We have much to learn about the visual representation of risk. For help, we can examine the process of discovery in molecular biology, where there is a deeply held tradition of building visual models. The visual approaches used in these fields offer invaluable insight into the identification, measurement and management of risk.
Their impact extends to the viability of the world’s greatest organisations and the soundness of the international financial system. They are relevant to the work of managers, management committees, boards of directors, shareholders and regulators.
Risk can be a difficult subject to grasp. It is an abstract concept. We commonly think of risk in terms of what can go wrong, yet we also realise that risk perse is not bad. We often hear the remark « I’ll take that risk » or « I like that risk ». Intuitively, we accept the proposition that risk and reward coincide.
We can describe risk in statistical terms and we can apply concepts such as distributions and deviations around the mean and confidence intervals. As Philippe Jorion observes, « Although in modern parlance the term risk has come to mean `danger of loss’, finance theory defines risk as the dispersion of unexpected outcomes due to movements in financial variables ».
This approach will be meaningful, however, only to those who are literate in statistics. Many will be excluded, among them individuals with substantial authority and experience, even though statistical discussion is graphical in nature.
Other types of discussion — those involving visual images and metaphors — should also play an important role. They can help us visualise the causes of risk and the interaction of different kinds of risk. They can also help us detect looming problems before they become major crises. We should not, however, expect to develop a single visual model of risk. Unlike the double helix for molecular biologists, there is no one organising principle that serves as the basis for all observable outcomes.
Risk is best understood using a range of models and visual images
Types of models
Emanuel Derman identifies three kinds of models relevant to financial risk: fundamental, phenomenological and statistical:
❑ A fundamental model is a « system of postulates and data, together with a means of drawing dynamical inferences from them »
❑ A phenomenological model is a « description or analogy to help visualise something that cannot be directly observed »
❑ A statistical model is a « regression or best fit between different data sets ».
A challenge of models is to reflect their subjects. According to Derman: « The real world is often an inchoate swirl of actions, occurrences, facts and figures. There are more things than we’ve even thought of naming or categorising. So even the finest model is only a model of the phenomena, and not the real thing ».
In finance, we construct models for various reasons: to provide better explanations for observed financial behaviour; to discern aspects of a problem that we haven’t considered before; to improve our ability to make predictions and to design better solutions to risk management problems.
Commenting further on the purposes of models, Derman observes, « A model is just a toy, though occasionally a very good one, in which case people call it a theory. A good scientific toy can’t do everything, and shouldn’t even try to be totally realistic. It should represent as naturally as possible the most essential variables of the system, and the relationship between them, and allow the investigation of cause and effect. A good toy doesn’t reproduce every feature of the real object; instead, it illustrates for its intended audience the qualities of the original object most important to them. »
With these thoughts in mind, let us now consider some familiar shapes to help us visualise risk. These include squares, circles, ellipses, ropes, lines, arrows and points. When assembled together, they can offer additional insight into the nature of risk. In constructing our images, we borrow from geometry, set theory and topology. We also rely on financial theory, as well as our own observations and intuition about risk. We can vary the colour, shape, patterns and other qualities of our images to highlight different aspects of risk. Each of our selected images tells us something different about risk, and also suggests related implications for managing risk.
One may ask about the practical implications of such of images. How do we relate them to our organisations? How do they help us measure risk? What hypotheses are we testing? What data should we be collecting? How can this « stuff » help us improve returns or reduce losses? These are reasonable questions. The answers speak to the fundamental value of visual images.
The visual image is universal. It transcends language, culture and personality. It is accessible. Its impact is immediate and lasting and it cannot be ignored. « It is in a world of symbols that man lives, » writes the graphics designer Paul Rand. « Seeing comes before words, » begins John Berger in his book Ways ofSeeing. He continues, « It is seeing which establishes our place in the surrounding world; we explain that world with words, but words can never undo the fact that we are surrounded by it. The relation between what we see and what we know is never settled. »
Such observations certainly seem uncontroversial. Yet it is interesting to reflect on these points in relation to our profession’s practices for communicating with others about risk. Our predominant approach is other than visual. We like numbers, equations and brief text. We like graphs, which are certainly visual, but not necessarily descriptive or evocative. We prefer our own abstract vocabulary.
Visual images play a central role in areas such as fractals, chaos theory and Bayesian theory. Writes Benoit Mandelbrot: « In the theory of fractals, ‘to see is to believe.' » Yet there is much more that we can do.
The benefits are substantial. Among others, there is an opportunity for heightened awareness, improved understanding and enhanced rigor. Let us explore these benefits further:
❑ Awareness: In a well-managed organisation, an awareness of risk exists at all levels, from the chairman to the non-officer clerk, from the PhD to the high school graduate. We can more effectively identify, measure and mitigate the risks we know well
❑ Understanding: Even the most complex ideas can be expressed in understandable ways. It has been said of the French mathematician Joseph-Louis Lagrange that he « believed that a mathematician has not thoroughly understood his own work till he has made it so clear that he can go out and explain it effectively to the first man he meets on the street. » (See Eric Bell’s enjoyable book, Men of Mathematics)
❑▪ Transparency: Transparency is critical given recent events. Many outside of risk management, including investors and analysts, are justifiably perplexed by the fatal mistakes of large and seemingly strong firms. Is this a failure of risk management? Is this a failure to apply risk management principles? How can apparent safeguards fail so quickly and extensively?
❑ Focus: In risk management, our energies should be directed less to making our models complicated and more to making them clear, accessible and relevant (which does not mean simplistic). The most powerful ideas in economics and finance can be stated succinctly and clearly
❑ Adaptation: If an organisation understands its risks, it can more easily adjust its exposures to different types and amounts of risk. It can monitor these exposures against its tolerance for risk. Certain business units may be able to assume more risk, whereas other areas may be taking too much or engaging in insufficient mitigation. What may seem intuitive may be inconsistent with the actual circumstances
❑ Perspective: There is value in approaching risk broadly, particularly when we find ourselves immersed in our day to day requirements, as often occurs. If we « step back » to obtain some perspective, we can more easily see connections and relationships about risk that we have not previously realised. This is critical to the process of discovery
❑ Rigor: A deeper understanding of a subject becomes possible if we can restate a problem using different language — in this case, a visual language. Weakness in processes will become more evident, as will the consequences of key dependencies. John Berger writes, « It is the actual act of drawing that forces the artist to look at the object in front of him, to dissect it in his mind’s eye and put it together again »
❑ Recognition: Risk has a human element that we do not sufficiently emphasise. Even our close colleagues — people we think we know well — can cause serious damage to organisations, including their destruction. A challenge in managing risk is the difficulty of predicting which specific individuals will engage in such extraordinary behaviours
❑ Enjoyment: In addition to being useful, visual images can also be enjoyable. Looking at images can also enrich our work and our larger lives.
Visual approaches do not exclude the traditional approaches based on statistics, finance and accounting. They complement and refine such approaches. Exploring this theme from a different perspective in her book Reading Images, Hermine Feinstein writes, « Because art makes values vivid and concrete, it enables us to see those values, to examine and question them for their merit, relevance and usefulness in our daily lives. » Mandelbrot in his book The Fractal Geometry of Nature: « Graphics is wonderful for matching models with reality. When a chance mechanism agrees with the data from some analytic view point but simulations of the model do not look at all ‘real’, the analytic argument should be suspect. A formula can relate to only a small aspect of the relationship between model and reality, while the eye has enormous powers of integration and discrimination. »
The process of discovery
Soon after publishing their initial findings on DNA in the spring of 1953, James Watson and Francis Crick would become internationally recognised for their discovery. Watson, Crick and Maurice Wilkins, a biologist at King’s College, would win the Nobel Prize in 1962. This ‘secret of life’ would lay the path to the elucidation of the genetic code and the human genome.
The first step in this revolution began with a spark of insight that arose from a visual image. As Horace Judson observes, « Watson stumbled onto his part of the solution visually, from a shape, a representation ». Years after the discovery, Crick wrote, « The shape of a chemical model can be embodied rather easily in a mechanical model, and it this that makes the ideas easy to understand. »
For risk management, we are at an earlier stage in the refinement of our ideas relative to our colleagues in molecular biology, although extensive work in risk has been done, and there is much excitement ahead.
Watson and Crick offer us valuable insight into the process of discovery. These and other scientists represent a great tradition, one of curiosity, questioning, visual awareness and model building. These same qualities can also help us understand our own fascinating subject of risk.