Editorial – Unsolvable Problems

In the US movie Pi (1998), Max Cohen is a number theorist who believes everything in nature can be represented and understood through numbers, including the stock market.

In his search for the ultimate solution, he stumbles upon a 216-digit number that seems to explain the very foundations of the universe.

And after a sudden epiphany about the meaning of this number, he seems to be able to see the pattern underlying the stock market.

Many investment strategies rely on the idea that there are patterns in the stock markets and we can develop strategies that can approximate these patterns.

But what if this assumption is wrong?

During an [i3] Luncheon in Melbourne last month, Professor Carsten Murawski, co-founder of the Brain, Mind & Markets Lab at the University of Melbourne, pointedly illustrated that certain mathematical problems can be represented by equations and formulas, but cannot necessarily be computed.

Some problems are not just hard; they are unsolvable.

It provides an interesting conundrum. If you follow this train of thought and apply it to financial markets, then you could argue investment problems fall in this category and so you might as well go passive, since there is no solution.

On the other hand, you can’t have a market with only passive participants as there would be no mechanism for setting prices in that scenario.

Perhaps both arguments view markets in the wrong light.

Research by the Brain, Mind & Markets Lab also shows investors treat financial markets as ‘intentional agents’, actors with their own beliefs and aspirations.

As a result, many investors apply Theory of Mind to anticipate the behaviour of markets.

But markets aren’t intentional agents. They are the culmination of all market participant behaviours.

It is the very existence of buyers and sellers with different agendas, interests and insights, coming together to trade, that makes markets work.

As such, financial markets have no solution.

That isn’t to say there aren’t underlying drivers of price growth that investors can identify and use to make informed decisions. There are.

But the idea stock markets are simply complex puzzles waiting to be solved will send you on a turbulent merry-go-round that will ultimately end in disaster.

Without giving away too much of the movie’s plot, it won’t come as a surprise Cohen’s story doesn’t end well. Right from the start, the grainy footage, combined with the frantic drum & bass score, makes it clear he was never going to end up wealthy and comfortable.

Cohen is often seen playing the game of Go with his old maths professor and in one scene this professor warns him not to get married to the idea of a single solution.

“When you become obsessed with a number, you will find it everywhere. But you are no longer a mathematician; you are a numerologist,” the professor says.

It is perhaps a nice reminder not to get carried away by purely technical approaches and to always remember to invest based upon the potential of individual companies to prosper.

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[i3] Insights is the official educational bulletin of the Investment Innovation Institute [i3]. It covers major trends and innovations in institutional investing, providing independent and thought-provoking content about pension funds, insurance companies and sovereign wealth funds across the globe.