (CF0, CFj, Nj) and the IRR key. Finally, obtain MWRR as the output of the function or calculator. This is the annualized rate of return of the portfolio based on cash flows and their timing.

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4 What are the limitations of MWRR?

MWRR is not a perfect measure of portfolio performance, and it has some limitations that you should be aware of. For instance, MWRR is sensitive to the timing and amount of cash flows, which can distort the true performance of the portfolio manager. Additionally, MWRR is not comparable across portfolios with different cash flow patterns, unless they have the same initial and final values. Furthermore, MWRR may not exist or may not be unique for some portfolios with complex or irregular cash flows. For example, if a portfolio has alternating positive and negative cash flows, it may have more than one IRR, depending on how many times the cash flow sign changes. Therefore, MWRR is not suitable for ranking or benchmarking portfolios with different cash flow patterns.

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Jeremy Goldberg, CFA, CFP?

Portfolio Manager and Research Analyst | M.S. in Finance
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Two other limitations: 1) MWRR assumes that all cash flows are reinvested at the MWRR itself, which might not always be the case in reality. 2) It can be difficult to compute MWRR manually for non-periodic cash flows, and it often requires the use of financial software or iterative methods.

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5 How to use MWRR effectively?

MWRR is a useful and widely used measure of portfolio performance, but it should be used with caution and in conjunction with other measures, such as TWRR, NPV, or risk-adjusted return. To use MWRR effectively, you should understand the assumptions and implications of MWRR, such as how it differs from other measures and reflects the impact of your investment decisions on the portfolio performance. Additionally, you should choose the appropriate time period and frequency for calculating MWRR that match your investment horizon and objectives, while also being consistent across portfolios. Furthermore, you may need to adjust MWRR for risk, fees, taxes, and inflation to measure the risk-adjusted return of the portfolio. For example, you can use the Sharpe ratio which divides the excess return of the portfolio over the risk-free rate by the standard deviation of the portfolio returns.

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6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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What are the advantages of using the money-weighted rate of return for investment portfolios?

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1 What is MWRR?

2 Why use MWRR?

3 How to calculate MWRR?

4 What are the limitations of MWRR?

5 How to use MWRR effectively?

6 Here’s what else to consider

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