The wealthy (allegory)

If you compare the total (or average) wealth of the world’s wealthiest individuals a few decades ago with the total (or average) wealth of the world’s wealthiest individuals today, you’ll certainly notice that the total (average) wealth of the wealthy has increased significantly faster than the total (average) wealth of the rest of us.

I won’t provide a single number to support this statement. It is true whatever you mean by “a few decades” (10 years, 50 years etc.), whatever you mean by the “world’s wealthiest individuals” (the top 100, the top 10% etc.) and for all reasonable definition of “significantly”. Clearly, you would be losing time trying to demonstrate the opposite.

One interpretation of that result is that the rich are getting richer (and the poor are getting poorer, at least relatively). This is the line of explanation given by Thomas Piketty (at al.): the richer you are today, the faster your wealth will increase in the future which means that, if nothing is done, the world’s wealthiest individuals as of today will possess everything in a more or less distant future.

That being said, let me share a first secret about the rich: they’re old.

For instance, as I write this piece, the top 10 richest persons in the world according to Forbes are 67 years old on average (and yes, that list include Mark Zuckerberg who’s only 34). That’s a constant: although there are, of course, exceptions whenever you think of the rich, you actually think of the bunch of elderly. Just give a look around you and ask yourself who are the richest persons you know: yes, they’re old and that’s no surprise since, by definition, they have been accumulating wealth for many years (and, luckily, we inherit from our parents quite late these days).

But you might wonder what is my point here. It’s time to share another secret about the rich: they, too, die. And since they are old, the odds are they’ll die shortly.

So the total (or average) wealth of the world’s wealthiest individuals a few decades ago was actually the total (or average) wealth of a bunch of elderly of which, presumably, an appreciable number died shortly after. In other words, the world’s wealthiest individuals today are very likely to be a different group of people meaning that the rich haven’t become richer (they died) and some non-rich took their place and eventually got even richer.

But, you say, today’s wealthy have inherited their fortune from the previous wealthy: these are the dynastic fortunes Piketty is talking about.

Well no, it’s unlikely. Granted, at some point in history one could inherit the entire wealth of its predecessors. But these times are gone and it has nothing to do with inheritance taxes. A few centuries ago, great fortunes came with a name, a title and lands, all of which was attributed to a single heir. This is how they maintained large dynastic fortune over generations. But today, the wealth of the rich is shared by their sons and daughters or even by their grandsons and granddaughters. So, at least, transmitting a large fortune through generations has become much harder.

It’s time to reveal the single most important secret about the rich: most (if not all) of their fortunes is made of shares, usually those of the company they have created (or inherited).

It is important for two reasons. The first is the well-known ‘third-generation curse’: if the sons and daughters of the founder frequently become successful business owners, the grandsons and granddaughters usually fail and destroy their inherited wealth. It’s not that much because they became lazy but rather because the third generation is made of many cousins who are therefore much harder to coordinate. I know a counter-example of this and I can testify that their success required (and still require) a huge amount of coordination to maintain the family group united and effective.

The second reason is that stocks are volatile and a single-company fortune is even more volatile. In other words, the wealth of the rich can go up or down significantly faster than the wealth of the rest of us. If, for instance, you had $42,500 on August 19, 2004 and decided to invest it all on Google shares at its IPO price (500 shares at $85) you would be a millionaire as I am writing this. But that also means that you would have had a hard time between the end of July and the end of December last year: your wealth would have collapsed by about 15% in just five months (allright, in this case you’d have recovered everything). Keeping this in mind, consider my initial claim and let’s tell an alternative story.

The total (and average) wealth of the world’s wealthiest individuals a few decades ago collapsed shortly after they were ranked in the top whatever-you’d-like percent. It happened because their fortunes were made of the shares they held in their companies and what brought them to the top of the wealth pyramid also brought them down. This is what happened to Japanese billionaires in Forbes’ 1989 first global ranking: they were all real estate magnates and lost most of their fortune when the bubble burst in 1992.

Meanwhile, a number of young entrepreneurs from the middle class or even poor households created innovative and risky businesses that eventually became extraordinarily successful. Because their initially modest fortunes were entirely made of the shares of their respective companies, they became even richer than their predecessors. I guess everybody knows who Jeff Bezos, Bill Gates, Larry Ellison, Mark Zuckerberg and Larry Page are. They are all part of the current top 10 according to Forbes.

Is my alternative storytelling consistent with statistical observations? Yes, absolutely. Is that consistent with Mr. Piketty’s interpretation? No, that’s quite the opposite.

The problem with the interpretation of Mr. Piketty is that it completely ignores a well-known logical error known to anyone having studied populations over time: the survivorship bias. The indisputable fact that the wealth of the top whatever-you’d-like has increased significantly faster than the wealth of the rest of us is, by no mean, a proof that the rich are getting richer.

To be clear: although Forbes confirmed numerous time than today’s billionaires are overwhelmingly self-made men and women, it would be an hazardous shortcut to generalize to the whole pyramid of wealth. There might be some truth in both explanations (after all, Francoise Bettencourt Meyers — L’Oréal, third generation — is the richest women in the world); the question is which of these two storytellings is closer to what has happened.

I have no definitive answer to that question but only a suggestion. Beware, readers, this is where this post becomes a bit technical.

A common way to simulate asset price movements over time is to use a random walk, that is, to describe possible future price developments as random processes and to see what could happen in terms of probabilities. With random walks, we can simulate the trajectories of anyone’s wealth as Monte Carlo simulations.

For instance, in a world of entrepreneurs, we might expect a high average growth rate in the value of assets (say 10%) but at the price of a high volatility (say 15%). This is what it would look like over 260 days and assuming the initial wealth for everyone is the same ($1):

Everybody own stocks

The wealth of the average person has grown by about 11.8% (slightly over 10% because of capitalization) but the third quartile (the minimum wealth one must process to be part of the top 25%) has grown by 22.3%, almost twice as much. Admittedly, it looks like what we observe in statistics: fast growing wealth but with striking inequalities.

Now, keeping the expected return of assets at 10%, let’s simulate Mr. Piketty’s world: a world of inherited wealth where everyone hold low-volatility assets (say 5%) :

Everybody has a private banker

This time the average person has made 10.7% and the third quartile only made 3.6% more than that (14.3%). In other words, this world also creates inequalities, more persistent inequalities but they grow much slower. That’s clearly not what statistics in the real world are saying.

To summarize, a world of explosive fortunes where today’s rich are much richer than their predecessors is much closer to a world of self-made entrepreneurs than a world of dynastic wealth. If Mr. Piketty was right, not only the top of the wealth pyramid should be filled with heirs (which isn’t the case) but they shouldn’t be significantly richer than their ancestors (which definitely is the case).

Also consider this: in my simulations, we start with a world a perfect equality where everybody has a dollar and then let these initial fortunes grow (or decline) randomly, picking variations in the same distribution (i.e. the normal distribution but this is of no consequence) with the same expected gain (ie. the mean) and the same volatility (i.e. the standard deviation). And what do we get in the end? Inequalities and a right-skewed distribution of wealth, just like in the real world.

In other words, inequalities and a right-skewed distribution of wealth is just a natural consequence of the fact that people may do what they want with their money. You don’t need any kind of bias or unfairness to obtain that result.

So Mr. Piketty is probably wrong: we’re not living in a world of dynastic, inherited fortunes and there is no justice in penalizing the successful. If we decide to do it anyway, we should think for a moment about the potential consequences. In my simulations, I assumed that the average growth rate of wealth would be the same in our two possible worlds, but history and basic economic data suggest the opposite: if we eliminate the incentives, we risk becoming all equally poor.