The Modified Dietz rate of return attempts to estimate a money-weighted rate of return (MWRR) by weighting each cash flow by the proportion of the measurement period it is present or absent from the portfolio.

Similar to the money-weighted rate of return, the calculation requires the investor to know the portfolio values at the start and end of the measurement period, as well as the cash flow amounts and dates when each cash flow occurs. Unlike the MWRR, the calculation does not require an exhaustive trial and error procedure, or sophisticated computing power.

*Source: CFA Institute*

The Modified Dietz rate of return can differ substantially from the time-weighted rate of return (TWRR) when large cash flows occur during periods of significantly fluctuating portfolio values (just like the money-weighted rate of return). This makes the Modified Dietz rate of return less ideal for benchmarking portfolio managers or strategies than the TWRR. For example:

- When a large
*contribution*is made prior to a period of relatively good (bad) performance, the Modified Dietz rate of return (ModDietz) will overstate (understate) a portfolio’s performance, relative to the time-weighted rate of return (TWRR). - When a large
*withdrawal*is made prior to a period of relatively good (bad) performance, the Modified Dietz rate of return (ModDietz) will understate (overstate) a portfolio’s performance, relative to the time-weighted rate of return (TWRR).

Using the values from our original example, we would plug in the appropriate numbers and calculate the rate of return for each investor.

** **

**Example: Calculation of w_{i}**

**Example: Modified Dietz Rate of Return (MDRR) – Investor 1**

** **

**Example: Modified Dietz Rate of Return (MDRR) – Investor 2**

*Performance Results*

Methodology |
Investor 1 |
Investor 2 |

Time-Weighted Rate of Return (TWRR) | 9.79% | 9.79% |

Money-Weighted Rate of Return (MWRR) | 8.98% | 10.64% |

Modified Dietz Rate of Return (ModDietz) | 8.97% | 10.66% |

As we can see in the chart above, the Modified Dietz rate of return is nearly identical to the money-weighted rate of return. In my final blog post of the series, we will examine how calculating the Modified Dietz rate of return over monthly time periods can help an investor better estimate the time-weighted rate of return.

AleJune 15, 2018 at 6:04 pmJustin,

Thank you for you quick reply. I finish to read 4 Pillar of Investing and the formula given in the book was

If there are no additions to or withdrawals from you portfolio, simply divide the end value by the beginning value and subtract 1.0. For example, if you start- ed the year with $10,500 and ended with $12,000, your return was (12,000/10,500) -1.0 = 0.143 =14.3%.

If you had inflows or outflows during the year, this must be adjusted for. (This is the mistake made by the Beardstown Ladies, who did not make this correction.) This is done by first calculating the net inflow. In the above example, if you added $1,000 and then took out $700 during the year, your net inflow was $300. You subtract half of this, or $150, from the top of the fraction, and add one-half to the bottom. So, (12,000 – 150)/(10,500 + 150) = 1.113; your return was 11.3%. If you had a net outflow of $300, then you do the reverse—add to the top, subtract from the bot- tom. So, (12,000 + 150)/(10,500 – 150) = 1.174; your return was 17.4%.

What do you think about this formula vs MWR & Dietz?

P.S. For my portfolio, I’m doing the calculation of a monthly return under MWR; Dietz & the 4 Pillar formula. The Dietz monthly sub-period return rate is almost the same as 4 Pillar formula (with small fluctuations). But there is a big discrepancy if I’m looking on the total annual return rate Dietz vs 4 Pillar…Based on the formula, 4 Pillar doesn’t look like a TWR more likely like a MWR; but as you mentioned earlier Dietz monthly sub-period return rate is closer to MWR where the overall rate for the return is TWR

Thanks & Great Post Justin!

AleJune 15, 2018 at 5:01 pmJustin,

I think I have found the answer in one of you posts, but correct if I’m wrong and looking forward for your insight. Thanks

Dietz rate is closer to approximate time-weighted rate of return (ATWRR)

https://www.canadianportfoliomanagerblog.com/how-to-calculate-your-approximate-time-weighted-rate-of-return-atwrr/

JustinJune 15, 2018 at 5:41 pm@Ale: This is a definitely a confusing topic. The Modified Dietz return approximates a money-weighted return. However, if you calculate the Modified Dietz return over monthly sub-periods and chain-link the returns together (which is how my calculator does it), the Modified Dietz return starts to approximate a time-weighted rate of return:

https://www.pwlcapital.com/pwl/media/pwl-media/PDF-files/White-Papers/2015-07-10_PWL_Bender-Bortolotti_Understanding-your-portfolio-s-rate-of-return_Hyperlinked.pdf?ext=.pdf

AleJune 15, 2018 at 4:55 pmHI Justin,

I have downloaded both calculators: Modified Dietz & MWR.

Every month I’m calculating the rate of my return based on both methods. The annual rate (JAN 1 to MAY 31, 2018) the Dietz rate is almost double vs MWR. At the beginning of this post you’ve mentioned that Dietz is a money-weighted rate of return. I’m wondering if Dietz is a TWR (timing). Can you explain the difference between Dietz vs MWR/TWR?

Thanks

Darrell RobbMay 3, 2018 at 2:19 amHi Justin…I have been using the modified dietsz calculator each year, and find it very helpful. A question came up today, which I can’t answer. For partial years, for instance end of April, the calculator returns a YTD percentage. Is this the annual rate for the full calendar year, if nothing else changes?….we know the values in May to December will go up and down, and I haven’t filled those dates in yet, but I wanted to know if for April 30 the percentage returned is an annualized rate, or just a simple percentage from December 31 of previous year to April 30.

JustinMay 7, 2018 at 2:24 am@Darrell Robb: The calculator does not annualize a partial year (so if nothing else changes by December 31st, the annual return should be the same as the YTD return as of April 30th).

AleMarch 8, 2018 at 2:58 pmHi Justin

I have the same question as Marcus

Is there a way to change the date of calculator?

Thanks

AleMarch 7, 2018 at 10:36 pmHi Justin,

From what I understand Modified Dietz rate of Return gives you are better result than money-weighted rate return which fluctuates based inflow/outflow cash. As you mentioned in your previous paper Modified Dietz is closer to time-weighted rate return and I have downloaded the calculator for Modified Dietz. The calculator is for 2018 and is not allowing to change the dates for 2017; is there a way to change those dates?

Thanks

JustinMarch 8, 2018 at 3:20 pm@Ale: I’ll consider updating the calculator in the future to allow for the changing of dates.

KyleJanuary 7, 2018 at 1:45 amThe white paper you and Dan wrote is most helpful. Suppose the example investors in that document each had a USD account as well and they wanted to calculate the monthly modified Dietz return across both CAD and USD accounts in CAD. Is it as straight forward as gathering all 13 month end exchange rates as well as for each USD cashflow event, convert the USD V0, V1 and CF values to CAD and combining them with the respective values derived from the CAD account?

JustinJanuary 7, 2018 at 10:04 pm@Kyle: You got it! 😉

Andre RobichaudDecember 25, 2017 at 1:52 pmHi Justin,

Are you going to be posting a Modified Dietz calculator for 2018? or do you have one that we would be able to adjust dates. I found your calculator extremely helpful.

As is the information on your blog

Merry Christmas

Andre

JustinDecember 27, 2017 at 1:51 pm@Andre Robichaud: Merry Christmas to you and your family 🙂 I will be posting a downloadable 2018 version of the calculator sometime in January 2018.

MarcusNovember 10, 2017 at 10:05 amHi Justin, is there anyway to change the date on your calculator from 2017 to 2016? Thanks for the calculator by the way.

JustinNovember 10, 2017 at 1:37 pm@Marcus: I’ll send you an email with a version that you can adjust.

DeeshaOctober 12, 2017 at 4:18 pmHi Justin, this is a great blog and it has helped me better understand performance figures! At the end of this blog, you have said your final blog will examine Modified Dietz over monthly time periods. Could you please provide me a link to this?

Kind regards,

Deesha

JustinOctober 12, 2017 at 4:25 pm@Deesha: I’m glad you’ve enjoyed the articles. Here’s a link to the Modified Dietz article, our white paper on calculating rates of return, and a downloadable Modified Dietz calculator:

https://www.canadianportfoliomanagerblog.com/how-to-calculate-your-modified-dietz-rate-of-return/

https://www.pwlcapital.com/pwl/media/pwl-media/PDF-files/White-Papers/2015-07-10_PWL_Bender-Bortolotti_Understanding-your-portfolio-s-rate-of-return_Hyperlinked.pdf?ext=.pdf

https://www.canadianportfoliomanagerblog.com/calculators/