In the investment world, it’s common to discuss average rates of return, both in a backward-looking fashion (e.g., to report investment results), and in a more forward-looking manner (e.g., to project the average growth rate of investments for funding future goals in retirement planning software). However, the reality is that because returns are linked to each other – the return in one year increases or decreases the available wealth to compound in the subsequent year – it’s not sufficient to simply determine an “average” return by adding up all the historical returns and dividing by how many there are.
Instead of this traditional “arithmetic mean” approach to calculating an average, in the case of investment returns, the proper way to calculate average returns is with a geometric mean, that takes into account the compounding effects of a series of volatile returns over time. Which is important, because in practice the geometric average return is never as high as its arithmetic mean counterpart, due to the fact that volatility always produces some level of “volatility drag”, which can be estimated by subtracting ½ of the investment’s variance (standard deviation squared) from its arithmetic return.
Fortunately, the reality is that most investment returns, as commonly discussed by financial advisors, are already reported as geometric returns, typically stated as either a Compound Average Growth Rate (CAGR), an annualized return, or some similar label. Which means, intended or not, most financial advisors already project future wealth values in a retirement plan using the (proper) geometric return assumption.
However, the variance drain on a sequence of volatile returns still matters when financial advisors use Monte Carlo analysis, which by design actually projects sequences of random volatile returns (based on the probability that they will occur) to determine the outcome of particular retirement strategies. Because the fact that volatility drag is already part of a Monte Carlo analysis means that the return assumption plugged into a Monte Carlo projection should actually be the (higher) arithmetic return, and not the investment’s long-term compound average growth rate. Otherwise, the impact of volatility drag is effectively counted twice, which can understate long-term returns and overstate the actual risk of the prospective retirement plan!
The good news is that some Monte Carlo software tools, recognizing that most financial advisors report returns using the industry-standard geometric averages, already adjusts advisor-inputted return assumptions up to their arithmetic mean counterparts. However, not all Monte Carlo software automatically makes such adjustments. Of course, in many cases, financial advisors may wish to use lower return assumptions in today’s environment, given above-average market valuations and below-average yields. Nonetheless, advisors should be cognizant of whether they are unwittingly entering lower-than-intended return assumptions into their Monte Carlo retirement projections, compounding geometric returns in a manner that double-counts the impact of volatility drag!
source https://www.kitces.com/blog/volatility-drag-variance-drain-mean-arithmetic-vs-geometric-average-investment-returns/?utm_source=rss&utm_medium=rss&utm_campaign=volatility-drag-variance-drain-mean-arithmetic-vs-geometric-average-investment-returns
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