# Dollar-weighted return (DWR)

The **dollar-weighted return** (**DWR**) measures the rate of return of an investment or a portfolio, taking into account the *timing of flows*. It is defined as

the rate of return thatequatesthe discounted ending asset value to the sum of the initial assets-under-management and the present value of the capitalflowsrealized over the life of the investment.

Dollar-weighted rates of return (DWRR) differ from the more commonly used **time-weighted rate of returns** (TWRR) in that dollar-weighted returns take into account an investor’s ‘behavior’. This is because the dollar-weighted return reflects the impact of flows on performance. In addition, dollar-weighted returns will more accurately reflect the actual growth rate of an investment or portfolio.

The above dollar-weighted return definition probably sounds somewhat abstract. Therefore, we will first provide the formula needed to calculate dollar-weighted returns and illustrate it using a numerical example. In addition, we also provide a simple Excel spreadsheet that allows you to calculate the dollar-weighted return of an investment yourself.

## Dollar-weighted return formula

The formula needed to calculate the dollar-weighted rate of return is

where **r _{dw} **is the dollar-weighted return,

**AUM**is the initial investment,

_{0 }**Capital Flows**are the flows in and out of the investment, and

_{t}**T**is time (in years). Basically, calculation of dollar-weighted returns amounts to ‘weighting’ the different capital- or ‘money’ flows in and out of the portfolio. That’s why this type of return is sometimes also referred to as the

**money-weighted return**(MWR) or the

**money-weighted rate of return**(MWRR).

To solve the above equation, we should therefore solve for the unknown **r _{dw}**. In particular, we need to determine the rate of return that equates the left-hand side and right-hand side of the above equation. This calculation is basically an

*internal rate of return calculation*that can be be performed using simple spreadsheet software.

## Dollar-weighted rate of return example

Let’s consider a numerical example that shows the usefulness of calculating dollar-weighted returns. In particular, let’s compare the money-weighted rate of return and the time-weighted return of an investment.

Let’s consider a small investor that buys 100 shares of the fund AlphaFund at $10 per share at time 0. Hence, his initial investment is **$1000**. Next, lest assume that the realized returns over the first period is 100%. At the end of time 1, the investor’s investment is worth **$2000**. Because of the good performance the investor decides to buy another 100 shares. Hence, he invests an additional **$2000** in AlphaFund. Unfortunately, the performance in the second period is bad. The fund loses **50%** of its value. Because of the bad performance, the investor decides to liquidate the fund.

Over this period, the time-weighted-return is **0%**. The investor’s return experience, however, is *negative*. He invested **$3000 **in total, but only got $2000 when liquidating his position. Applying the above formula to the provided data

we find that **d _{wr}** should equal

**-26.7%**for the left-hand side to equal the right-hand side. The following figure illustrates the investor’s return experience.

Of course, the opposite case is also possible. Suppose the fund initially underperformed and it lost **50%** of its value. Despite the bad performance, the investor decides to buy additional shares in Alphafund. In particular, he also invests **$2000** at the end of time 1. The fund subsequently recovers and the investor again decides to liquidate the fund.

In this case, even though the time-weighted return of the fund is the same, the investor’s return experience is markedly different. In particular, the investor realizes a **45%** gain.

In the spreadsheet below we further illustrate how to perform a money-weighted rate of return calculation. We show this using the above formula as well as a built-in formula in Excel. The built-in function is called XIRR and allows you to calculate internal rates of return.

## Summary

Money-weighted returns better capture the return experience of investors. They capture the impact of capital flows on an investment’s performance.

### Dollar-weighted return calculator

Want to calculate the dollar weighted average return yourself? Download our Excel spreadsheet: dollar-weighted-return