### What is the Modified Dietz Return?

##### The Modified Dietz formula is used to calculate the return on a portfolio of investments and is written as:

##### But don’t worry, you don’t need to be Einstein to understand it! **I will try to break it down to plain English.**

##### First, the numerator just equal to your Profit or Loss. It takes what you ended with minus what you started with (aka Ending Value – Beginning Value) and then the “- Cash Flows” simply removes any money you contributed or withdrew from the portfolio.

##### And the denominator is the same thing as how much money you had invested on average.

##### Next, let’s use a simple example to illustrate:

##### • You start with $100 at the beginning of June, contribute $50 in the middle, and end up with $180 at the end.

• Your profit was $30 for the month

• The $100 was invested for the full month, and the $50 was invested for half, so the average capital invested was $125.

• So your return will be $30 / $125 = 24%

*Here is a link to a sample calculation spreadsheet with a more intensive example:*

##### Modified Dietz Calculation

### How and When Is It Used In Practice?

##### It can be used as an approximation of the True Time-Weighted Return (TWR) or the Internal Rate of Return (IRR).

##### In my experience, it is more frequently utilized as an approximation of true TWR because:

##### • TWR requies daily valuations, which is difficult for firms to get sometimes. Therefore, Modified Dietz provides a good alternative in that situation since it only requires monthly or quarterly valuations.

##### • IRR actually requires less inputs, so why use the Modified Dietz as an approximation of the true IRR calculation? The IRR does require an iterative computer program, but those are more readily available now (namely, Excel).

##### Here is an excerpt from the GIPS Standards Guidance Statement on Calculation Methodology

Calculating a time-weighted rate of return is not an easy task and may be cost intensive. For these reasons, firms may use an approximation method to calculate the total return of the individual portfolios for the periods and sub-periods. The most common approximation methods combine specific rate of return methodologies (such as the original Dietz method, the Modified Dietz method, the original IRR (internal rate of return) method, and the Modified BAI (Bank Administration Institute) method) for subperiods, and then geometrically links the sub-period returns.

### Why Modified Dietz Is A Blend of True TWR and True IRR

##### Below I have done a comparison of the three formulas (Mod Dietz, True TWR, and True IRR) so you can get a sense of what the Modified Dietz is doing.

##### But, I strongly encourage you to first understand the true time-weighted return calculation and the IRR calculation, before trying to wrap your head around this.