Thursday, May 09, 2013

The Mathematical Impossibility of Retirement

Permit me some really rough mathematics.

In my introductory course to basic personal finance and investing, one of the first things I have my students do is go to this website and calculate how much they need to save for retirement.  It's a good exercise for everybody to go through, but the primary point is that (if you tinker with the calculator) you'll realize each person needs roughly $1 million in savings to retire.

With 6.5 billion people in the world that ads up to $6.5 quadrillion (the number after trillion) in required savings to invest.

Now, I'll grant you "retirement planning" and things like 401k's and RRSP's are really more of a western phenomenon and most people in 2nd and 3rd world countries don't have retirement plans, so let's just say the roughly 1 billion people in countries where they do have some kind of retirement program need to save up for retirement.

That brings the total amount of required savings down to $1 quadrillion.

Just one problem.

There isn't $1 quadrillion worth of stocks or bonds in the entire world.  Matter of fact, according to the World Federation of Exchanges, there's only about $55 trillion in equity and $82 trillion in bonds, leaving us with $137 trillion in securities, only 14% of the total amount required to finance the retirements of 1 billion people (it is duly noted here there are other securities, however, bar commodities, things like mutual funds and ETF's are merely compositions of stocks and bonds.  I admit we could throw in the commodities market and REIT's, but you'll soon see the point I'm trying to make).

There are some other problems as well.

First, the majority of the $137 trillion in securities is owned by the richer classes.  It is not equally spread out across the 1 billion westerners.  So the average 401k schmoe is less likely to have the $1 million in his account.

Second, though primarily held by 1st world nations, some of that $137 trillion IS held by 2nd and 3rd world countries.  In other words, the above optimistically assumes all the stocks of the Shanghai stock exchange are held by westerners solely for their precious little 401k plans which simply is not the case (heck, foreigners hold most of our debt anyway). 

Third, the bond market has a ton of debt that is, frankly, never going to be paid back and be defaulted upon.  $16 trillion (intra government holdings duly noted) alone of which is the US federal government and roughly an equivalent amount in those kick-the-can-down-the-road socialist utopias in Europe that are currently already defaulting.

So of that $137 trillion, can we roughly assume only a third of it is going to go to help finance people's retirement plans?  So roughly $46 trillion, i.e. 95% short of the amount necessary for people to retire.

Now there is one other variable I have not accounted for (and, truthfully, am having some difficulty figuring this one out, but I think I have it pegged, though would appreciate any criticism or thought on it)

Not everybody is going to retire on the same day.  

As the 401k Clergy will rush to point out,

"See!!!  See!!!  The stock market goes up though!  You're not assuming any growth!  You're assuming everybody cashes in today when they will in fact amortize out and we all know the stock market will go up by the magical amount to pay for everybody's retirement!  See!!  See!!!"

And they're right.  Not everybody is retiring today and the markets will grow.  So let's do a little more (admittedly rough) math.  The magical $46 trillion needs to grow into $1 quadrillion to pay for the current 1 billion westerners' retirement plans.  And while these people vary in ages from new borns to nearly dead, assume 35 years for the markets to grow (half of people's life expectancy to roughly approximate the old and young).  We'll also optimistically assume an 8% annualized growth rate, meaning the market will increase roughly 15 fold in those 35 years.  Even with this idealistic scenario (where governments never default, corporations provide annualized returns of 12%, there's no inflation, and Obama's Magical Job Unicorn farts out jobs), the total global market capitalization for stocks and bonds will be....

$665 trillion. 

Still about 35% short of the total.

Now, again, this was VERY rough mathematics and I'm sure somebody will find something wrong (and please do inform me if you do), but using this very rough litmus test it shows once again conventional retirement planning is flawed.  The amount of growth necessary in the capital markets will not be sufficient enough to pay for everybody's retirement.  And it is not even so much the rate of growth in the prices of stocks and bonds will be inadequate, but rather the increase in earnings, profits, dividends, and solvency of bond issuers will not be there to legitimize or rationalize current prices.  In English, this means as people flood the market with retirement dollars P/E ratios will go up, dividend yields will go down, and financial deadbeats (in the form of most western governments) will continue to borrow money at low rates they will never be able to pay back.

People who are planning for retirement need to consider other forms of retirement beyond their IRA and 401k's.  They need to look at skills, property, commodities or just working till they're dead.  Not just because they didn't save up for retirement, but because the prospects for growth just isn't there.

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Fred Z said...

I'm 60, semi-retired, by which I mean I work on my own stuff.

Your analysis excludes property, specifically income earning property.

I know lots of guys about my age who own a strip mall or two, small apartment buildings, a few rental houses and so on.

What's your analysis show if all such property is added to the pool of investments available for saving? What's the value of all the worlds income producing real estate?

Have you ever noticed that shareholder equity in, for example, bank stocks, is a huge juicy pool of value very attractive the socialist political classes. I'm dumping my bank stock, and likely all stocks in favor of dirt. I'm of central European genetic extraction and you just can't get the dirt out of the peasant I guess.

As my dad always said, if the economy collapses, everybody needs a roof and maybe they can pay with chickens, potatoes or cigarettes.

Anonymous said...

Or, you know, ye olde retirement. A farm and 12 kids.

Finding a proper wife for that, now that'll be a difficult.

Anonymous said...

Doesn't take a mil to retire in Africa, or probably most of the world. Everything else is spot on.

Captain Capitalism said...

Hi Fred Z,

Yes, I thought about that. Real estate and commodities would also play a role. And for the most part people are "saved" when they retire by either their own property or inheriting others. But unless you're investing in REIT's there is no 401k investment in real estate.


Glen Filthie said...

Retirement will not be an option for the majority of us - nor should it be.

A mere two generations ago you worked the minute you could pick up your dad's tools, till the day you literally couldn't hold them anymore. Then you went home to die, usually surrounded your family after a life well lived. That will be the way of it for most of us - and what of it?

I have seen the spoiled elderly, rattling around their houses, annoying their wives and kids and neighbours out of sheer boredom. They are welcome to it! I have things I would rather do.

MoscowEast said...

Looking at your chart at:

I don't suppose you have an updated version you'd be willing to post?

David Foster said...

Interesting analysis. Many company, "nonprofit," and government retirement funds do own property, private equity, and venture capital assets directly...not sure what % of the overall defined-benefit portfolios these represent.

For the individual managing his own funds, direct investment in small businesses, either as debt or equity, may makes sense. Regulatory barriers against this seem to be coming down.

Gary said...

Instead of a 401K put that money down on a duplex or triplex. Then the rent collected will pay off the loan for you.

One of my clients "works" full time just being manager for his own batch of small income properties that he bought over the years.

TheCynical1 said...

Some people argue that those masses of humanity in the world out there, who currently don't own stock, should actually be viewed as potential stock purchasers in the future -- who could drive up stock values and increase the size of the stock market over time. I wonder what the answer to this argument would be.

sth_txs said...

Good points! The funny thing is some of these retirement guys always like to assume an 8% or higher growth rate which is simply not possible.

I'd say realistically you are doing good to make 5% on any investment.

Real estate would be nice, but it has to be location, location, location. Plus, you have the extra leftover income to buy it along with keeping up with general living expenses.

Anonymous said...

Retirement is something that only really happened in the second half of the 20th century. For lower-middle class folk to spend the last 20 years of their lives not working, after working only 40 years, there needs to be some kind of Ponzi scheme where a large number of workers are supporting a small number of retirees.

The glory days of getting social security and a General Motors pension at 58 were never sustainable, planning on working until the bitter end may now be the best way to go for most.

gauthijm said...

Brilliant analysis Aaron

Ballpark, youre spot on, there's not enough cash, property, stocks, bonds and especially Growth to sustain a 35 year window of retiring people.

If you dont have the million yet(?) at 50-55 already, there's no way the market will "bail" you out

Add the following facts & observations;

a) that the Major Leg of the retirement pool is Social security and Medicare, already in negative mode (more coming out than going in). This applies to my Canada (less) but we WILL have rationing, guaranteed

b) the Fed and all other central banks, don't blow teh whole world up with their QE crap; Gold has been a disaster, so theres no place to hide P.S> if you bought gold anytime before 2009 youre golden (:)) but 2010 and later, not so much..
c) One good thing, is I think DEFLATION has taken hold, and inflation, with lower and lower money velocity will stretch a good dollar, or a million a lot further, if You HAVE it, and no debts..

What you need now to make it, in my opinion

1- 1 Million in cool net assets, apart from the house, or sell the house too and live in low expense contry; difficult but possible

2- Ne Debts at all; or debts but #1 above is still over a mill, or a bit more. Also possible , Im 2 for 2

3- Everything is invested conservatively, like rental property, dividend blue chips, REITS and stuff. I'm 3 for 3

4- a Good marriage or a good divorce, before the you-know-what can get most of teh above amount; Im still working on that, but it's gonna hurt, what a surprise....Im 3 for 4 on the Good, 1 for 1 on the bad, so this is a negative for me..

5- a normal or low standard of living, like a guy that junked #4. above and can live w/o all the crap western females "need" to live off.. What BS...

I think I can do it, all my hobbie's costs are pretty low, expect for a computer every couple of years...

Still Aaton, that was 1 hell of a good article, and I find very very curious no one's ever tried to expose something like this, in the MSM/LSM.

THEY suck!

You, fortunately, are on the ball Cappy Cap!


PS I particulalrly enjoyed your description of Phyllis in 1 of your early books, I work for a male version of the you-know-what right now, it's painful...

Anonymous said...

Agreed with the Anon @8:01, there are several places even in the US where you could live comfortably in perpetuity for $500k or less. One example would be Arkansas, where you could buy a $25k house and live off $15k-$20k a year from withdrawing from a $500k portfolio. There are also cheaper places, even within the U.S.

>>But unless you're investing in REIT's there is no 401k investment in real estate.

There are many mutual funds that invest in mortgages or promissory notes or tax/other liens on real estate, and they are typically selectable in a 401k.

Paul M. Jones said...

McArdle appears to agree with you.

sth_txs said...

I played with the retirement calculator. It proves to me, at least for me, that we should return to commodity money.

Anyone who tells me inflation is good or necessary is a damn fool, especially if they have an MBA behind their name. Neither my salary nor my investments have matched the real inflation rate.

Fearsome Pirate said...

Your rough mathematics are too rough. They're barely even an order-1 approximation, if that, i.e., you should probably be rounding everything to the nearest quadrillion when you're done. The problem is that you're trying to model a calculus problem with algebra. You have several important changing variables:

1. The rate at which people retire.
2. The rate at which retirees die.
3. The birth rate.
4. The growth rate of assets in the world.
5. The rate at which capital is turned over from retirees to the non-retired.

At no point, ever, will 100% of the world's people be retired. This is especially a bad approximation because assets ultimately have value from the economy's wealth-producing ability, which only exists when people are employed.

Aeroguy said...

There was something significant you left out. People will only have the level of wealth required for retirement at the moment they retire. Unless they stash enough to live exclusively off the interest the principle they have stashed away will deplete over the course of their retirement. There is also the process of accumulating the retirement money in the first place. Since people make progressively more money as they age due to gaining experince, growing their business or climbing the corporate ladder their retirement money has an exponential growth pattern. So if you use the style of retirement planning in your privided website to calculate the money needed you would need two charts, the first showing exponential growth peaking at retirement age and then falling off at a roughly linear rate transposed against a population age distribution chart (distortions in this are what killed the Japanese economy, is in the process of killing the boomer's retirement plans, and will kill China's economy in the future) in order to calculate the amount of money people would actually be saving at a given point in time. A frugal and financially savvy boomer in the upper-middle class can have their retirement (at 60 instead of 55 like they originally planned) however that is a small minority of people. Mind you I agree with your ultimate thesis that the boomers retirement savings are distorting the markets and that they're delusional if they think they can all retire comfortably.

Anonymous said...

You could do a self directed IRA with real estate if REIT's aren't your thing.

bluto said...

Capt is very right, there's no possible way 6.5 billion people can be so produtive in roughly half their life to pay for leisure and specialized learning to become productive in the remainder. Retirement could work if it consisted of either insurance for the left half of the livelihood bell curve (ie the retirement age is set at the same age as the average person's death), but few people remain congatively "there" that far into their lives to be productive in such a specialized world, either.

Al in La Paz said...

At 60 years old my wife and I sold everything we owned and moved to Mexico. We live on $35K a year in a 2000 sq. ft. house with a pool. Just got back from a 3 week cruise. If we moved to a smaller house and travelled less we could manage on $25k with no problems. It's paradise!!!

Roberto Severino said...

If I were making 85,000 dollars annually and had 35 years until retirement, I would need to save up about $2,556,777.18 considering a 2% annual inflation rate and a yield on the balance of 5%.

Maybe even saving a million is going to be harder than I previously suspected!

Ten Mile Island said...

Ceterus paribus.

Or, multiply and/or divide by zero.

Seriously, do we need to re-invent the ISLM curve?


Anonymous said...

It gets worse, the new hotness is social justice investing and 'low-profit' corporate structures where you'll get 1% return on your capital and like it. Because, the environment and social justice.

Since you have the free time and I do not, google 'benefit corporation' or 'triple bottom line' and be appalled. And maybe write it up fancy for the box seats!

Ofay Cat said...

This is an exageration. You don't need that much money to retire. It depends on how you plan to spend your last years on the planet. Also depends on how long you live after retirement or how old when you retire.

Forget Freedom 55, that was disney shit.

Most folks will have some small pensions from government or jobs. Government workers need not worry so forget those pigs at the trough.

Set yourself up to live within your means and also don't count on being able to afford a lot of expensive travel.

You may just have to enjoy a smaller life with fewer toys and a lower overhead.

I retired at 68 and I don't have a million, but I do have enough, along with various small pensions, to live well and have fun without breaking the bank.

The bottom line is that you have to deal with reality.

Finally, some folks aren't going to be able to retire and many will die before they get to retire.

So it's all good. If you work hard, use your head and stay the hell out of debt, you will achieve some lovely retirement years.

Keep you gun though. You never know.

tz said...

The window where retirement - pensions - were possible was made possible by the baby boom. If there is 4x the workers when you retire, there will be surplus. But the boomers brought us contraception and abortion and "every child a planned and wanted child" to quote the surgeon general under Clinton.

Fred Z said...

Am I right that a 401K is the same as a Canadian RRSP?

If so, sorry, time to bite the bullet, pay taxes in full and invest outside 401ks and RRSPs.

Because they're going to steal both 401Ks and RRSPs. Such a nice rich cash pool, how could they resist? I'm guessing they'll start with a major inheritance tax and grab what's left when you croak. Because we're provident, savers, and we'll never spend it all. Or maybe they'll restrict your annual income, or cap the plan at 2 or 3 Mil and seize the rest or whatever. Cyprus.

Even if they don't out and out steal from you, the registered nature of these plans gives, way, way too much information to federal tax collectors.

Anonymous said...

I haven't seen anything about life expectancy yet. Maybe I missed it.

Just one example: India. There are over 600 million men there, which is 8 or 9 percent of all the people on earth. So it's a big example.

Current life expectancy at birth for Indian males is 62 years. So, the amount that the average Indian male needs to save for retirement is: $0. (Of course, he won't know that until the day he falls over.)

And there are dozens of countries in still worse shape. Bottom of the list is the Central African Republic, whose lucky male population can expect to live for a whole 44 years.

Jokah Macpherson said...

I agree with your basic point that the retirement "industry" is mostly bullshit.

However, even though I don't have much training in Economics, I think that Fearsome Pirate is right. Existing wealth in the 401ks of retirees is going to get circulated back into the economy, where it will enable those currently working to purchase assets in the place of those retirees. Therefore, there will not be a need for the quadrillion dollars worth of assets to which you refer.

I think I've seen arguments elsehwere that the whole concept of saving is one which is only of value if not everyone is doing it, i.e. if everyone was ultra-frugal, it would all be a wash because there would be less spending to bolster the value of equities. It's almost like a more opaque version of the lottery - a tax on the low-IQ.

Interestingly, I'm a 3rd generation defined benefit pension holder. My material grandparents had pensions from the state from being teachers and my dad had one from the feds from working for NASA. I've tossed around the idea of cashing out on my pension under the assumption that the state can't sustain its obligation over the long haul but I ended up just adopting the Stoic attitude that although it probably will be much less than promised, a risk free income in retirement is better than trying to accumulate wealth to ride out your life expectancy.

Anonymous said...

I don't know if the retirement business is BS, but at age 60, with assets (excluding the paid off house) of around $1 million, I sure feel better about having that million than I would without it.

My advisor says I'm in good shape and could retire tomorrow if I wished, but I'm not ready and my wife is definitely not ready for me to retire - she insists that I work until 65 and longer.

paulmurray said...

A better question is: the labour of how many younger people are you going to need to support you in retirement? Money is a mirage.

Anonymous said...

Retirement is a fantasy created by entitlement states. It is not possible for a society to pay for the existence of 20% dead weight. Before social security, people expected to die working. After social security, now people somehow believe that 20% of your life should be free of production. It is a lie, retirement is bullshit.

Anonymous said...

I'm 72 years old and I was never allowed to work when I was 47. I made sure that by the time I was 65 I had no debt and my mortgage was paid. My wife and I make about $35K per year. We both have modest savings accounts (RRSPs and TFSAs).

We live good productive lives and don't really want for anything.

This talk about needing $1-million to retire is a bunch of hooey put out by people selling retirement plans, mutual funds and investments.

If you retire at 65 and had a decent job, you will probably receive $1600 per month in CPP and OAS. On average you only have about 20 years left to live. If you "need" another $20,000 per year to live, all you need is $200K.

You'd be surprised how well you can live after retirement without a million dollars.

Joe Bar said...

I was advised that I could take full advantage of my retirement plan at the end of the month. I am 56, have a 401K worth over 400K, and not many debts. I could make it work.

My wife, however, insists I work another 4 years. At that time, my Army reserve retirement will kick in.

I wholeheartedly agree.

All you Gen Xers and Millenials go ahead and hate. I will be dead when I care.

Father Marker said...

Third world citizens have the retirement formula right. Their kids are their superannuation. Have a larger family and get them to look after them when they are old.

It's a bit harder for Governments to flog their kids than funds out of super accounts.

Anonymous said...

What about this:

To make it simplier imagine for a while you are somehow isolated. You don't need money till let's say you are 20 (parents feed you). Then you are productive for 45 years. Then you retire at 65 and live to 90. Provided there is no inflation, no interest and everything else remains constant, including your consumption, you need to produce enough income during 45 years to cover those years and on top of that 25 years of retirement.

You need to cover 45+25=70 years but working only 45. 45/70=0.64 - you can consume 64% of your income during productive years, the rest must be saved.

To save a third of your income does not seem unrealistic, ha?

And if there is a chance to have some interest on that savings? Maybe saving a fifth would be enough. Just guessing, too many variables here.

And if there would be deflation what is the natural way due to increasing productivity, it would be even less.

People retired normally dozens of years ago and the productivity was lower that time. Now it shouldn't be a problem at all. Only if the governments wouldn't stick their dirty fingers into our pockets...

So what remains is the easy task to convince your government not to inflate or outright steal your savings. Better go and start to talk to them NOW.

It's that easy dear Watson...


Norok said...

I too, love rough math, because nothing is assured in finance and I can still get to my conclusion.

Re-blogging this. Thanks brew!