Unremarkable thoughts

Some of the things we do, produce right skewed distributions.

In certain cases we want to be on the left side of the right skewed distribution, and in different ones we want to be on its right side.

Left side

Examples here are the time needed in sports like running a marathon, or the time needed to solve a math test. In all these cases we quickly experience diminishing returns after a certain point.

In appreciation of the effort required to achieve the corresponding nevertheless impressive results, we have built mechanisms to reward the people who manage the rare by definition feat to be at the leftmost side. We give gold medals or scholarships to the first, and we sponsor the people at the top. We may even use a projected scale that tries to make apparent even smaller differences. Nevertheless, the difference between the top 0.1% and 1% is not that huge in absolute terms of outcomes compared what happens on the right side. That is, the top athletes may finish a marathon with difference a few seconds or minutes, while the bottom participants may have a large difference in times or even never finish. Similarly in chess, a single mistake at top level may end up to a loss while at lower levels it may even go unnoticed.

Right side

Examples are some categories of financial returns, soft power from being a top athlete/politician/celebrity, or socioeconomic outcomes of children with similar background and capabilities in some kinds of societies.

When we recognize the effects of the skewed distributions, especially in cases where we deem them adverse for the social good, as defined by what would benefit the majority of the people, we develop counter-mechanisms like tax system, education, rotation of officials, separation of powers etc.

Sum game

Sometimes we play the game of adding the results. A relay race is such an example of adding the times when we care for the left side. Wealth is an example of adding the financial gains when we care for the right side. In a relay race, the difference between the first and a team in the middle is huge in terms of effort, but happily enough for the organizers, they may all still fit within a single day event. When we compare the wealth of individuals, we see final outcomes where are vastly different.

Conclusion

From an individual point of view, it seems worth focusing on repeated games where the positive outcome on the right side of right skewed distribution. From a system point of view, the two sides serve very different objectives.

This post was inspired during my role as team captain of an amazing SOLA race team.

Generations ago, you were starting work at your early teens and working until almost the end. As technology advances, people can now start working later (school, studies), retire earlier (pension), receive benefits, or build enough assets and stop working. It seems we have various dials (political, cultural) to keep or enforce a relative balance of who gets the benefit of having to work less. Asset price over median income appear to be an financial tool that also affects this balance.

• Did you misplace your theater tickets? Ignore their cost and buy new ones.
• Was your bike stolen? If it made sense to buy one before and you are in a similar situation, buy a new one.
• Have you invested a lot of money/effort towards a specific direction of a company? Ignore the costs and change to the “correct” directions. (Usually, by changing CEOs).

These arguments are based on the sunken cost fallacy. There are mores. I find that they are coming from a good place but they are oversimplifications that may lead to wrong conclusions if taken at face value.

• You can be upset you misplaced your theater tickets and develop a system of where you put such tickets so this doesn’t happen again.
• The value of the bike may not have been just financial but also sentimental after going many rides with it. Trying to recover it, or getting some time to process its loss is not lost time.
• A company doesn’t have a direction in the abstract sense only. There are people who implement it and their morale may be affected by a sudden, not sufficiently well justified, change. Paying attention to these extra costs may change the equation.

In conclusion, the sunken cost fallacy makes sense in some closed systems, but sometimes the systems may (have the opportunity to) change significantly enough that this is an oversimplification.

Alice starts with 1 million and has no income. Bob has no starting money but a salary of 30k. We examine three scenarios, starting from the simplest.

Simplest

Assuming no externalities (taxes, investments, expenses), Bob needs about 33 years to reach the money that Alice has.

Investment

Assume an investment with a return of 3% available to both. Bob will never reach Alice. Their difference will always be 1M.

It is simple to see why. Alice makes from the investment in the initial year as much as the Bob’s income. In the later years, Alice 1M will give in return as much as Bob’s salary. The rest that Bob will have saved will be equal to what Alice has saved. In other words, Bob has to get a salary of 30k just to be able to keep a constant difference from Alice, while Alice doesn’t do anything.

Taxes

Let’s include taxes in the previous scenario. In this case the conclusion depends on where Alice and Bob are located. Nevertheless, in many (most?) cases, Bob is surprisingly worse off, since income is usually taxed at higher rates than wealth.

Remarks

• The differences are even more pronounced if the initial capital is much higher than 1/r, where r is the rate of return (here r=0.03).
• Working for a salary will never make you as rich as someone who starts with a lot of money and does nothing, as long as there is the possibility of investments.

A common financial trick is to have a bunch of uncorrelated assets that you balance over time. Assume you have access to assets A and B, with about similar returns. You can have a portfolio of 50% A and 50% B. If A gets overweight, because for instance it went up a lot in price, you sell a little bit and buy B. Similarly with B. Traditionally, for private investors, this has happened with stocks and bonds, even though their returns have diverged significantly in the last years which may not be a great strategy anymore.

Anyway, this strategy is very beneficial to the owner of this portfolio. It comes with something called rebalancing bonus. The idea behind it, is that you sell high and buy low. That happens because, as we said, when A becomes much more expensive than B, you sell A and buy B.

For this trick to work, you need the following properties:

• Low correlation
• Similar returns
• Volatility (see: Shannon’s Demon)
• Low trading fees

This trick is known for many years. Many financial firms seek actively uncorrelated returns and they are happy even if the returns they can get from alternative asset classes are not as good as what say the stock market would give them. This is a reason why we observe such an expansion of the private markets in the last years.

The trick has though its side-effects. By following the strategy above, we increase the correlation between the assets in the portfolio. When we do that at scale, that decreases the effectiveness of the strategy.

In other words, we can extract returns from uncorrelated assets with the side effect of increasing their correlation. This is already happening to a large degree in our world and is one of the reasons why we observe seemingly unrelated areas of the economy being heavily correlated (stocks, bonds, cryptocurrencies, gold, etc). Other reasons include central bank monetary policy and interest rates.

The increase in correlation between financial assets presents systemic risks. That’s why I call it financial pollution. See also the previous post about fat tails.

Rare events are more frequent than what a normal distribution predicts.

Andrew Lo, professor in MIT, showed evidence against the popular “Random Walk” hypothesis. The idea was that if we have some variance V_w in a week, we should have V_m = 4 * V_w in a month. This was not true. He published his book “A non random walk down the Wall Street” where he talks about this idea. Unfortunately, this book reads more like a collection of papers stapled together. Much more readable is the “Adaptive Markets Hypothesis”.

The Black-Scholes model assumes that the prices of the underlying asset follow a log-normal distribution. This is found to be empirically wrong, since real-world financial markets follow more a leptokurtic distribution. To fix that, people employ different “hacks” (use implied volatility, Heston model, Merton’s model,…).

I believe the observations above come out due to coordination effects that are happening. Big events are not (only) the result of small events adding up randomly in extremely (un)favorable way, but there is often an underlying reason. We can motivate change, resist it, hedge against it, or ignore it. But change will come and with bigger force than “normal”.

There are things we do as kids, that we stop as we grow up. May be because priorities are shifting, obligations pile up, our environment is changing or something else.

Recently, I learnt that Age of Mythology had a new version. One of my favorite late childhood games was available again. I used to like to play as Norse. A very aggressive civilization, where soldiers can build. I used to win or lose very quickly due to this aggressive style. I played again. I had some fun playing again as Norse, but much less interest playing as any other civilization. Learning again the mechanics, build orders and so on is very hard when the time is limited.

What I liked was to remember how it felt when I was a kid. I am not a kid, though, anymore.

Buy enough pairs for two weeks of the same socks. Make sure you can buy the same ones from time to time, once some of the socks need replacements.

Enjoy the benefits:

• No longer having to sort your pairs of socks.
• No longer having to decide what socks you should wear.
• No longer having to decide what socks to buy.

You can still keep 1-2 special pairs of socks.

I understand this advice is not applicable to everyone, but if it is applicable to you, it may change your life for ever and you won’t even notice it.

Is this advice silly? People usually don’t have time to reconsider core beliefs that shape their decisions for life. This gives them back some of the time that would be wasted on choosing socks.

One of my favorite sayings by Alan Kay is:

“A change of perspective is worth 80 IQ points.”

…but not for socks. Socks should be decided for life.

To get an idea of the upcoming changes due to AI, and the automation/delegation of knowledge work, we can look at what happened after the automation/delegation of manual labor for many people and at least in big part. This change happened in much slower pace than what is projected of AI. Admittedly, there were also other big events (like World Wars) which also contributed in big societal changes (like women’s rights in western countries).

Childhood: After a few short years, around 8 – 10, kids were expected to participate in the labor force. There were no “teenager” years since a kid was going directly after childhood to working life without much of preparation. Compulsory schooling and kids having their circles and private lives before getting married came later. This increased social mobility, since a child’s profession was no longer solely determined by their father’s occupation. It also rebased the year’s calendar from religion to the school’s calendar.

Old age: Pensions were mostly established in the previous century. The proportion of the population that can enjoy this benefit is ever since increasing. Before that, old people had to rely on their families and local communities.

Weekend/40 hour week: Men, who were participating in labour force, were mostly guests at their home in early 19th century. They were working 6 days per week while there was some daylight. Women had to devote many hours to washing clothes manually and together with the rest of house chores and logistics, they were sinking around 50-60 hours per week. The chores were also physically demanding, given that there were no modern facilities like warm water.

Food: Due to physical limitations, food was mostly sources locally and it was seasonal. While that sounds great, there was a lot of food insecurity. People also couldn’t store easily for longer times food, unless salted, given that there were no fridges.

Distance: Before cars, many things had to happen locally. That also meant that the future wife would almost always meet her future husband in vicinity of her parents home which also allows room for the Victorian era ethics.

Mass production/consumering: Before, most items were produced by someone you knew. Most likely, you were also producing several things for others. With the advancement of technology we shifted towards mostly consuming goods. A good example are clothes, which were expensive and hard to obtain while now they are treated as much more disposable.

Medicine: Good luck if you were sick. Most of what we know about medicine didn’t exist back then. Miasma, “bad air”, was the main explanation why someone gets sick. As our knowledge of medicine expanded, at some point, not that immediately we also made the perhaps humbling realization/turning point that doctors shouldn’t only treat some sickness/accident, but also consider the patient they handle and ask them about what they want.

Pollution/Recycling: It was not a topic in the same sense as today. There were some issues, mostly from misunderstanding that burning coal is not good for health and not just a sign of wealth, and sewage disposal.

Housing: Surprisingly, it was also an issue in the 1850s. People couldn’t build new houses fast enough. Sanitation or lack of it resulted in cholera and typhoid outbreaks. The materials used were not good.

There have been big changes in the last couple of generations. It is incredible how different our modern society is compared to what was experiences by the grandparents of our grandparents. Of course, the changes described above have not happened with the same pace or to the same extend in the whole world, but hopefully, they are indicative of what a big technological change may bring as a side effect.

Multiple people on the field expect AGI within the next 5 – 10 years. How will that affect our lives? It feels like it is worth pausing for a moment and wondering. This is speculative. I only hope it will make some readers annoyed enough to form their own thoughts.

AGI won’t be selfish. Simply because it doesn’t need to and it won’t be selected for that. I feel that the selfishness we know from humans is a helpful heuristic to keep them alive and make the prosper in their environment. Nevertheless, the various agents can piggyback on humans. We are already transforming our planet to make AGI possible with an astounding effort that was not even dedicated to Pharaohs while creating the pyramids. The investments in this area, creating huge data centers with power consumption compared to cities are already astounding and keep growing.

Humans will still be selfish. A single individual or group of people had limited impact on most of our history. Once people found leverage through weapons, sometimes they used them to flatten whole cities or chase down/exterminate specific populations. We needed new morals/solutions which came through a lot of pain only a couple of generations ago to learn to live together in a more globalized world.

Public policy will be delegated to AI. Not only the politician’s speeches, or the details of some policies, but even the agenda. How long we will keep the human face of the political Centaurs may linger in the fine balance of human control vs frustration of human corruption.

AGI can be local and private. Humans have AGI by burning around 20 Watts. Therefore, there is not a physical limit why we can’t have devices that are as smart as we are and have them portable and with us.

Big models will still matter. Having direct access to the aggregate human/agent knowledge and vast amounts of processing power will unlock new capabilities well beyond the world we now know. Countries will be reshaped based on the output.

The internet will be for agents. And our usage of Internet will be through the agents. Agents are born from the contents of internet/web. Agents will be updated from it. This is how our hive mind will stay up to date. How agents will talk with each other won’t a simple static API.

New scarce resource. Economy is the management of scarcity. Our society mostly has already overcome the scarcity of human power modulo practicalities of more extended deployment. Soon, we will get rid of the scarcity due to intelligence. Some new factor/resource will emerge as the limiting function of what can be done. Will that be consensus? Or control of hardware? Or the agents emerging beliefs?

Cities will change. Similar to the introduction of car, more things will be possible. Because of the new capabilities due to the agents and perhaps the new limitations, cities will change their shape.

If we don’t need to think, we may need to retain agency. But this may be a thought for another post.

There is a financial concept called the Future Value of Annuity. Despite the complicated name, it boils down to a simple math formula that can bring you an additional 1 million CHF in Switzerland under some conditions.

Formula

The formula is:
V = C × ((1 + r)n​ – 1) / r

where:
V = the money you will have n years
C = the money you put every year (the capital)
n = the number of years
r = the interest rate, or more precisely the annualized net return. A value r = 0.01 corresponds to 1%.

In other words, it tells you that if your bank account has an interest rate of r, and you put C amount of money every year, that’s how much money you will have after n years.

Calculation

Two examples, where we put about 600 CHF/month, or to make things more round, about C = 7000/year. Let’s say we do that for while we work until we get a pension. That is from 25 until 65, which results to n = 65 – 25 = 40.

So, with C = 7000 and n = 40, let’s see two examples of the importance of r.

Example 1 with r = 0.01 (interest rate 1%)
V = 7000 * ((1 + 0.01)40 – 1) / 0.01 = 342,205 CHF

Example 2 with r = 0.07 (interest rate 7%)
V = 7000 * ((1 + 0.07)40 – 1) / 0.07 = 1,397,446 CHF

The difference is clearly more than 1 million CHF, or to be precise 1,055,241 CHF.

Conclusion

The two examples are not arbitrary in Switzerland. You can put around 7,000 CHF per year in third pillar. You can do that will you work, which is around 40 years. You mostly have two categorical choices for third pillar: insurance which has returned, if you are lucky, around 1% per year and in a broad index fund which has returned around 7% per year. Their difference amounts to 1,000,000 CHF under the above assumptions.

Notes

The numbers were calculated with Python:

>>> f = lambda r : 7000 * (((1 + r)**40 - 1) / r)
>>> f(0.01)
342204.61351175496
>>> f(0.07)
1397445.7839206983

Sanity check (interest rate 0%)
V = 7000 * 40 = 280,000

Simplifications

What we oversimplified but it is mostly common factor in both scenarios:

• Taxes: By putting money on third pillar, you also save based on your marginal tax rate. That means it is cheaper to put this 7000 CHF than it looks.
• Inflation: This is the nominal value of money. In 40 years, a million francs may have about half of the value that it has today. Same applies to the rest.
• Volatility: Both in terms of performance of the portfolio but also in income availability.
• Capital: The amount that someone can contribute to 3rd pillar is increasing every year.
• Accessibility: The money is locked during the contributing years. It is really meant for old age (or if you buy a house/leave the country).