Most of the time, when authors produce these charts, they talk about how the tail of the chart narrows over time. But something else is true, too, which is the tail never compresses to a single value.

Are you talking about the tail after a predefined period, e.g. 30 years? If so, this is trivially true. If not, please provide proof. I seriously doubt that's the case.

Gerardc,

I may not understand your comment, but I'm thinking you're asking for proof there's tons more variability in outcomes than many people commonly believe. So I'm going to address that issue... try to "provide proof"... I'm also going to break this response out into sections so people can choose a method of proof that meshes with the way they like to process information.

**For People Who Know How to Use cFIREsim and Microsoft Excel:**In message response #12 above, I provide the steps for using the cFIREsim online calculator to calculate the average, worst and best case returns historically for a given retirement savings plan. I also describe how to use Microsoft Excel to quickly calculate the average annual returns for the investor who experienced the worst case scenario, the average scenario, and the best case scenario.

Going through the steps of using cFIREsim takes less than a minute (I just timed myself)... And this exercise will provide proof.

**For People With Good Spatial Reasoning and Chart Reading Skills**

Another pretty easy way to prove this to yourself is to look at any--

*any*--funnel chart you see in books or on websites talking about long return returns.

What you will see is that the worst case and best case scenario returns never converge to a single percentage. The charts always show a gap between the worst and best case. Always, always the charts show this.

The gap varies. Portfolio Charts, it looks like, shows the range of possible average 30-year returns as maybe 5%-ish to 8%-ish for the portfolio I use.

In John Bogle's books and Burton Malkiel's books, the chart shows, roughly, the same sort of 3%-ish to 4%-ish gap.

That gap is what we're talking about here. What I'm saying is that gap exists. That gap is the proof.

And two things to note: First, if the average return of a portfolio is 6% but you or I earn 5% or 4%, that 1% or 2% shortfall over thirty years makes a huge difference.

Second, note that you shouldn't look just at the point on the chart that displays the range from best to worst at the 30-year-marker... some of your or my contributions to an IRA or 401(k) will get 30 years of returns... but some of the money we contribute will only be "in" the market for 2 years or 5 years or 10 years. So look at the range of outcomes at those points in the chart too.

Looking at the funnel charts you see with this mindset will provide the proof every time you see them from now on.

**For People Who Just Want to Read a Quick Little Narrative**

I did the very best job I could do to explain this in two posts at my blog:

Unreliability of long return stock market returns and

Retirement Plan B: Why You Need One...

If someone doesn't want to use cFIREsim or doesn't want to try and read the funnel charts, they might want to look at those two blog posts.

BTW, as part of the little "retirement plan b" blog post series I did, I also provides step-by-step instructions to make many of the sorts of calculations one needs to make to see this variability.