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.

 

 

• Inputs:
o You can see that in terms of data requirements, IRR requires the least, simply cash flows and ending value.
o TWR requires the most, daily values and flows.
o Modified Dietz is somewhere in the middle, requiring periodic valuations but not daily like True TWR.
• Formulas, Numerator, and Denominator:
o You can instantly see the similarities between Modified Dietz and True TWR, with Profit or loss in the numerator and just different capital bases in the denomintor.
o It may not be clear why Modified Dietz is an approximation of IRR, but if you read through this post on IRR, you will see how the IRR is using an average balance of capital invested similar to Modified Dietz.
• Multiple Time Periods: Here is where Modified Dietz gets closer to resembling true TWR, according to David Spaulding. Why? Because when you link returns from one period with another, like a true TWR, you do not take into account whether a period has more or less money invested. It’s like a growth of $1 chart. On the other hand, an IRR does take into account the money invested. Example:
o Let’s say you start with $100 and you have a return of 5% and end the period with $105. Then you contribute another $95 to start the next period with $200. In the next period you have a return of 10% for a gain of $20.
o You will notice that the return doubled from 5% to 10% but your profits went from $5 to $20 because you had more money invested in the second period.
o If this period was 1 year, your IRR would be approx 17% and your TWR would be 15.5%.
o The IRR takes into account that you had more money invested when you had the higher return.
o The TWR, by linking the two separate periods of 5% and 10% assumes both periods had the same amount of money invested, hence like the “growth of $1.”

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