# Money-Weighted Rate of Return

## What Is the Money-Weighted Rate of Return?

The money-weighted rate of return (MWRR) is a measure of the performance of an investment. The MWRR is calculated by finding the rate of return that will set the present values of all cash flows equal to the value of the initial investment. The MWRR is equivalent to the internal rate of return (IRR).

### Key Takeaways:

• The money-weighted rate of return (MWRR) is a measure of the performance of an investment.
• The MWR is calculated by finding the rate of return that will set the present values of all cash flows equal to the value of the initial investment.
• The money-weighted rate of return is equivalent to the internal rate of return.
• The MWR sets the initial value of an investment to equal the future cash flows such as dividends added, withdrawals, deposits, and the sale proceeds.

## Understanding the Money-Weighted Rate of Return

The formula for the MWRR is as follows:

PVO=PVI=CF0+CF1(1+IRR)+CF2(1+IRR)2+CF3(1+IRR)3+...CFn(1+IRR)nwhere:PVO=PV OutflowsPVI=PV InflowsCF0=Initial cash outlay or investmentCF1,CF2,CF3,...CFn=Cash flowsN=Each periodIRR=Initial rate of return\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}

### How to Calculate the Money-Weighted Rate of Return

1. To calculate IRR using the formula, set net present value equal to zero and solve for the discount rate (r), which is the IRR.
2. However, because of the nature of the formula, IRR cannot be calculated analytically and must instead be calculated either through trial and error or using software programmed to calculate IRR.

### What Does the Money-Weighted Rate of Return Tell You?

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

The MWRR sets the initial value of an investment to equal the future cash flows, such as dividends added, withdrawals, deposits, and sale proceeds. In other words, the MWRR helps 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.

### Cash Flows and the Money-Weighted Rate of Return

As stated earlier, the MWRR for an investment is identical in concept to the IRR. In other words, it is the discount rate on which the net present value (NPV) = 0, or the present value of inflows = present value of outflows.

It’s important to identify the cash flows in and out of a portfolio including the sale of the asset or investment. 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