The Science of Uncertainty

Uncertainty pervades investing — Godel, Popper, and Heisenberg examined uncertainty in their respective fields — Investors can benefit from understanding the science of uncertainty.

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THE SCIENCE OF UNCERTAINTY

"Nothing is so difficult as not deceiving oneself." - Ludwig Wittgenstein

Active investing is a profession mired in uncertainty. This uncertainty makes it challenging to identify successful investments, evaluate skilled investment managers, and build resilient portfolios.

Active investing is also a profession that is impossible to quit. Allocators may choose passive strategies, but embedded in these strategies are active portfolio allocation decisions supported by the, potentially waning, pricing mechanism provided by active stock pickers.

All that can be done, acknowledging that decision making in this field is highly uncertain, is to face reality and do our best in difficult conditions.

Godel’s Incompleteness

Kurt Godel is famous for his “Incompleteness Theorem” published in 1931. In short, this theorem says that any consistent formal system cannot prove its own consistency. Said differently, a system cannot use its own rules to demonstrate that it is free of contradictions.

Investment philosophies are systems that guide investment decisions. The validity of these systems is endlessly debated: value or growth, high quality or low quality, long-term or short-term? There are no provable answers.

Investors cannot conclusively demonstrate to allocators that their investment philosophies will consistently generate alpha. Since we cannot prove the consistency of any investment philosophy, we are left with empirical results, “mostly” valid statements, and ultimately personal preference.

Popper’s Falsification

After choosing an investment philosophy, arbitrarily or not, an active manager must find investments that fit this philosophy. Once again an impossible task.

Karl Popper has shown that scientific theories, or investment hypotheses, cannot be proven true, but can only be falsified. In this way, it is impossible to ever “prove” an investment fits with a philosophy.

An active manager’s daily task is simply falsifying or eliminating potential investment candidates. Whatever remains may be a good investment, but the only way to know is to invest and test.

Heisenberg’s Uncertainty

Once an investment philosophy has been chosen, with full knowledge that it is not provably valid, and investments have been selected, with full knowledge that they do not provably fit the portfolio, the active manager runs into the final barrier, the uncertainty of any specific market outcome.

Heisenberg identified a fundamental limit in quantum mechanics, not due to measurement technology or scientific skill, but due to true physical uncertainty. This physical uncertainty pushes quantum mechanics into the realm of probabilistic outcomes. Nothing is certain, only more or less likely.

There is an element of luck associated with every investment. A philosophy can be valid and an investment can fit the philosophy, but the investment may still fail. Like trying to measure both the position and momentum of a particle, an active manager can, literally, never be sure.

In this probabilistic realm, skilled managers are only successful with slightly more than 50% of their investments (or less given extraordinary returns in a single investment can offset a poor “batting average”).

Decision Making Under Uncertainty

Active managers choose an investment philosophy – a hypothesis about the types of stocks that outperform. Godel says we cannot prove any philosophy is always correct or free of contradictions. So the manager must empirically test the philosophy by creating a portfolio.

The stock portfolio is a collection of hypothesis tests run by the manager. Each investment is a test, guided by the investment philosophy. But the investments cannot be proven to fit the philosophy, as Popper shows it is only the investments cannot be falsified that join the portfolio.

Finally, Heisenberg-ian luck drives much of the outcome of each investment. Even if a philosophy is valid and a stock fits the philosophy, success in active management can simply be chalked up to luck.

The World We Live In

But this is the world we live in. This is the world in which all investors and allocators must make decisions. And there is no escape as even passive investing is an active decision to have no investment philosophy.

The only answer is to keep working, empirically testing investment philosophies, refining our experimental methods (stock selection), and recognizing that incremental progress, over time, can compound into extraordinary gain.