Navigating information

Claude Shannon was a genius of the twentieth century, the sort of person whose intellect bridged multiple fields of inquiry. Today, he is best known for his work on information theory and his seminal work The Mathematical Theory of Communication,¹ published in the late 1940s during his time working at Bell Labs in America. Shannon’s ideas touch us whenever we use a telephone or computer. His key insight was to change the conception of what information is and how it is transferred. He realised that, when thinking about the engineering behind communication, semantics were not so important, but the information content of a message was vital. Shannon showed that, when sending information over a ‘noisy’ channel (one that introduces errors) it is always possible to transmit virtually error-free, provided the rate of transmission doesn’t exceed the capacity of the channel.

Let’s bring that back to the befuddled Twitter user, looking at both the rate of transmission, and the noisiness of the channel. The rate of transmission (about two billion tweets a month from the top 10% of users²) is extremely high in the daily media flood. So too is the noise, as facts (are there still such things?) are ‘interpreted’ by any number of media outlets, politicians, and so on. Yet the channel capacity of our busy daily lives is rather restricted. Perhaps we should not therefore be surprised when the result is ineffectual information transmission with little to gain, other than elevated stress levels.

The trend in investment in recent years has definitively been towards the more information, the better. 

The bridge to the world of finance is not a long one at this point.

Markets are distillers of information, representing clearing prices for securities given the current state of information. There are layers too. Information about a factory’s widget production affects the company’s revenue, which affects the share price, which conveys a kind of short-hand to investors. Noisiness has ready analogues as well, from uncertainty about the company’s operations, to varied and conflicting reports by analysts and the media, to volatility in the share price.

The share-price-as-a-signal is a primary way that finance borrows from information theory: return is weighed against risk (proxied by volatility) in determining which assets are most attractive. The relationship of assets to each other is brought in to create the mean-variance framework – a flawed but still dominant paradigm for investment analysis and decision making. Some of the flaws arise because return (especially prospectively) is a poor proxy for information and because the variance of returns is an insufficient description of the noise and true risk facing investments.

While information theory doesn’t quite give us a cheat-sheet for choosing investments, it does provide a way to think about how information is processed. The trend in investment in recent years has definitively been towards the more information, the better. Countless data sets are created, sold and subscribed to, from retail sales to surveys of manufacturers, to satellite data showing occupancy rates of car parks. Yet what should by now be abundantly clear is that, when investing, quality trumps quantity. An information source is only as useful as the returns it can potentially generate. There is far too much low-quality information being paid for.

As the response to the pandemic has shown us (see next section on ‘Application du jour’), information quality depends in part on an understanding, even a curation, of the underlying data. This in turn determines its usefulness. Again, Shannon can help investors. In his reframing of the information problem, he realised it would be more useful to think of information content probabilistically. That is, the more unlikely a message is, the more information content it has. This sounds cryptic, but, if we consider a message that makes us think “That’s obvious”, then that message can be said not to contain much information. But a message that makes us think “Wait, what?!” is likely to be far more informative and, before the fact, seen as more unlikely.

There are investors who have shown that a command of information quality can be hugely valuable, most notably the hedge fund Renaissance Technologies. Various near-insiders have revealed enough over the years to suggest that one ingredient in their success has been an incredibly detailed, comprehensive and clean set of market information.³ This is then scoured for unusual and unlikely – but repetitive enough – patterns that are exploited to produce stellar returns on average. There is a beauty in the notion that they have abstracted from the usual investment information channels – such as company earnings and central bank announcements – and looked directly at price movements. In a way, they have dulled some of their investment senses to evolve a hyper-tuned feel for prices, those shorthand distillations of information in finance. Indeed, some have postulated that Renaissance Technologies have somehow ‘solved’ markets – surely a ludicrous notion?

For much of 2020, covid-19 case counts were a dominant variable.

Government policies are set by them. The media reports them. And people’s behaviours, livelihoods and health depend on them. Case counts are widely compared and contrasted between regions and countries. They are seen as a measure of relative success and failure.

Yet, as the pandemic began to spread, it became obvious that case count numbers were complex. The degree of testing being undertaken played a huge role in the numbers of cases reported – a country with a substantial testing programme will find more cases than a similar country with little testing. This was also true of changing testing rates through time.

What about the quality of the information? Are the test types comparable and similarly reliable? What is the false positive and negative rate? Are asymptomatic people being tested, as well as those with symptoms? Are positive antibody tests being counted? Is the presence of live versus dead virus being accounted for?

Even in countries with similar disease incidence and testing rates, genetic, cultural, demographic and environmental factors may make a positive case far more dangerous and consequential in one place than another.

To make sound policy decisions, governments need to be skilled at navigating information.

When we talk about solving something, we implicitly mean with reference to degrees of freedom, or the idea that we pin down different aspects of a problem until a solution is possible. Consider a rugby team. The coach needs to put each of the 15 players in a position for a match. At first, there are 15 degrees of freedom, as each player can be placed in any position. But as the coach progresses, the number of players and available positions declines, until 14 players take up 14 positions. At this point, the coach has no choice, no degrees of freedom – the final player is placed in the only remaining position. The team is ‘solved’. While this example is trivial, degrees of freedom prove vital when considering higher-order problems, such as investing across thousands of markets, or working with quantum physics.

A gauge or measure is an important means of standardisation that gives us a language to convey information. When we shift between gauges, such as travelling from a country using the metric system to one using imperial, it’s useful to know how to translate our measure. This translation is a very basic form of what we might call a gauge theory, and this becomes indispensable when thinking about the weird world of quantum physics.

In different areas of quantum enquiry, various properties are useful when seeking to make sense of the often-strange behaviour of particles. These properties don’t always play nicely together, however. Sometimes, they become almost contradictory.⁴ Here, introducing a gauge theory comes to the rescue – by giving us some redundancy.

By explaining how we should think about the relationship between properties, we can continue to analyse the different areas without worrying about local differences and contradictions. In effect, what we have done is allow enough degrees of freedom to unify our approaches, without sacrificing tractability in any one case. The tension between finding a local solution and understanding the global system is key.

The application of gauge theories has led to amazing progress in complex problems, such as understanding the brain. For example, researchers realised that, if we had an overarching theory for how neurons in the brain respond to external stimulus, then we would be able to model anything from a single neuron to overall brain activity.⁵ This would give us insight into how the brain works at every scale and inform our understanding of phenomena such as action and perception.

If our information sources are set to reduce noise to an appropriate level then unexpected messages provide us with the most useful information: unusual price movements, or relationships changing.

One emerging idea in this field – the free energy principle, developed by neuroscientist Karl Friston⁶ – offers utility for our task at hand: navigating information. The essence is that systems (and potentially, people) attempt to minimise surprise. It sounds simple, but the implications are not.

People have a model or idea of what the world is like. We constantly update this, incrementally, according to what we perceive. If we are met with something that doesn’t fit with our model, that counts as surprise; we minimise the effect by updating the model, and also through action. This is a complementary insight to Shannon’s on the unlikelihood of a message, but Friston gives us a model by which systems (and people) cope with surprising information. Free energy as a gauge theory looks to be a promising way forward in complex fields, having already proved useful in several areas – most recently in modelling the covid epidemic.⁷

What is an investor to take from this world of physics, gauges and free energy? From Shannon, it is to ensure our information sources don’t introduce too much noise. More is certainly not always better, lest our processing capacity be overwhelmed and lead to bad investment decisions. If our information sources are set to reduce noise to an appropriate level then unexpected messages provide us with the most useful information: unusual price movements, or relationships changing.

From gauge theory and neuroscience, the takeaway is that understanding the unifying fabric of a system can yield powerful results. By design, Friston’s principle works on many levels. Markets generally act to minimise the surprise of new information, driven by the wants and needs of buyers and sellers. But, as individuals, we have a call to action, either to update our views of the world or to adjust our portfolios. With the right gauge to help us navigate, we can make vast strides in understanding markets, if not quite in solving them.

And, finally, what to take from the artist Sam Winston? Is it time to turn out the lights and meditate on the nature of darkness, to heighten our other investment senses? Fund managers have certainly resorted to stranger things.⁸