I’m going to show you why giving money to other people may actually make you wealthier in the long run. Not richer in the spiritual or psychological sense, but truly wealthier in a monetary sense. In doing so the whole of society will be better off too.
This concept might seem strange but many of my articles start out with unusual premises. Give this one a chance.
Compound Growth
My blog focuses on maximizing compounding growth in investing. I have laid out the mathematical framework to do this in a simple example with two assets.
The general concept is pretty simple. You allocate the wealth inside the portfolio to each asset based on its expected return and the volatility.
The wealth is allocated to maximize a tradeoff between increasing return and simultaneously reducing volatility of that return (the Kelly criteria).
Then you rebalance the portfolio back to those percentages as often as you can. This often entails taking money from the best performers (selling them) and re-distributing it to lower performers. Moving the wealth from the best performers to the worst keeps the wealth balanced appropriately between all assets, maximizing the long-term compound growth rate of the entire portfolio.
This can seem a bit counterintuitive as many people like to let the winners run. I’m saying constantly take money away from them.
Some may think this is a mean-reversion strategy, but I’m selling an asset and moving money to a lower performing asset, even if I believe the asset I’m selling will out-perform the one I’m buying. Find someone else who tells you to sell the winner, buy the losers, and doesn’t believe in mean reversion (and for anyone who doubts this works….it does).
I know this concept feels strange. But when you’re dealing with random compounding systems, this is the mathematically proven method to maximize growth.
Equality of Wealth
The easiest way to divvy up your portfolio is to just assume all investments are equal. From a purely stock perspective this is clearly flawed but it is not an awful assumption.
If your investments are equal, then the optimal growth portfolio is an equal weight portfolio.
In this world, when some stocks outperform others through randomness, you would re-distribute the gains from the high performing stocks to the stocks that did poorly. That way you have the same amount of wealth invested in each stock at all times
The goal is to have zero allocation inequality in your investments. When all stocks have the same expected return and volatility, zero allocation inequality should produce the highest portfolio growth.
I’ve shown that if you do this with stocks–equal weight them and then rebalance frequently–you will outperform the stock market given enough time.
It’s the Same Math for Society
Let’s take my example of maximizing growth and overall wealth in an investment portfolio and apply it to society. How would you take the “societal wealth portfolio” and allocate it if you were looking to maximize growth and progress?
In my example replace stocks with people, and the portfolio’s wealth with society’s wealth. If we stick with the assumption that all people have the same “production capability” and same “output volatility”, then you come to the same conclusion as above:
Society as a whole grows the fastest and progresses the fastest when wealth is equally distributed among all people.
Relating the analogy to society, “taxes” on high incomes rebalance wealth back to the less wealthy keeping the wealth distribution flat.
I could try and explain further here, but Marc Elsburg has already explained this pefectly in the “Farmers Fable” story.
Please watch this video before going on further, or visit the website here www.farmersfable.org for a more interactive version.
You can see that when the two farmers share their resources, their combined wealth grows faster over time. When Ann has a good crop and Bill has a bad crop. Ann shares her surplus wealth with Bill. This way they start out every new planting season equally. In doing so, they reduce their individual output volatility, and increase their combined compound return.
But notice something else, Bill and Ann’s total wealth when they cooperate is higher for both of them when compared to not cooperating.
By giving the other farmer some of their own harvest, they don’t just help the other farmer, they help themselves too.
The cooperation literally makes them both richer.
“Anything that grows exponentially grows faster (all else being equal), when pooling and sharing reduces fluctuations.”
Mark Elsburg
So next time you think about redistribution of wealth through income taxes, think about this example.
The Big Assumption
However, there is a really big assumption at the start of this example. Do people really have the same “production capability”? It doesn’t seem like it.
I watched the Space X launch this past weekend like many in absolute awe of the accomplishment. A private organization sent two people into space. In many ways though, it wasn’t a private organization. It was the sole desire and dream of one man, Elon Musk.
Elon Musk seems to be a bit of a lunatic. But he is crazy productive. He helped found and build PayPal, which has been pretty useful for the world. He became extremely rich from this. Instead of sitting on his riches, he reinvested it into Space X and then Tesla.
Space X is an amazing company that will likely change the trajectory of human travel forever. It’s already saved NASA billions and billions of dollars in costs. And the company provided everyone a bit of inspiration at a time when we all needed it.
Tesla is unquestionably changing the entire worldwide automotive industry, most would say for the better. Energy usage (and production) as we know it across the planet is rapidly evolving simply because of Elon Musk.
The thing is, if Elon Musk had to return his millions and millions of dollars from Paypal, if he had to rebalance it all back to society, none of this would have happened. He used only his own money to create Space X, and he used enormous amounts of his own money for Tesla.
Honestly, who thought 15 years ago it was possible to create a private space company? Who thought they could take on the automotive industry with a new car company? The former hadn’t ever been done. The later hadn’t been tried in decades. Nobody was taking up these challenges.
I like to think I’m a productive member of society. I like to think I’m capable of great things. I’m not one to put limits on myself. Case in point, I’m writing a blog as an outsider explaining why the finance industry is sometimes mistaken.
Yet I look at Elon Musk and think, there is no way in hell I could accomplish a tenth of what he’s accomplished. I’m not capable of that. But I’m really glad he is, and I’m really glad he had the resources to pull this off.
Elon Musk isn’t the only one in this category . Steve Jobs come to mind as well. And there are many, many smaller level super-producers who are doing great things for their communities similar to what these visionaries accomplished at the global level.
Wealth Distribution with Unequal Capabilities
The point is society benefits greatly when people of great capabilities have the necessary wealth to accomplish great things. Furthermore, the math of maximizing compound growth says that those that can produce more, should have more to produce with.
An example with investing. When I have a portfolio of stocks and bonds, I usually think stocks will meaningfully out-produce bonds. Therefore, I will allocate more of my wealth to stocks. Plenty of my wealth will still be in bonds though (think 60/40 as an example). When the super-producer stocks do outperform bonds as expected, I will move some of the profits back to bonds, so that the wealth ratio between them stays the same. This rebalancing maximizes long term collective wealth.
When the super producers have more with which to produce, everyone should benefit as well. This is because even when the super producers start with more wealth, the math still says the super producers should rebalance some of their production back to the average producers.
The key here is that even when the math supports unequal wealth, it still calls for some of the wealth to be rebalanced back to all participants. Importantly, the rebalancing ensures that wealth inequality does not change.
The only reason the rich should get relatively richer is if their “production ability” goes up, not because they actually produce more.
What About Real Life?
In my investment framework, I need to constantly estimate the investments’ return and volatility. This is a big challenge. The estimates are guesses and I have no idea what they truly are.
Apply this framework to society, and the estimating problem becomes overwhelming. How would you estimate someone’s production capability? How do you do this fairly and accurately? I have absolutely no answer for this problem. Even trying to estimate this seems insensitive on an ethical level.
My idea looks good on paper, but is really hard to apply to the real world. I want to believe we are mostly equal. But it’s obvious that’s not entirely true because of people like Elon Musk. I want people who can do great things to be able to do great things. But how do you know who’s capable of great things?1 Where is the balance point between these two sides?
There are also psychological issues that come into play. My example is overly simplified since it assumes people are robots.
You can demonstrate to a super-producer that giving back large chunks of their income through taxes or charitable donations helps both them and society in the long run. But it is a very counterintuitive concept and it’s understandable why they might stop “super-producing”.
You can demonstrate to someone why Elon Musk trying to solve the world’s energy problems and climate crisis on his own is a good thing for everyone. However it can still be a tough pill to swallow when both are working just as hard.
The Benefits of Cooperation
So have I solved anything with this post? Not really. If the problem was easy to fix, we would have already solved it. But I’m hoping you will think about wealth inequality a bit differently now. Maybe someone somewhere will strike inspiration from this post and repurpose these ideas into a greater one. If you are that person, I hope you will focus on these key points:
- High levels of wealth inequality are mathematically bad for society.
- Rebalancing some income from the rich to the poor can be supported as good for everyone.
- Some people are super-producers and society benefits when they have more wealth.
- Even when super-producers posses more wealth, a portion of their income must still be redistributed back to optimize individual and societal progress.
And most importantly:
Cooperation Benefits Everyone in the Long Term.
1-This is actually why you need to rebalance in the first place, as you don’t know where the best performers will come from in the future.
I believe the system of capitalism has seen the best growth of any system largely because it does efficiently redistribute wealth (“allocates capital”), and does so from a bottom-up approach. For example, people who have no otherwise productive use for their capital deposit it in banks or lend it to super-producers like Elon (via purchasing Tesla stock, for example), who can create more value with it. So in this way, the “market” is deciding how to efficiently allocate the capital. Each investor or banker is tasked with determining the production capability of the person, firm, or country they are looking to lend to and allocate accordingly.
That said, I do believe the increased financialization (HFT and derivative trading, corporate raiding, hedge funds, etc.) in the last 50 years or so has pulled us away from this, and given capitalism a well-deserved black eye. But the fundamental engine is good.
The farmer case is compelling, but I fear too simplistic as to be misleading. Extend this to 1,000 farmers, for example. Who controls the pool of wheat? Is there a central authority that now has it’s own incentives? Should farmers with less arable land, fewer farm hands, and shoddier equipment get a smaller share of the wheat? If a farmer shirks his duties, how is that recognized and controlled for now that there isn’t as much social pressure to maximally produce (1 out of 1,000 may not be noticed)? If a farmer decides to consume his guaranteed crop yield instead of using it for more production, how do we account? It seems like the on-paper ideal is to remove any variability (aka volatility) due to luck — one farmer’s bad weather should not affect his yield and another farmer’s good weather should not allow him more. Maybe we use something like taxes and compelled insurance?
At the end of the day, this did make me think a lot, but as the rubber meets the road in a society of hundreds millions of people and unspeakable amounts of complexity and issues, I’m still not convinced that a redistribution scheme can be both adequately determined and implemented as to produce more for all. Perhaps for a more realistic solution, we should look closer at ways to better capitalism’s innate lending facility: to make easier for poorer people to acquire education and healthcare (increase productive capability) or start ventures (realize productive capability). These things I am more open to now after reading the article.
Its very complicated, and I’m not convinced of an answer either. I think you understand the underlying point of the post though, and I apricate the depth and thought you put into this reply.
So, great post, a good start to thinking about this problem. A few random thoughts:
1. First we must define wealth in an analogous way to your geometric balancing model. One problem with the way that wealth is commonly define,d as net equity on a financial balance sheet, is problematic in 2 ways: 1) it can be negative (whereas, in yours any one component can be negative – leveraged – but the total has to be positive, and 2) it ignores a BUNCH of stuff (namely, commonly held resources – think, SS/medicare, etc – and human capital – most people’s most valuable asset). That these latter can’t be be traded on the market doesn’t change these facts. So applying, your model would require attempting to bring these onto the ledger.
2. More importantly, what is the point of wealth, but to consume it. So, while wealth, income, and consumption all try to get at the same things, the first two measurements are merely proxies.
3. So the common refrain is that wealth inequality has risen over time, at least in the US. My point would be that it may or it may not have, but we don’t know because 1) we are measuring wealth poorly, and/or 2) we are not really paying attention to consumption at all. It may be that wealth inequality, defined as the unequal capacity to consume, has remained stable over the same time period that poorly/partially measured wealth inequality has increased (there is actually some evidence for this). This is especially true if you allow for the possibility that some things that count in a person’s measure of wealth, like assets they will eventually give to others, are actually consumed by others, and more appropriately apportioned to the eventual consumer’s wealth.
4. There are some things in a human society model that are not present in your portfolio model, namely: status. Whereas growth of a portfolio or material consumption is positive-sum, status is zero sum (and negative sum to the extent we expend resources to stay in place). Most people’s mental model of the economy is underdeveloped because they ignore this latter component. Humans expend A LOT of resources to jockey for relative position is society, only to take from Peter to pay Paul. I’d have to think more deeply how to incorporate into you model.
5. Then there is the practical notion of how this accomplished, a tax on the stock (wealth) or the flow (income). Say you have a wealth portfolio that earns 10% (arithmetic) with 15% risk. You could pick a 20% tax on the income, or a 2% tax on the principle, and the tax would be equivalent. But when you do the math the geometric return (both absolutely, and relative to risk) would be harmed in the wealth tax scenario vs. both the income tax scenario and no tax scenario. In other words, the income taxed scenario can be levered back up to achieve the same risk/return profile, but if the base wealth is taxed “equivalently” the risk/return profile would be worse. I would need to think more about the implications of this society wide.
Thanks again for a great post.
It is a deeply complex problem and all 5 of your points are valid. I definitely over simplified the issues. The status part is maybe the most important aspect here because as a zero sum game, the cooperation part doesn’t really work the same way.
As long as long-term benefits, like the future of our kids, have no value in “the market”, it will (sadly) care little about them.
Regarding Paul’s comment “make easier for poorer people to acquire education and healthcare or start ventures”, it’s interesting to take a look at the US: It doesn’t do that and still it’s the most successful capitalist society. Instead it chose to give extra privileges to the strong in order to attract foreign talent from countries, that provide proper education and healthcare.
For your further research, you might want to investigate open-source software projects. They greatly demonstrate the superiority of cooperation over pure self-interest.
If I may say so without being patronizing: I am not sure you chose your example wisely.
Your contribution to society through this blog seems to me much more positive than Mr Musk’s.
Thank you. Who knows maybe one day it will be.
Paul,
“That said, I do believe the increased financialization (HFT and derivative trading, corporate raiding, hedge funds, etc.) in the last 50 years or so has pulled us away from this, and given capitalism a well-deserved black eye. But the fundamental engine is good.”
My take is that financialization in and of itself isn’t bad. It’s when it’s bailed out under the guise of “too big to fail” using public monies that could otherwise be used productively. This form of capital allocation is atrocious, in my view.
The farmer fable is very interesting to me, actually from a farming point of view. In USA most broad acre crop farmers take advantage of government subsidized income insurance. This generally does what the farmer fable points to. I guess all insurance does this as long as the cost to manage is low?
But in Australia most broad acre crop farmers don’t buy insurance but we have a bigger need for it due to higher income volatility from more volatile weather. Our gov doesn’t subsidize it which is one factor and I guess farmers feel the insurance companies costs and profits are too high to see a benefit.
But you have me wondering how to show the benefits or otherwise of crop insurance to farmers using some Monte Carlo simulations like the farmer fable video showed. Thanks for the insight.
There is an argument that insurance makes wealth grow faster and is good for everyone involved (obviously if priced fairly). This paper is a bit technical but describes the math behind it, and it is essentially from the same concepts as the farmers fable.
https://arxiv.org/abs/1507.04655#:~:text=Ole%20Peters,%20Alexander%20Adamou%20Voluntary%20insurance%20contracts%20constitute,parties%20must%20sign%20for%20such%20contracts%20to%20exist.
Thanks. I read it and it solves a big part of the puzzle for me. But why is symbolic math used to prove and explain these concepts while Monte Carlo simulation is so much easier to understand and prove. Don’t you think if they just ran that ship insurance problem in a Monte Carlo sim it would prove the same thing much more visually and simply?
Kind of. The problem with running a bunch of monte-carlo simulations is that you then create and ensemble of simulations, and you can’t take the arithmetic average of them. So and if the difference is small, it can be hard to see it with Monte Carlo simulations. This is why my examples have such large standard deviations in coin flips. It makes the effect really obvious. The math however makes it concrete. They are also Physicists, so they like fancy equations.
I agree with the vast majority of what I’ve seen on this blog, which is why you’ve never seen a comment from me. I believe your methods provide an efficient and reliable way to calculate a safe and productive portfolio:
The one method in particular that stood out to me was the inverse association of negatively correlated asset variance in mix ratios, a concept I understood intuitively but had no frame of reference for quantifying. When your graphical method lead to the same result as my previous calculations with a covariance matrix, I knew that including this particular asset in my portfolio despite its lackluster individual performance was justified.
So understand that what I say next has no ill intention toward you, your methodologies or your philosophies. It’s a mistake many, many people have made, including some of my closest friends.
Elon Musk is hardly responsible for any success by Tesla, and his culpability in the success of SpaceX has only been in persuading the government to give him even more money than he’s already received for co-opting and ruining Martin Eberhard’s company.
That money was give to some bright-but-not-exceptionally-so individuals, who were then given access to virtually all of NASA’s data and materials knowledge with none of the agency’s safety and budgetary restrictions.
NASA has held their hands through SpaceX’s many and continuing failures, and guided them to success.
It infuriates me to see this company receive accolades for doing what our increasingly misguided government has actively prevented NASA from doing, largely at the behest and to the benefit of individuals such as Elon Musk. The situation is no different than Postmaster DeJoy slowing down the Post Office so that Amazon’s consistent two-day shipping can shine the brighter. It’s a problem hardly unique to SpaceX or Amazon, and it has grown worse with each passing year.
i understand if you’d rather not have politics on your blog and you have every right to delete this reply.
But I feel a need to emphasize that actions and policies which hamper the Public good for Private profit and accolades diminish us all deeply, in much the same way that rebalancing your portfolio only toward assets that grow will ultimately destroy it.
I look forward to your continuing exploration of quantified investing, and may your coming years be even better than your portfolio’s.
BJM
Note that this idea calls for welfare/bailouts for the rich as well, to rebalance.