# Modified Dietz Return Calculations

A reader sent in a question asking about the Modified Dietz Method for reporting portfolio performance. Specifically, her investment statement noted that this was the method used to calculate returns for clients and she just wanted to know if this was normal or not. It’s a good question. How many people have ever heard of the Modified Dietz Method before?

# Performance Reporting for Investors

You would be surprised how much more (relatively) difficult it is to calculate portfolio performance when you are not dealing with lump sum investments made at the beginning of a reporting period with no distributions (or re-invested distributions). For example, it’s really easy if you start the year with \$100,000 and at the end of the year you have \$110,000 and no distributions were made during the year. It’s easy to figure out that you earned 10%.

But what happens if you’re portfolio spat out \$10,000 in a dividend on June 30th, and you still ended up with only \$110,000 by the end of the year (and the \$10,000 was re-invested)? Your \$100,000 earned 10% for 6 months, but then your \$110,000 earned 0%. Your end performance would therefore have been less than 10% overall.

There are two main categories of calculating and reporting performance: Time-weighted returns and Dollar-Weighted Returns (aka Money Weighted Returns and both are also used interchangeably [depending on who you ask] with IRR, or Internal Rate of Return).

# Time Weighted Returns

Time weighted returns aren’t as precise when you have large cash flows in a portfolio. For example if a portfolio had three years of 20% returns each year and then 0% return for the next three years the time-weighted return is 10% over the 6 years (arithmetic return, and we’ll ignore geometric returns for the purpose of this post). But what if you had \$1 invested the first three years and then added \$100,000 at the beginning of year 4? At the end of year 6 you would have just under \$100,002. That certainly doesn’t seem like an average 10% return does it?

# Dollar Weighted Returns

A dollar weighted return would calculate the above as follows: \$1 earned 10% for 6 years, and \$100,000 earned 0% for three years. Since the bulk of the portfolio did nothing, this would be reflected in the dollar weighted return being really close to 0%.

So which is the Modified Dietz?

The Modified Dietz is actually somewhat of a dollar weighted return which becomes time-weighted because performance is calculated for sub-periods which are then linked together. Huh? It’s funny if you look it up because some authoritative sources call it time-weighted, and some call it dollar weighted. Perhaps the mathematicians out there (Michael James?) can help us out on this. Here is the wikipedia link for Modified Dietz and the formula.

From the formula you can see it is dollar weighted, but by linking the returns between periods (which is a time weighted method on top of the dollar weighted calculation) it is somewhat of a hybrid.

# Can you just tell me if it’s good or not?

Yes, it’s fine most of the time. The only time it will really distort your results is if you have multiple cash flows within one period and the markets are volatile (2008 & 2009 anyone?). This is because the sub-periods require proper portfolio valuations at the beginning and end of those periods and it is very onerous to do so. The Modified Dietz assumes an average rate of return for each sub-period. The Modified Dietz is (currently) an accepted methodology for portfolio performance reporting according to the GIPS standards (Global Investment Performance Standards), but it should be noted that GIPS (which is run by the CFA Institute) has recommended that performance reporting start calculating portfolio valuations when large cash flows occur (positive or negative) so that a more accurate rate of return can be calculated (as opposed to just using quarterly or monthly valuations and ignoring large cash flow timing as it stands now). These recommendations are to be adopted in January of 2010 (don’t know if it will apply to the reporting of dealer firms to retail clients though).

In the end, Modified Dietz is fine most of the time, but it’s not perfect.

Preet Banerjee
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• Doctor Stock

Nice article – a simple post for the average reader.

• Michael James

The Modified Dietz method of calculating portfolio return is a reasonably good approximation of the internal rate of return (IRR) in most cases. The IRR is a dollar-weighted measure that is simply the rate of return that causes the net present value of all cash flows to be zero.

When the portfolio starting value and ending value are large compared to other cash flows in-between, just about all methods of calculating return give close to the same result. In Preet’s example where the added \$100,000 is very large compared to the portfolio starting value, the time-weighted return fails miserably, but the Modified Dietz gives a reasonable answer of just a hair over zero percent return. The Modified Dietz is a much better approximation to the IRR than time-weighted measures.

Saving computing power isn’t much of an excuse any more for using approximations. It’s not that much harder to find the IRR than it is to use Modified Dietz, and who cares if a computer is doing the work? The exception would be if you run an investment company and your software already does Modified Dietz, the last thing you want to have to do is change it.

In the vast majority of cases, the IRR and Modified Dietz return are going to be so close that it doesn’t really matter.

• Melissa

Thank you Preet, this has been very informative. I especially like the “Can you just tell me ….” section.

• Patrick

Michael – the IRR is not well-defined if there is a mixture of positive and negative cash flows, and is generally not a good way to compare investments because doing so would give results at odds with expected utility.

• Michael James

Patrick:

It’s true that IRR is not always well-defined. However, all methods of calculating return have their warts. For example, Suppose that we invest \$10,000 initially, it grows to \$12,000 by then end of the first year, and we withdraw \$11,000. Then the remaining \$1000 doubles to \$2000 by the end of the 12th year. By any reasonable measure, this is a good, but not spectacular return. However, the Modified Dietz says that the total return over the 12 years is -3600%! The IRR is a more reasonable 14.5% per year.

Most of the time, when calculating just a one-year return on a portfolio with only small cash flows relative to the portfolio size, just about any method will give reasonable answers. However, there will always be situations where IRR and IRR estimates like Modified Dietz will fail.

Methods involving expected utility and presumed reinvestment rates of cash flows have their problems as well. While they tend to give more stable answers in the more extreme cases, they require that we build in assumptions about utility or expected returns on cash flows. In the end, the best measure will depend on the individual and what they plan to use the calculated return for.

• Patrick

Thanks Michael. Some interesting points to consider.

• Alan

In modified Dietz, how to you handle net cash withdrawls on the denominator..For example, if I start with 50,000 and over a 10 year period, 150,000 was depositied but 350,000 was withdrawn and the ending value of investments is 700,000. Net cash outflow = -200,000 Weighted cash = -125,000

Thank you