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:

#### Refinance Your Mortgage

Mortgage rates are still low. I saw rates as low as 3.625% for 30-year fixed, 2.875% for 15-year fixed, with no points and low closing cost. Let banks compete for your loan. Get up to 5 offers at LendingTree.com.

nik says

Hi Finance Buff. Do you know of any online web-based calculators for TWR/Modified Dietz. I’ve built something i’d like to verify and am looking for a 3rd party tool. thx.

Harry Sit says

@nik – Gummy is the master on these calculations. See Time Weighted Returns and Do the Dietz.

Al says

Should Dollar Weigted Return calculations include all dollars in a brokerage account even if they are not invested but sitting in a money market account for example. A simple example wold be a 100K account that had 50K invested in equities during the year with the other 50K earning .75% interest. The 50K invested earned 5K.

John Perez says

I have an ING account which states that my ROR is 11% from Jan to Sept. It says this return is based on dollar weighted rate of return which brought me to your sight because I wondered if this “calculation” was including my contributions which in my mind distorts the true return of money invested earning interest *vs* money invested earning interest with contributions being added in to inflate the true return. I am wondering if the only true and *correct* way to calculate a *ROR* is to seperate each contribution into the fund choice, then calculate that return over the period it was invested. Is there a way to get a “true” ROR that accounts for just interest earned and not contributions made?

Bill Kay says

If I have two separate portfolios for which I am calculating time-weighted rates of return (MDM approx) I am able to calculate combined performance for the two simply by summing their market values and cash flows then applying the standard time-weighted calculation… however, if I have two separate portfolios and I am calculating a time-weighted return for one and a dollar-weighted return for the other (IRR) is there a way to calculate returns for the two portfolios combined, as if they were a single portfolio? My gut tells me I must use one method or the other.

I appreciate your comments.

Bill

Harry says

Bill – Yes, one method or the other.