Real Options in Radical Uncertainty: Part 1—The Nature of Risk and Uncertainty
By Bryon Robidoux
Risks & Rewards, September 2023
This is the first of a series of articles that will address how to calculate the economic value of physical tangible assets under radical uncertainty using real options theory. Real options theory analyzes the value of managerial flexibility to adapt and revise future decisions to capitalize on favorable future investment opportunities or to limit downside losses from adverse market developments, which is vital to long-term corporate success in an uncertain and changing marketplace.[1] It helps practitioners know when to expand, wait, defer, or abandon a project. But before understanding how to value options under radical uncertainty, one must understand the fundamental differences between risk and uncertainty, which will be explored in depth in this article. Risk and uncertainty are vastly different concepts with vastly different origins. Understanding this difference fully will facilitate a more robust approach to value projects, which will be expanded upon in part two.
Deriving Uncertainty
There are two kinds of uncertainty: Resolvable and radical. Resolvable uncertainty is equivalent to risk, which occurs in stationary processes with well-defined events in well-defined event spaces.[2] Risk only happens in games of chance like Monopoly[3] and Yahtzee, where all possible outcomes are known in advance and there is no uncertainty in the likelihood of each outcome. Radical uncertainty is everything else. Radical uncertainty is the range of possibilities between unlikely events described by potential and the world of the unimaginable.[2]
An alternative way to phrase it comes from financial market theory. Risk is when an agent cannot observe the immediate state of the world but has complete knowledge of the probability space. Uncertainty is when an agent does not know perfectly the probability of events.[7] Almost all literature glosses over this distinction. This difference is profound and will result in significant insights in part two.
Black Swans
Radical uncertainty produces what Nassim Taleb calls “black swan events.” Black swan events have four characteristics:
- The event is an outlier because it lives outside regular expectations.
- It carries an extreme impact.
- Even though it is an outlier, people will try to explain it after the fact making it appear as if it was predictable.
- It was not predictable before the fact.
The name black swan was applied to such events by Europeans because they were only accustomed to white swans. But when they traveled to Australia for the first time, they unexpectedly encountered black swans.[3]
The Nature of Information and Computation
How does uncertainty come about? Physics provides the answers because it is the root of information and computation. Computation can be defined as creating an ordered output from disordered inputs using energy. For example, if a system contains two hydrogen atoms and enough energy is applied to it, they will fuse together to form a helium atom. Therefore, the infusion of energy caused the process to transform from a less ordered state to a more ordered state. The new state of matter solidifies as information. Only systems far from equilibrium and full of energy go through this computation process. Applying more energy produces more computation, creating more information and complex structures.[4]
In thirteen billion years, the universe's computation created white and black swans, trees that know how to compute when to shed their leaves for the winter, salmon that know how to find the location of their birth to lay their eggs, and primates that learned how to build and fly airplanes. The information nature uses to create living organisms becomes codified into their DNA. Therefore, the world was computing and producing information long before humans arrived.[4] The DNA of human cultures is the information programmed into computers, the objects manufactured, and mankind’s social networks.
The Universe's Algorithm to Create Black Swans
What algorithm did nature use to create all this complexity? Contrary to common wisdom, the world is not objectively based. This misunderstanding is deeply embedded in Western culture. Kenneth Stanley and Joel Lehman have thwarted the belief that humanity was created with an objective in mind. The book Why Greatness Cannot Be Planned: The Myth of the Objective explains that objective algorithms work by finding solutions that move the user ever closer to a defined target. But unfortunately, algorithms that hyperfocus on a target may get stuck and unable to reach the solution. The path to the answer may require moving sufficiently far away from the target in order to reach it eventually. In other words, objectives have algorithms that focus on similarities to the target, which is a deceptive criterion.
Creating the best, most innovative, and most complex solutions requires “minimal criteria novelty search” (MCNS). The minimal criteria descriptor indicates that the solution search requires only the constraints to work within and no objectives supplied. Novelty is finding the solution that is most dissimilar to the previous solution, which implies the algorithm is searching the entire universe of possibilities for increasingly unique solutions. Believe it or not, this search is faster than the traditional objective search! The constraints significantly reduce the available search space, allowing the algorithm to search for more creative solutions without getting stuck in a limited space of possible answers.[5]
The Origins of Radical Uncertainty and Black Swans
What does this have to do with uncertainty? The exact reason that it is impossible to plan greatness is also why predicting the future is impractical. The universe uses MCNS to recompute a new, more complex state at every moment in time.[4] This can be called universal innovation. Hence, there was a past, and there will be a future. But no past or future exists; there is only the current moment in time.[4] Sorry, Marty and Doc, your DeLorean is out of order!
Physics postulates that the universe is just a giant supercomputer. It has no objectives. It only has the constraints of physics to find increasingly novel combinations of its previous states. Universal innovation is like slime mold learning to find the most original solutions to feed into the following search iteration. All of the universe’s magnificent beauty and complexity emerges through this search process—including each one of us! Uncertainty is the insecurity produced by the inability to predict how, why, and when this process will have a particular outcome.
Event Spaces
Actuaries deal with uncertainty using the tools of probability theory. The calculation of probability requires events and event spaces. The event space is all the possible outcomes that can occur. The event is the outcome of interest. The understanding of the event space is where all the confusion exists between risk and uncertainty.
The event space is relative to a reference frame. For risk, the reference frame is a fictitious world humans dream up, such as games of chance. Humans make up all the rules in these artificial worlds and use them to define the event space. Therefore, all knowledge about the event space and its possible events is certain. Events are stationary until someone changes the rules. In this reference frame, practitioners can ignore energy when calculating the likelihood of events within the event space.
Uncertainty's Reference Frame
Uncertainty's reference frame exists in the real world. Humans cannot create, control, or adequately define the entire event space, which is the responsibility of the universe and the laws of physics. The event space is the universe! All humans can do is put additional constraints upon it through rules and regulations, which are only relevant to the degree they can be enforced.
All of the information available in the universe at any point in time is the event space in that instant. All available information is the input to the universal innovation process to create the event space for the next instance of time, indicating uncertainty's events are anything but stationary.
Uncertainty requires the practitioner to define an arbitrary event space in order to make calculating event probability tractable. The context and perceived materiality of parameters determine the arbitrary event space. In other words, practitioners refine the actual event space to make calculations practical, but it does not limit the actual event space, which is far more vast and complex.
An event is the combination of inputs that produces an outcome due to universal innovation. The energy required to blend the information into the new result is inversely proportional to the likelihood of the event occurring. If this idea seems far fetched, consider the example of the near perfect correlation between gross domestic product and energy consumption.[6] The monetary cost of a good or project is a potential proxy for the energy required to produce it. This result is intuitive on a physical and personal level. The more energy required to complete something, the less likely I am to do it. My wife will happily confirm this fact!
Understanding Dependence
Dependence is the degree in which one random variable changes with another. Independence would imply no direct link. In risk theory, dependence is measured by correlation.[3] Dependence in an uncertain world is associated with the ease of transferring energy from an object or event based on their connectedness. Stronger connections increase the likelihood of events occurring together.
For example, think of a cue ball smashing into a rack of independent billiard balls on a pool table. The energy transferred through the billiard balls will dissipate quickly after the cue ball collides. This is analogous to the strength between molecular bonds or the degree of connection between companies. The link is substantial if the relationship between companies involves many contracts and debt obligations. The energy from a positive or negative event can quickly transfer through the connected companies holding the contracts and debt. To see this vividly, look no further than to the 1929 stock market crash, the collapse of long-term capital management, and the 2007–2008 global financial crisis.
The Bottom Line
To be able to apply real options theory to problems properly, it is required to understand the nature of risk and uncertainty. For too long, human beings have blurred the lines between the two.[2] But this fundamental review of key concepts demonstrates that risk and uncertainty have nothing in common.
An actuary has never dealt with risk one day in their life! Risk is the job of casino managers that can define their world and its rules. Casino managers can know with certainty all aspects of finite event spaces. The event spaces are stationary until the casino managers change the rules. Understanding the energy requirements to produce the outcomes is independent of the outcomes.
On the other hand, actuaries are waist-deep in uncertainty every second of every day of their lives because they manage opportunities and crises in the real world. Therefore, they have minimal control over the event space and its rules! The event space is infinite, unknowable, and changes every moment based on minimum criteria novelty search, which implies that there will be events that occur that can easily surprise us. The likelihood of a given event requires knowing the relative energy necessary to produce it and its degree of dependence on other events.
The confusion between risk and uncertainty has deeply concerning implications for the life insurance business. Suppose the boundary between risk and uncertainty is not crisp, as described above. The spectrum connecting risk and uncertainty is the degree in which the probability space is knowable. It can be argued that over the last 40+ years, life insurance has migrated from the risky business of mortality to the radically uncertain business of market guarantees. This migration has fundamentally changed the nature of the industry. The change occurred while creating a fiat currency to expand globalization. These developments increased the energy in the system and the strength of connections between all market participants. This has significantly increased uncertainty and observations of black swan events!
The distinction between risk and uncertainty is fundamental. Determining the probability distribution of outcomes and how much learning is possible from historical data will be further explored in part two.
Statements of fact and opinions expressed herein are those of the individual author and are not necessarily those of the Society of Actuaries, the newsletter editors, or the respective author’s employer(s).
Bryon Robidoux, FSA, CERA, is assistant vice president of Product Development at Constellation Insurance. He can be reached at bryon_robidoux@constellationInsurance.com.