After reading my post about estimating overall personal rate of return, a reader Brian asked:

“I have a Fidelity serviced 401(k) and I had always wondered about how they calculated the personal rate of return. Do you know how/if other providers calculate personal rates of return? If I were to open a brokerage account, is there one company that does this better than others?”

Rates of return fall into two major categories: Dollar Weighted Rate of Return and Time Weighted Rate of Return. They measure different things and they should be used for different purposes.

*Dollar Weighted Rate of Return* measures how much your investment dollars returned on average. Use this measure when you want to see if your return is above or below your long term return objective. The method for calculating the Dollar Weighted Rate of Return is XIRR. You will need to know the beginning balance, the date and the amount of your *every* contribution (and withdrawal, if any), and the ending balance. With a computer, the calculation itself is not difficult but collecting all the data can be tedious.

*Time Weighted Rate of Return* measures how much the combination of your investment choices returned on average, without the influence of the size and timing of your own contributions or withdrawals. There’s a subtle difference here. Time Weighted Rate of Return ignores the effect of the external cash flows, that is, the cash flows from *you*. Use this measure when you want to see how your investment choices taken together, including any changes you made to your investment choices, returned compared to other choices or an index. There are two primary methods for calculating the Time Weighted Rate of Return: *Daily Valuation* and *Modified Dietz*. Daily Valuation is more accurate. Modified Dietz is a close approximation. For practical purposes, there’s not much difference between those two calculation methods.

**The personal rate of return you get from a financial service provider like Fidelity or Schwab is usually a Time Weighted Rate of Return.** If you want a Dollar Weighted Rate of Return, you will have to do it yourself.

Let’s put these in an example. Say you had $10,000 at the beginning of the year and your investments did great in the first 3 months. Your $10,000 turned into $12,000 without you adding a penny. Now on April 1, you put in $20,000 more, but your investments stalled in the rest of the year, and you end the year with $32,000. So you made 20% on $10,000 in the first 3 months and you made 0% on $32,000 in the next 9 months. If you plug in these values in a spreadsheet and use the XIRR function, you get 8%. This makes sense because:

10000 * (1 + 8%)^{1/4} = 10194

(10194 + 20000) * (1 + 8%)^{3/4} = 31988

Pretty close except for rounding. If you didn’t put in additional $20,000 on April 1, your return would’ve been 20%. That’s how your investment choices did and that’s how Fidelity or Schwab will report to you. There’s a big difference between the 8% Dollar Weighted Rate of Return and the 20% Time Weighted Rate of Return because the cash flow in this example is unusually large. If we change the additional contribution on April 1 from $20,000 to $1,000 and have the end of year value at $13,000 instead of $32,000, the two returns would be much closer. The Dollar Weighted Rate of Return would be 18.6%, and the Time Weighted Rate of Return would still be 20%.

Finally, because financial service providers typically provide only Time Weighted Rate of Return, and because the actual calculation methods for Time Weighted Rate of Return (Daily Valuation and Modified Dietz) yield similar results, there is no reason to believe that one company does it better than another.

For more information on Dollar Weighted Rate of Return, Time Weighted Rate of Return, Daily Valuation and Modified Dietz, if you are not afraid of math formula, please read this article from dailyVest:

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