Mathematics is the language of the universe and has arguably been humanity's most important field of study. You might argue that science, economics, or other social sciences have played a bigger role. However, we must understand that these are downstream products of mathematics and are only possible with the foundational backing of mathematics. If we apply the first principles of thinking, we would conclude that most scientific/ economic knowledge boils down to mathematics, but Mathematics does not boil down to anything. It stays itself!
Now that we understand its role for humanity let's use a few mental models to understand its role in investing.
Sampling
Sampling is an essential part of studies and data analysis. Suppose we were to understand the impact of an event on the whole population. In that case, we can not take data from the entire population because it is excessively time-consuming and expensive. Hence, we take a sample of that population, which can mimic the population the best. Having a large sample size emulates the population better and can give 'fit' test results. Hence, the larger the sample, the lower the margin of error and the higher the sampling confidence level, meaning the more probable the results will be generalised to the whole population.
How does it help in investing? It can help us overcome some forms of biases. How often have we heard the story of some kid dropping out of school and becoming a billionaire? How often are kids enticed to listen to this and, hence, decide to do the same? Anecdotes form opinions and are a strong tool of rhetoric. However, Sampling helps tackle this as it puts an objective view of the situation and helps us gauge it from a different perspective.
Hence, do not fall for stories because, more often than not, they are exceptions, and the larger picture portrays something else.
Another essential lesson is the use of Sampling with process. Investing is best done when results are detached from the process. Sampling helps as the main goal of investing is to increase our terminal value. If we extend our terminal value by not taking risky bets, we allow Sampling to work out, and results will eventually align with the process. Despite the correct process, a few mistakes are bound to happen, but ensure that they do not wipe you out completely because you can only be rewarded if you stay long enough.
Randomness
All of us believe in having an order. Ask my friends; I plan my day a few times a day and a hundred times a week. The reason is that I need stability and order in life. I need to control the variables of my life, and I hate it when I can't. Due to this obsession, I emphasised the times when my day didn't go as planned, which was at least a few times a week, and hence, I realised how relevant and important randomness is.
Randomness can be challenging because it makes the universe seem less friendly and comprehensible than we might wish. It's hard to accept that much of what happens in our lives is chance, not ordained. The world throws random dots at us, and humans constantly try to draw lines between them, even if none exist. Randomness thus forces us to confront our lack of control over outcomes in many situations. Understanding this is all you need to become an investor. Even Jerome Powell or Nirmala Sitaraman can't control everything; how can we? Accepting that randomness dictates multiple parts of our lives and investments is necessary to sleep peacefully and succeed.
Mean Reversion
How often has it happened in sports that some team does the unthinkable and then returns to their poor selves the next day? Single events are determined by luck and merit. However, luck becomes less important as we add more events to the data.
Suppose I study a day before the exam and score around 60% on average. One day, exactly what I learned yesterday came, and I scored 85%. Was that my hard work or luck? It was mainly luck because I barely prepared, but I got lucky with what came. However, the following few exams don't repeat that, and I come back to my average scores.
Mean reversion occurs with individuals and companies.
Many companies get lucky when the macro environment favours them and allows margin expansion. For example, Import tariffs on China forces U.S. companies to buy from India and hence temporarily inflate the demand for our domestic companies. Sooner or later, competition catches up with their supply, or the tariffs loosen up, and Margins crash down and revert to their usual.
Valuations, too, follow Mean reversion. A parabolic rise in valuations and expectations is often met with disappointment, and hence, valuations revert back to their mean.
It is a strong mental model because it is relevant in investing. Understanding and applying this mental mode will save you a lot of trouble in the future and help you time your purchases.
P.S.: Most deep-value investors or contrarian investors work on this underlying idea.
Equivalence
Things do not have to be the same to be equal. Equivalence as a model helps us see that there are usually many paths to success. One of the ways equivalence is most useful as a model is when our traditional solution to a problem is no longer viable. We know we must now do things differently, yet we wish to achieve an equivalent result. It also reminds us not to focus on apparent differences but to look for the underlying equality of experiences if we want to better connect with others.
Equivalence teaches us there are no absolute answers. There are a thousand ways to Nirvana and anyone can choose any of them as they see fit.there is more than one way to solve most problems. Using equivalence as a lens helps us appreciate the richness of the solution space. We can better appreciate the efforts of others who took a different path and found a common language to share information and experiences.
This marks the end of my blog and my favourite mental models from mathematics. There are so many more, and there could be a hundred more write-ups that could be written on this, but I think this is it from my side. I tried my best to include different and interesting models and not emphasise the ones already well-known (compounding). Mathematics is a field of abundance and has a lot to learn from. Shoot me an email if you find interesting models from the field, and I would love to share them with everyone!
Credits
Beaubien, Rhiannon ; Leizrowice, Rosie. The Great Mental Models Volume 3: Systems and Mathematics. Latticework Publishing Inc. Kindle Edition.
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