XIRR vs. Modified Deitz for Return Calculations

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Robert T
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XIRR vs. Modified Deitz for Return Calculations

Post by Robert T »

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There will likely be a thread or two on portfolio returns in 2009, but I think its important to distinguish between the two measures of returns often used.
  • (i) Dollar Weighted Returns, commonly referred to on the forum as “XIRR” and

    (ii) Time weighted Returns, commonly calculated using the Modified Deitz methodology.
Both are useful. Dollar weighted returns measure the average return on each dollar invested. While time weighted returns provide a useful return comparison against portfolio benchmarks (eg. Compared to S&P500, TSM etc).

Here’s an example, taking a portfolio 100% invested in the MSCI US Broad Market (Vanguard Total Stock Market) this year. The return of the MSCI US Broad Market Index YTD is 30.1% (The underlying index is taken for illustration as monthly return data are easily accessible for this simple example). Few points:
  • (i) Time-weighted estimates (e.g. using the Modified Deitz approach) will be the same as the Index returns e.g. 30.1%

    (ii) Dollar weighted return estimates (XIRR) will only equal 30.1% if there are no savings/additional investments or withdrawals during the year. And will be higher or lower dependent on the size and timing of additional investments, withdrawals, and the distribution of returns over the year.

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A few examples: assuming a portfolio of $100,000 at the start of 2009 all invested in a US Total Stock Market Portfolio.

                                              Time-weighted      Dollar-weighted
                                              (Modified-Deitz)      (XIRR)       

No savings/withdrawals                            30.1               30.1         

Saving $1000 at start of each month               30.1               31.2
Saving $5000 at start of each month               30.1               34.6

Withdrawing $1000 at start of each month          30.1               28.9
Withdrawing $5000 at start of each month          30.1               21.7

Assuming poor returns (Jan-Feb 2009), occurred at the end of year, (Nov-Dec 2009), not at the beginning (Jan-Feb changed with Nov-Dec) :

Saving $1000 at start of each month               30.1               28.2
Saving $5000 at start of each month               30.1               22.4

Withdrawing $1000 at start of each month          30.1               32.2
Withdrawing $5000 at start of each month          30.1               44.3

The message => when comparing against benchmarks, use time-weighted calculations (e.g. the Modified Deitz) for an apples to apples comparison. As the above illustrative example suggests, in a year like 2009, if adding the same monthly investments, high XIRRs may just reflect the poor relative returns earlier in the year (and better relative returns at the end of the year), not outperformance of benchmarks.

At least my understanding.

Robert
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rwwoods
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Post by rwwoods »

Gummy has a spreadsheet for the Dietz method.
http://www.financialwebring.org/gummystuff/Dietz.htm
"I'm not so much concerned about the return on my money as the return of my money" - Will Rogers
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empb
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Re: XIRR vs. Modified Deitz for Return Calculations

Post by empb »

Bringing this one back from the grave and looking for another set of eyes...

I've calculated my XIRR and Dietz returns, annually and overall, since 2009.

I'm comfortable the annual returns and the overall XIRR are calculated accurately. However, the overall Dietz return (calculated as per: http://goo.gl/CbGIh9) and the overall XIRR differ widely (14.15% versus 7.30%).

I'm presuming this difference is due to the bulk of the returns occurring early in the sequence with relatively few dollars invested but, admittedly, I don't entirely have my head around the intuition. The overall XIRR figure also includes 2016's year-to-date losses, Dietz does not.

Do the below figures pass the smell test?

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year		xirr		dietz
2009		44.22%	43.62%
2010		29.07%	28.83%
2011		-3.53%	-3.52%
2012		16.24%	16.18%
2013		22.79%	22.64%
2014		0.25%	 0.25%
2015		-0.85%	-0.94%

annual	7.30%	14.15%
longinvest
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Re: XIRR vs. Modified Deitz for Return Calculations

Post by longinvest »

There are two types of personal returns: investor return (internal, money-weighted, XIRR), and portfolio return (comparable, time-weighted, mutual fund).

You'll find an explanation along with examples in our wiki: Calculating personal returns page.

Modified Deitz is a hybrid of both.
Variable Percentage Withdrawal (bogleheads.org/wiki/VPW) | One-Fund Portfolio (bogleheads.org/forum/viewtopic.php?t=287967)
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Oicuryy
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Re: XIRR vs. Modified Deitz for Return Calculations

Post by Oicuryy »

empb wrote:I'm presuming this difference is due to the bulk of the returns occurring early in the sequence with relatively few dollars invested but, admittedly, I don't entirely have my head around the intuition.
It could be the difference between time-weighted rate of return (Dietz) and dollar-weighted rate of return (XIRR). See http://www.gummy-stuff.org/fund-you.htm

Ron
Money is fungible | Abbreviations and Acronyms
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