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Beware the linearity bias

November 2, 2022

We tend to think of our world in linear terms, where the output of a system is proportional and directly correlated to its inputs.

In daily life, this is true of many things. For example, when buying groceries, increasing the total number of apples in my cart results in a corresponding increase in the final bill I pay at checkout. Assuming a person runs twice as fast as they walk, they’ll get from point A to point B twice as fast by running. In physics, Hooke’s Law describes how the amount of force required to extend a rubber band is directly and linearly proportional to the distance you want to stretch it.

But this is untrue for other things. Many relationships or systems are more complex and dynamic. Nonlinearity abounds, and with it, unpredictability—even chaos (see the double pendulum). Impacts that may be easily identified in a linear relationship become increasingly difficult to understand or predict.

Take the weather for example. Hour to hour, it’s reasonably easy to forecast whether it’s going to rain, even for the average person with no equipment. Are there clouds overhead or on the horizon? If the answer is no, it is fair to assume there is low probability of precipitation. But it would be foolish to look up, see clear skies, and use that single datapoint to forecast a lack of rain next week. That is because weather is a nonlinear system: small shifts can produce complex and outsized reactionary effects throughout. We’ve all consulted the forecast in planning a BBQ, beach day, or hike for the next weekend, only to get rained out.

To be fair, our tendency to examine and define cause-and-effect relationships as simple linear associations is rational: many complex relationships can often be reasonably approximated by linear associations within some range of inputs. And that can be a good thing, enabling quick decisions via mental shortcuts. But there is, of course, danger in this line of thinking—and often with more serious consequences than simply getting a little wet when skies turn dark. The problem comes when we assume linearity across the entire range of inputs.

When you can’t draw a straight line

Let’s return to the rubber band. The earlier statement that it is governed by Hooke’s Law isn’t entirely true. Sometimes, by stretching the rubber band far enough, the rubber band can become deformed and over-stretched, permanently redefining its elastic properties. Worse, pull hard enough and it will snap.

As investors, we’ve been thinking a lot about Hooke’s Law and nonlinearity lately given the inflationary environment we find ourselves in and the impact of rising input costs on profit margins. One way to deal with rising input costs is to pass them through to customers through price increases. Another is to reduce expenses in order to support margins. By and large, companies have been able to do a bit of both, perhaps explaining why corporate earnings have generally remained strong and why consensus earnings growth estimates for the S&P 500 for the next 12 months remain in the double digits. But a key question facing investors has to be whether these are indeed linear relationships, and to what extent management teams can continue using both levers without weakening their businesses. Initial SG&A cuts may trim excess fat, but they can only persist for so long before they start chewing into bone and eroding the very competitive advantages that support the business model longer term.

Pricing power—or the ability to increase prices without impairing both demand or competitive position—is almost assuredly nonlinear. Competitive advantages tied to brand strength, economies of scale, criticality of the good or service provided, supply exclusivity, or network effects may allow companies to stretch the rubber band for a considerable period, but past a certain point, they may snap. There are dangers to abusing pricing power—namely, losing customers, incenting competition, and attracting regulatory scrutiny. Nassim Taleb, who has written much on the subject of nonlinearity, suggests that falling a distance of one metre ten times is very different than falling a distance of ten metres just once. We can be immune to the cumulative effects of changes of small magnitude, but may be greatly impacted by changes of larger magnitude. Similarly, companies that have been able to regularly increase prices by 2-3% over the past 20 years may learn that this ability doesn’t extend to 7-8% without consequence.

The dangers of assuming linearity

Consider the newspaper industry. Nickel and dime increases for physical newspapers were accepted with minimal attrition for decades until suddenly, readers had enough, canceled their subscriptions in droves and didn’t come back. They moved on to one of many new substitutes: free (ad-powered) online publications, Twitter, Facebook, Reddit, etc. The inelastic demand that had defined the industry snapped.

Earlier this year, Netflix reported their first loss of subscribers in more than a decade. This came a quarter after management had confidently forecast growth of millions of subscribers for the period. Who could blame them? The last decade had seen Netflix grow metronomically. To be sure, increased competition and password sharing were noted as contributors, but coincidentally, the company had also recently passed through price increases to a customer base that has an ever-growing list of options, including free content via YouTube.

High-quality companies with strong competitive advantages, non-discretionary demand for their products and services that provide genuine value to their customers, and that are led by adept management teams are more likely to delay this nonlinearity.

Nonlinear thinking is key for managing risk

Beyond companies, where else might we be reliant on the assumption of linearity? Recent relationships we’ve all had to rethink include the geopolitical stability of Europe’s increasing reliance on Russian gas over the past decade, the efficiency gains from just-in-time supply chains, and political protests in countries such as Kazakhstan, Sri Lanka, and Pakistan in the face of higher costs of living. Going forward, some of the bigger macro risks are likely nonlinear as well:

  • the size and pace of central bank rate hikes and their impact on the economy;
  • how increasing geopolitical tensions between China and the U.S. (e.g. via Taiwan) may evolve;
  • the impacts and costs associated with accelerating climate change; and
  • the relationships between increasing wealth inequality and social stability.

The key takeaway here isn’t to predict, but rather to be prepared and to constantly question our assumptions and biases—to think wider and be open to scenarios outside of our best estimates. We know we can’t forecast the future and as such, we embrace this uncertainty. Our culture values behaviours like candour, curiosity, and trust, as this allows team members to challenge each other’s opinions and curb each other’s biases. We find this particularly valuable in periods of such heightened volatility and uncertainty, and we believe this approach to investing puts the odds in our clients’ favour.

This blog and its contents are for informational purposes only. Information relating to investment approaches or individual investments should not be construed as advice or endorsement. Any views expressed in this blog were prepared based upon the information available at the time and are subject to change. All information is subject to possible correction. In no event shall Mawer Investment Management Ltd. be liable for any damages arising out of, or in any way connected with, the use or inability to use this blog appropriately.