### Author Topic: Can this long-term average investment growth assumption really hold?  (Read 4114 times)

#### IrishMustacian

• 5 O'Clock Shadow
• Posts: 27
##### Can this long-term average investment growth assumption really hold?
« on: December 03, 2015, 03:03:11 PM »
Warning: this is a fairly philosophical post!

I very much embrace the mustachian lifestyle, and live well below my means and try to invest my savings in index funds, which I hope continue to increase in value. But, as a mathematically minded person I have a hard time believing the long-time validity of our assumption that you should expect about 5% real value increase in invested money, or even any positive long-time average fixed real return. Hopefully someone can explain this to me.

My confusion can be summarized in the following simple argument/estimate:

Basic googling indicates that about a tenth of the total assets and money in the world are owned by about 0.1% of the people on the planet. Supposing that these people do not spend much of their wealth each year and have it invested, then we would expect their real return to be about 5% per year. By real return, I mean above inflation, which I will assume to be equivalent to their fraction of the total wealth in the world. In fifty years, their fraction of the total world wealth would therefore be expected to increase by about a factor of 11.5 = (1.05)^50. But this is clearly not possible, since they cannot have more than all of the assets in the world. Therefore we conclude that a 5% average real return cannot hold long term as it leads to a contradiction.

To try to pick holes in my own argument, we could say that we should not expect 5% of real return, but something less - but then it will just take a little longer before the richest 0.1% own everything, and the contradiction will still arise. Or maybe we could say some of the wealthiest 0.1% will actually squander lots of their money instead of investing it, but again, we could just focus on a subset of the group who do invest most of their wealth and eventually their share of the worlds assets, growing at some fixed positive rate, will reach the point that they own everything.

The only way I can think of to counter my argument is that I should not take the real value of an individuals wealth to be equivalent to their fraction of the total wealth in the world. Clearly over the past hundred years, the world population has increased a lot, and we have also increased the average standard of living by destroying the planet, such that the real value of an individuals wealth has not been tied to their fraction of the total wealth. But if we expect that in our lifetimes, the earth's population will plateaux and we will begin to run out of extra resources we can extract from the finite planet that we live on, then I would expect that the real value of an individuals wealth will indeed become tied to their fraction of the total wealth.

If someone can point me toward another thread or a good book which could help me understand these issues a little better, I would be very grateful!

#### arebelspy

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##### Re: Can this long-term average investment growth assumption really hold?
« Reply #1 on: December 03, 2015, 03:16:50 PM »

My confusion can be summarized in the following simple argument/estimate:

Basic googling indicates that about a tenth of the total assets and money in the world are owned by about 0.1% of the people on the planet. Supposing that these people do not spend much of their wealth each year and have it invested, then we would expect their real return to be about 5% per year. By real return, I mean above inflation, which I will assume to be equivalent to their fraction of the total wealth in the world. In fifty years, their fraction of the total world wealth would therefore be expected to increase by about a factor of 11.5 = (1.05)^50. But this is clearly not possible, since they cannot have more than all of the assets in the world. Therefore we conclude that a 5% average real return cannot hold long term as it leads to a contradiction.

I'm not following this. The top 0.1%'s fraction of the world's wealth will always be...0.1% of the world's wealth. By definition.

If their wealth is increasing as a percentage/fraction of the total wealth, then there's no hard cap, because it's a percent.

Other than that, from what I can see your argument's major flaw is assuming a fixed amount of wealth.

That'd be like saying "There was \$X million dollars in the world in 1600, so clearly no one can grow their wealth to over 1 billion" but that's simply not true.

Unless you think the same total wealth exists today as 400 years ago, clearly wealth has grown in real terms.

How much that wealth will grow in the future is debatable, but there's no reason it can't grow in real terms. For those 0.1%ers to grow their wealth, the total amount of wealth in the whole world needs to grow.

You are assuming that can't happen, it seems.

If I understand your argument correctly, you're saying we have \$X dollars total in the world, the 0.1% own most of that, and if you increase their dollars in real terms, they'll own more than \$X dollars.  Well sure, of course they will. But by that point, there will be more than \$X in the whole world.

If not, what am I not understanding about your question?
I am a former teacher who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and am now settled with three kids.
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#### IrishMustacian

• 5 O'Clock Shadow
• Posts: 27
##### Re: Can this long-term average investment growth assumption really hold?
« Reply #2 on: December 03, 2015, 03:35:59 PM »
Thanks for the response. I apologize for my poor choice of phrasing. By the "top 0.1%" I mean the wealthiest 0.1% of people on the planet (i.e. the richest 7 million people), who can (and do) own much much more than 0.1% of the total wealth.

I totally agree that the total wealth in the world is not the same today as it was 400 years ago, even correcting for inflation. I was trying to acknowledge this in the last paragraph but clearly didn't do a good job of explaining it clearly. The thing is that even though it has been true that the total (inflation corrected) wealth in the world has been increasing for hundreds of years, I don't believe this can continue indefinitely. Basically, (I believe) this increase in total wealth has only occurred so far because the earths population has been increasing, and because we add "stuff" to our economies by extracting things from the earth, which will eventually run out. When the population stops increasing and we begin to run out of stuff to extract from our finite planet, I expect the total wealth will not grow any more.

I hope this clears up the confusions caused by the initial post!
« Last Edit: December 03, 2015, 03:56:57 PM by IrishMustacian »

#### arebelspy

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##### Re: Can this long-term average investment growth assumption really hold?
« Reply #3 on: December 03, 2015, 04:16:49 PM »
Huh. I believe the opposite--that wealth in the world will continue to grow at an even faster rate than it has, based on the crazy new technologies we're seeing.

Like, wealth grew faster after the industrial revolution than before it. And wealth grew faster last century than the one before that.

I don't see a reason why it won't continue for a good while to come.

If all our wealth was based on depleting resources, sure. But it's not.

Sure, our natural resources may run out in a few (hundred? thousand?) years, but certainly not in our lifetimes.

So worrying about the long term average investment growth based on running out of resources on earth seems silly.

It seems to me by the time we hit that, we'll be multi-planet, with many ways to strategically use or make new resources.
I am a former teacher who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and am now settled with three kids.
If you want to know more about me, this Business Insider profile tells the story pretty well.
I (rarely) blog at AdventuringAlong.com. Check out the Now page to see what I'm up to currently.

#### jjcamembert

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##### Re: Can this long-term average investment growth assumption really hold?
« Reply #4 on: December 03, 2015, 04:53:47 PM »
What is wealth? The US is not on the gold standard anymore, so equating dollars to raw resources is not a valid comparison. If you own the last barrel of oil on Earth, your wealth in dollars will be extremely high because of supply/demand. Total wealth resource-wise would be decreasing, but money-wise would be increasing as resources deplete.

Huh. I believe the opposite--that wealth in the world will continue to grow at an even faster rate than it has, based on the crazy new technologies we're seeing.

Like, wealth grew faster after the industrial revolution than before it. And wealth grew faster last century than the one before that.

I don't see a reason why it won't continue for a good while to come.

If all our wealth was based on depleting resources, sure. But it's not.

As an example, Apple sells electronic gadgets that are "worth" hundreds of times their raw material cost. Apple creates the value by providing a product that people want, and they create wealth by attracting a larger market share than their competitors. Their growth isn't dependent on an increasing population, just increased sales.

#### MDM

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• Posts: 10717
##### Re: Can this long-term average investment growth assumption really hold?
« Reply #5 on: December 03, 2015, 05:57:15 PM »
Supposing that these people do not spend much of their wealth each year...

One could suppose that, but there are plenty of counterexamples to suggest that is not a good assumption.  E.g.,
http://givingpledge.org/

#### IrishMustacian

• 5 O'Clock Shadow
• Posts: 27
##### Re: Can this long-term average investment growth assumption really hold?
« Reply #6 on: December 03, 2015, 06:16:45 PM »
Thank you arebelspy, MDM and jmj - these responses definitely make headway towards resolving of my confusion.

It seems from these comments like there are two kinds of inflation which are relevant: inflation in terms of the buying power of money (and this is the one we usually say is around 4%) and inflation of the overall wealth (assets and money) in the world. I have no idea what the approximate average value this second kind of inflation has historically (I wonder where I could find out?). In my argument, I was assuming that eventually these two kinds of inflation would start to match each other as we reach equilibrium in terms of population number and newly added resources, but I see that this is not necessarily the case.

So I guess an argument of the type I gave would tell us that in the long run, it should not be possible that the average interest rate of investments is larger than the rate of the second kind of inflation. So for living off passive investments to work out in the long run, we should hope this second kind of inflation stays pretty big.

Supposing that these people do not spend much of their wealth each year...

One could suppose that, but there are plenty of counterexamples to suggest that is not a good assumption.  E.g.,
http://givingpledge.org/

Yes, I totally agree that some people in the top 0.1% will not passively invest their money for all eternity, but the argument I was giving should just require that some do.

#### lakemom

• Bristles
• Posts: 402
##### Re: Can this long-term average investment growth assumption really hold?
« Reply #7 on: December 03, 2015, 06:28:06 PM »
Go find the book "History of Money" which I listened to on cd and it was an excellent explanation of how money and modern uses of money (interest, investments, gold, real estate) all evolved and are still evolving.  I think I only made it through about 2/3-3/4 of the book (had to return it) but it was a lot of fun listening to.  I really ought to find it in print and read it.

#### arebelspy

• Senior Mustachian
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##### Re: Can this long-term average investment growth assumption really hold?
« Reply #8 on: December 04, 2015, 02:40:07 AM »

So for living off passive investments to work out in the long run, we should hope this second kind of inflation stays pretty big.

Yes. Our ER bet is that:
1) We won't run out of natural resources in our lifetime and,
2) People will keep creating, inventing, discovering, making new things, and improving things in our lifetime. I.e. We won't slide back into some sort of dark ages via total economic collapse.

Seems like a good bet.

But further, by making yourself FI, you learn the skills and frugality and happiness that will put you in a better place if we do have one of those problems, and you lose everything. A job certainly won't help you in those cases. So if something happens that kills your ER, it'd likely kill your job too. Who needs accountants (or computer programmers, or whatever) in those times?

So, in short, I wouldn't worry about natural inflation outpacing real growth due to human productivity in our lifetimes, short of something completely catastrophic.
I am a former teacher who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and am now settled with three kids.
If you want to know more about me, this Business Insider profile tells the story pretty well.
I (rarely) blog at AdventuringAlong.com. Check out the Now page to see what I'm up to currently.

#### Axecleaver

• Magnum Stache
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##### Re: Can this long-term average investment growth assumption really hold?
« Reply #9 on: December 04, 2015, 07:28:34 AM »
Read _Capital_ by Piketti. This explains the history behind inflation (an artificial economic tool used by governments to inflate their way out of debt) and the trends behind growth and concentration of wealth.

Your primary flaw is in ignoring market growth. The US has a very mature economy with small to moderate growth. Take a look at some of the opportunities in China, India, and third world nations. You can see GNP of 20% per year in those places (with corresponding higher risk). Wealth can be used to expand and grow, increasing economic output. This is the concept behind a rising tide lifting all boats, sharing a smaller slice of a bigger pie, etc.

http://data.worldbank.org/indicator/NY.GNP.MKTP.KD.ZG

#### jjcamembert

• Stubble
• Posts: 153
##### Re: Can this long-term average investment growth assumption really hold?
« Reply #10 on: December 06, 2015, 06:42:51 PM »
Another perspective on economic growth vs resources that I came across today: http://www.investopedia.com/articles/investing/120515/infinite-economic-growth-finite-planet-possible.asp