## What is a 'Money-Weighted Rate of Return'

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

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## BREAKING DOWN 'Money-Weighted Rate of Return'

There are many ways to measure returns for assets, and it is important to know which method is being used when reviewing asset performance. Money-weighted rate of return incorporates the size and timing of cash flows, so it is an effective measure for returns on a portfolio. Another popular return calculation is the time-weighted returns method.

## Calculating Money-Weighted Rate of Return

A money-weighted rate of return is identical in concept to an internal rate of return; it is the discount rate on which the net present value (NPV) = 0, or the present value of inflows = present value of outflows. Start by identifying all cash inflows and outflows. When applied to an investment portfolio:

Outflows
1. The cost of any investment purchased
2. Reinvested dividends or interest
3. Withdrawals

Inflows
1. The proceeds from any investment sold
3. Contributions

Example:
Each inflow or outflow must be discounted back to the present using a rate (r) that will make PV (inflows) = PV (outflows). For example, take a case where we buy one share of a stock for \$50 that pays an annual \$2 dividend, and sell it after two years for \$65. Our money-weighted rate of return will be a rate that satisfies the following equation:

PV Outflows = PV Inflows = \$2/(1 + r) + \$2/(1 + r)2 + \$65/(1 + r)2 = \$50

Solving for r using a spreadsheet or financial calculator, we have a money-weighted rate of return = 17.78%.

## Money-Weighted Rate of Return versus Time-Weighted Rate of Return

The money-weighted rate of return is often compared to the time-weighted rate of return, which many consider the industry standard because it is not sensitive to withdrawals or contributions. Fund managers tend to use the time-weighted rate of return in calculating the performance of mutual funds or broad-market indices. Time-weighted is defined as the compounded growth rate of \$1 over the period being measured. The time-weighted formula is essentially a geometric mean of a number of holding-period returns that are linked together or compounded over time (thus, time-weighted). In short, MWRR differs in that it takes into account investor behavior via the impact of fund inflows and outflows on performance. If there are no cash flows then both methods should deliver the same or similar results.

## Money-Weighted Rate of Return and Shortcomings

The money-weighted rate of return considers all the cash flows from the fund or contribution, including withdrawals. Should an investment extend over several quarters, for example, the MWRR lends more weight to the performance of the fund when it's at its largest size, hence the description "money-weighted." This can penalize fund managers because of cash flows that they have no control over.

Put simply, if an investor adds a large sum of money to a portfolio just before its performance rises, it equates to a positive action. This is because the larger portfolio benefits more (in dollar terms) from the growth of the portfolio that if the contribution had not been made. On the other hand, if an investor withdraws funds from a portfolio just prior to a surge in performance, it equates to a negative action. The now-smaller fund sees less benefit (in dollar terms) from the growth of the portfolio than if the withdrawal had not happened.

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