Understand Money-Weighted Rate of Return (MWRR) With Simple Examples

What Is the Money-Weighted Rate of Return (MWRR)?

A money-weighted rate of return (MWRR) evaluates an investment's performance by considering the timing and size of cash flows, such as dividends and withdrawals. MWRR is synonymous with the internal rate of return (IRR) and provides a comprehensive view that incorporates investor behavior into performance assessments. Distinct from the time-weighted rate of return (TWRR), which removes cash flow effects, MWRR offers insights into how your actions affect investment returns.

Understanding the Mechanics of Money-Weighted Rate of Return

There are many ways to measure asset returns, so it is important to know which method is used when reviewing asset performance. The MWRR incorporates the size and timing of cash flows, so it effectively measures portfolio returns.

MWRR aligns the initial investment value with future cash flows, including dividends, withdrawals, deposits, and sale proceeds. In other words, the MWRR helps to determine the rate of return needed to start with the initial investment amount, factoring all of the changes to cash flows during the investment period, including the sale proceeds.

Calculating the Money-Weighted Rate of Return

The formula for the MWRR is as follows:

$\begin{aligned} &PVO = PVI = CF_{0} \, +\, \frac{CF_{1}}{(1\, +\, IRR)}\, +\, \frac{CF_{2}}{(1\, +\, IRR)^{2}}\,\\ &\qquad\quad\, +\, \frac{CF_{3}}{(1\, +\, IRR)^{3}}\,\, +\,... \frac{CF_{n}}{(1\, +\, IRR)^{n}}\,\\ &\textbf{where:}\\ &PVO = \text{PV Outflows}\\ &PVI = \text{PV Inflows}\\ &CF_0 = \text{Initial cash outlay or investment}\\ &CF_1, CF_2, CF_3, ... CF_n = \text{Cash flows}\\ &N = \text{Each period}\\ &IRR = \text{Initial rate of return}\\ \end{aligned}$​PVO=PVI=CF0​+(1+IRR)CF1​​+(1+IRR)2CF2​​+(1+IRR)3CF3​​+...(1+IRR)nCFn​​where:PVO=PV OutflowsPVI=PV InflowsCF0​=Initial cash outlay or investmentCF1​,CF2​,CF3​,...CFn​=Cash flowsN=Each periodIRR=Initial rate of return​

Steps to Calculate MWRR With a Spreadsheet

The MWRR formula can be complex, often needing trial and error. A spreadsheet or calculator simplifies estimating returns, so we will show how to calculate it using a spreadsheet:

1. Purchase one share of stock for $50, receiving a $2 annual dividend.
   
2. Record two dividend payments for two years.
   
3. In the third year, sell the share for $65.
   
4. Input these cash flows into a spreadsheet (initial purchase, dividends, final sale).
   
5. Use the spreadsheet's IRR function, omitting the rate guess, to determine the MWRR.
   

	A	B	C
1		Outlay and Cash Flow	MWRR
2	Year 1	($50)
3	Year 2	$2
4	Year 3	$2
5	Year 3 sale price	$65	= IRR(B2:B5) = 11.73%

In the spreadsheet, the IRR function requires values, and you can enter an optional rate guess:

= IRR ( cashflow values, rate guess )

To use the function, highlight the cells that contain your cashflow values so that the column and cell numbers are entered into the field between the parenthesis, skip the rate guess, and press enter.

Analyzing Cash Flows in Money-Weighted Rate of Return

MWRR works like the IRR: it's the discount rate where d value equals zero, or where the present value of inflows matches outflows.

Therefore, it's important to identify the cash flows in and out of a portfolio, including asset sales. Some of the cash flows that an investor might have in a portfolio include:

Outflows

• The cost of any investment purchased
• Reinvested dividends or interest
• Withdrawals

Inflows

• The proceeds from any investment sold
• Dividends or interest received
• Contributions

Comparing Money-Weighted and Time-Weighted Rates of Return

MWRR is often compared to the time-weighted rate of return (TWRR), but they differ in key ways. The TWRR is a measure of the compound rate of growth in a portfolio. TWRR is used to compare investment manager returns by removing distortions from money inflows and outflows.

Determining earnings on a portfolio can be hard since deposits and withdrawals distort returns. Investors can’t simply subtract the beginning balance, after the initial deposit, from the ending balance since the ending balance reflects both the rate of return on the investments and any deposits or withdrawals during the time invested in the fund.

The TWRR breaks up the return on an investment portfolio into separate intervals based on whether money was added to or withdrawn from the fund. The MWRR differs in that it takes into account investor behavior via the impact of fund inflows and outflows on performance but doesn’t separate the intervals where cash flows occurred, as the TWRR does. Therefore, cash outflows or inflows can impact the MWRR. If there are no cash flows, then both methods should deliver the same or similar results.

Recognizing the Limitations of Money-Weighted Rate of Return

The MWRR considers all the cash flows from the fund or contribution, including withdrawals. In long-term investments, MWRR emphasizes performance when the fund is largest, which is why it's "money-weighted."

This weighting can penalize fund managers due to cash flows they can't control. In other words, if an investor adds a large sum of money to a portfolio just before its performance rises, it equates to positive action. This is because the larger portfolio benefits more (in dollar terms) from the portfolio's growth than if the contribution had not been made.

Conversely, if an investor withdraws funds before a performance surge, it is seen as a negative action. The now-smaller fund sees less benefit (in dollar terms) from the portfolio growth than if the withdrawal had not occurred.

What Are the Advantages of MWRR?

The MWRR allows you to view whether your investment generates a consistent return with an interest rate. If your rate is not consistent, your rate of return begins falling.

Should I Use Money Weighted or Time Weighted?

The MWRR allows you to see how your changes affect your investment, eliminating its usefulness as a comparison tool but letting you see how your decisions affected it. TWRR lets you see how your investment performs without your changes, which lets you compare it to similar investments. Which you use depends on what you want to view.

What Is Better, Time Weighted or Money Weighted?

While each indicates how your investment has performed, they demonstrate performance accounting for different investing actions. So neither is better or worse; they can be used together or separately to determine how an investment is performing.

The Bottom Line

The money-weighted rate of return measures investment performance by incorporating the size and timing of cash flows, offering a comprehensive view of how an investor's activities—such as contributions, withdrawals, and reinvested dividends—affect returns. Unlike the time-weighted rate of return (TWRR), MWRR reflects the impact of portfolio inflows and outflows, making it ideal for investors who want to assess the effect of their financial decisions on their investment performance. Use MWRR to see how these actions influence the growth of your portfolio.