Friday, July 22, 2016

The Whoosh! of Exponential Retirement

I recently read a couple of articles on artificial intelligence, one an interview with historian, Yuval Noah Harari, and the other written by computer science geek (like me), Tim Urban. I was intrigued not by the technology discussion, but by the discussion of the exponential nature of human history.
Quick math refresher. An exponential curve is a function that increases by a power of x (2, 4, 8, 16, 32 . . .). A linear curve (a straight line) increases by a factor of x (2, 4, 6, 8 ,10 . . .). The following graph shows four exponential curves with growth rates of 3%, 7%, 15% and 55% per period. The 55% growth rate is extreme but comes into play shortly.

Urban explains the exponential nature of human development in an interesting way that I will summarize here. An adult from 1750 would be overwhelmed if he were transported forward by time machine 266 years to 2016. To achieve a similar state of awe in 1750, a person living in that year might have to have been transported back 14,000 years in time, according to Urban.

Meanwhile, we Baby Boomers would probably have been shocked back in 1960 to see what life would be like today, 56 years later.

In 1985, there were no cell phones, let alone smartphones, my Telemail email account was a rarity (most people had no idea what email was), global terrorism wasn't nearly the issue in the U.S that it is today, the Cold War had just ended, personal computers stored data on 10-megabyte hard disk drives (1/100,000th the capacity of today's one-terabyte hard drives), and driverless cars were a pipe dream.

In the early 1990's, I flew the supersonic Concorde from London to New York. My grandfather rode to school on a horse. In 1991, the Cold War ended.

Urban also includes the following illustration of exponential growth courtesy of I won't repeat the entire explanation here since it's explained well at the post, but here's the gist. If you started refilling a dry Lake Michigan in 1940 by adding 1 ounce of water and then doubled that amount every 19 months, after 70 years you wouldn't have much more than a very large, extremely shallow puddle. But, “by 2020, you have about 40 feet of water. And by 2025 you're done.” Exponential growth can crawl along glacially for a long time and then whoosh! right by you.

If I handled such large numbers correctly, the annual growth rate in the Lake Michigan demo is about 55% a year. Not many things grow that fast for any sustained period, let alone 85 years, but the whoosh! effect is pretty dramatic at this rate. The greater the growth rate, the more dramatic the difference between “waiting forever while nothing much happens” and “whooshing! by”.

Consider it an exaggeration for effect.

The demo also explains rather dramatically why a bear market late in our careers can be devastating. Half of the six quadrillion-gallon lake is filled in the last 18 months of the 85-year process. Your 401(k) growth is not nearly so dramatic, but your balance could double in the last 10 years of your career. Not as awesome a whoosh! as filling a lake at 55% annual growth, but still, one you don't want to miss.

As you can see, the length of time required to inspire awe becomes shorter and shorter at an amazingly fast pace. That's the nature of exponential growth. The implication for retirees is that if human development (and computer development, as the AI argument goes) continue at this incredible rate of growth, it is not only unreasonable to believe that you can predict how your life will change over a 30-year retirement, but it will become more and more unreasonable for future generations to do so.

We retirement planners are massively overconfident in our ability to predict the future.
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Still, nothing much grows this fast for very long.

Exponential growth usually doesn't last forever. Whether or not these exponential growth rates of human development and computer technology can continue is unknown and unknowable, but highly questionable. Moore's Law is showing signs of age.

Microsoft went through a super growth phase, as most successful startups do, but as annual revenues became huge, it became harder and harder to increase them exponentially. Microsoft reported $119M in revenues in 1984 and $95B in 2015, according to It's much easier to grow $119M by 20%, increasing sales by $24M, than to grow $95B 20%, increasing sales by $19B. Super-growth can't last forever.

A company can grow revenues 100% in a year when previous year sales were a million dollars. When sales are in the billions, 8% growth would be good. Pretty soon, if you're McDonalds, you need to sell hamburgers on Mars to create any kind of real growth. If the curve of history continues at an exponential growth rate, we will soon be awestruck annually and that doesn't seem reasonable.

Reasonable exponential growth in investment portfolios can continue for a long time – Harvard's endowment is an example – but probably not forever. As William Bernstein has reminded us, cataclysmic change can occur in a few decades, as Germany demonstrated twice in the first half of the 20th century, ending all growth, at least for a while.

There is bad exponential growth, as well. Exponential growth of malignant tumors, for example, is self-limiting. Exponential growth in cost is also bad. Inflation grows exponentially, but currently at only about 1% a year, which is manageable. Health care costs are growing around 3.6% annually and are quickly becoming unmanageable, as seen in the following chart from

Change can seem to whoosh! This is the fallacy of retirement strategies that suggest trying risky things and then bailing out if and when you see danger approaching. If you've read my posts on elder bankruptcy, they don't seem to result from a long, slow degradation of one's standard of living, but as a quick and deadly combination of correlated setbacks.

In Why Retirees Go Broke, I wrote about the positive feedback loops that characterize elder bankruptcies, referencing the research work of Dr. Deborah Thorne. These loops start slowly, gather speed and then whoosh! by. The two families I watched go into bankruptcy during the Great Recession went from comfortable middle class to insolvency in less than a year.

Exponential curves are representative of several retirement finance components. The current rate of change of our society makes planning a 30-year retirement mostly guesswork. On the other hand, exponential growth of investments enables many households to save enough to retire comfortably. I often hear clients who have saved a sizable nest egg say, “I'm not sure how this happened. I didn't really have a lot of savings until the end of my career.”

It isn't voodoo. The Rule of 72 tells us that a portfolio earning 7% annually will double in value about every decade. It will seem to grow slowly for many years and then – if you're lucky enough to avoid a bear market just before retirement – your nest egg balance will appear to whoosh! by in the exhilarating final decade of your career. On the other hand, if the bear gets you just before retirement, the biggest part of the whoosh! will fizzle. It will sound more like "who?"

Aging after you retire feels exponential, too. By age 70, most retirees stop traveling internationally. By age 80 most stop traveling domestically. By age 90, the roughly 30% of us who are still around may rarely travel much beyond the backyard.

These rapid changes affect retirement planning. We shouldn't plan on spending the same amount when we're 80 as we do at 65, though David Blanchett (downloads PDF) and Sudipto Banerjee (downloads PDF) have shown that spending typically declines roughly 1.5% to 2% a year as we age. That's exponential growth, but so slow it's almost linear.

What does this mean for retirement planning? A few things, I think.

First, when you're “standing on an exponential curve”, it probably looks linear into the immediate past and future. Don't fall for projecting this straight line. Interest rates are historically low and have been since December 2008. You might assume that they will stay that way for the rest of your retirement now, but that is highly unlikely. One day they will increase, and it will seem to happen quickly. The following diagram from Urban's post explains.

Second, and more important, I have recently explained in several ways that trying to predict an individual's retirement wealth several years into the future is impossible. Our limited data on historical market returns is such a small sample that our estimates of return have a huge confidence interval. Our future liabilities are probably more uncertain than market returns. The length of our retirement is unknowable.

Moshe Milevsky has written that we can be 95% certain that a shortfall probability of 15% actually lies somewhere between 5% and 25%. Gordon Irlam showed us an example in which the optimal asset allocation has a huge 95th-percentile confidence interval of 10% to 82%. Simulations are informative but not predictive.

The exponential nature of societal change provides more evidence that predicting our financial situation 30 years or more into the future is a fool's errand. Let's face it – we have no more idea what life will be like in 2046 than we could foresee today in 1986. With exponential change, the next 30 years will see a lot more changes than the last 30.

Lastly, when you see computer output that appears to predict your wealth from age 65 to 95, make sure you understand precisely what you are seeing. It's a pro forma wealth statement that shows one example of what might happen. (If you want a chuckle, ask the provider for a guarantee.) This shouldn't be the central tenet of your retirement plan. If you base your retirement plan on your ability to predict the future, you are likely to be sorely disappointed.

We humans are massively overconfident in our abilities to predict the future, and we retirement planners (ourselves included) are even more overconfident in our ability to predict the future wealth of a single retiree.

What does an 80's comedian have in common with bad retirement advice? Check out my next post, Exit Row Strategies.


  1. Just wanted to say that this is a fantastically written article that helps keep things matter how tirelessly you plan your retirement, the future is wildly unknown. Thanks!

  2. Dirk,

    I read that Warren Buffet's three words of advice are 'margin of safety'. I guess that is the best one can hope for in retirement planning, and as evidenced by your blog even then it is no guarantee. Brad

  3. Dirk,

    Nice illustration of what exponential REALLY means.

    One minor quibble. By most accounts the Cold War ended with the fall of the Soviet Union in 1991, not in 1985. Your end of the cold war comment would fit better in the paragraph referencing the early 1990's.

    Love reading your blog!

    1. I love my readers! One once pointed out that I had placed a period outside quotation marks. (I corrected that, too.) 1991 it is!

      That's what I call reading closely! :-D

  4. No big deal, I just lived it that's all.

    Thanks for all you do.

    1. I lived it, too. I should've caught that. I'm rather OCD about my writing and really do appreciate the chance to correct errors – even a period out of place.


  5. Dirk this is a fantastic blog post. It really highlights the importance of sequence of returns better than anything. Thanks!

    1. Thanks, Andy. It is certainly relevant to sequence of returns risk. I believe most people would bail out of a purely probabilistic investment strategy after a long period of poor returns early in retirement when it became evident that their plan was in trouble. Then the question becomes, when do you bail out?

      Will you bail out before going broke? Almost certainly. Will you bail out before you have permanently lost standard of living? Not so clear.

      Thanks for the comment!