# Money-Weighted Rates of Return that are Better than the IRR - What I've Learned from the Academics – Part 1

10 Pages Posted: 28 Jun 2016 Last revised: 5 Jul 2016

Date Written: July 3, 2016

### Abstract

Common knowledge is that the IRR is some sort of an average rate of return but, in fact, it is a constant rate of return. The distinction may sound immaterial, but the IRR’s fixation on a constant rate of return is a major shortcoming. The fact that, in certain circumstances, it can result in multiple solutions or no solutions is well-known, but is deemed unlikely enough as to be inconsequential to most. However, what is not well known at all is that, in forcing the rate of return to be constant for each cash flow period, in essence, IRR is concocting interim valuations for the investment that contradict the true valuations of the investment at the end of each and every cash flow period that have likely either been estimated (e.g., real estate appraisals) or may even be precisely known (e.g., stock prices). Less obvious, but no less valid, is that these concocted values render the constant IRR result artificial which, in this case, is another way of saying that the IRR is simply the wrong rate of return answer.

Where IRR’s more subtle failings are more evident is when one attempts any sort of attribution, even if only informally, meaning that one wants to reconcile how the IRR result has changed when either another asset has been added to the portfolio or when another time period has been added to the investment horizon. In short, the requirement of IRR to always produce a constant answer for each cash flow period forces it to retroactively ‘change its mind’ about the values of the assets in all prior time periods. This chameleon-like property of IRR is a serious flaw that, in effect, makes IRR unworkable for any sort of incremental analysis.

Fortunately, in 2011, a more flexible money weighted rate of return (“MWRR”) metric was created by a scholar named Carlo Alberto Magni [see Magni, 2011], a metric which avoids all of the IRR’s flaws by computing a simple 'weighted-average' of the periodic rates of return which, as a result of the aforementioned information on periodic valuations of the investment, are inherently variable. Not only is this metric simpler to calculate in that it does not require a computer iterating in search of a solution; but, in fact, it can be calculated on the back of an envelope. Yet, it has none of the problems that the IRR has, the most prominent one being that, unlike the IRR, it always produces a single, unique rate of return solution.

**Keywords:** IRR, AROI, ex-post, ex ante, DCF, invested capital, PME, MWRR, MWR, money-weighted rate of return, internal rate of return

**JEL Classification:** C63, E12, G23, G24, C53

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