Uncertainty and risk |

Uncertainty and risk

How do we assign probabilities and expected returns to fat tail events? Often, when people can’t estimate the impact of certain events, the tendency is to guess wish it away, ignore it, or guess it doesn’t exist. Yet, if asked what is the GDP of the US, should you guess “Zero” because you don’t know the answer? Of course not. And so, policy-makers and investors (for our purposes) are often called on to make decisions based on incomplete information. Sometimes, the return profile can be estimated; at other times, we have to make decisions without even knowing the shape of the distribution.

In a recent paper David Farber, a law professor at University of California, explored different tools we can use, or at least that can prompt some healthy debate. While some of the issues he discusses are not directly financial (like global warming or terrorist threats), they are related and the ideas discussed are very relevant. I’ve included his conclusion from the paper.

Our society faces serious problems, many of which would be difficult to manage under the best of circumstances. Addressing these problems is all the more difficult because they often involve threatened harms whose dimensions are only understood imperfectly. In particular, we are often unable to quantify the probability of harm with any confidence. It is sometimes tempting to ignore such hazards as speculative. That is clearly the wrong response. Just because you do not know exactly how big a number is, there is no reason to assume it to be zero. (Q: What is the GDP of China? If you don’t know, should you guess zero?)

A better response would be to use some variety of the precautionary principle, which at least keeps the threatened harm on the agenda and counsels caution in dealing with it. But the precautionary principle, or even the catastrophic risk precautionary principle advocated by Sunstein, falls well short of providing concrete guidance. This Article has explored developments in economic theory that may provide more clarity in dealing with unquantifiable uncertainties.

As we have seen, such uncertainties can be associated with fat tailed distributions – either because we know the distribution and the expected risk or its variance turn out to be infinite, or because the nature of the distribution prevents us from setting key parameters accurately enough to determine the expected risk or variance. There is some reason to think that, because of internal feedbacks, both climate change and financial crashes may have such characteristics.

In other situations, we may simply have no good idea of how to assign probabilities in the first place or of what the probability distribution might look like. In those situations, we need to think about a variety of possible scenarios. Examples include estimates of the medium-run risks and benefits of nanotechnology, or the long-term risks of nuclear waste disposal. Ambiguity theory helps address these situations, and the most easily applied models advise assessing decisions based on a combination of the best-case and worst-case scenarios. This leads to the α-precautionary principle, which weighs the best and worst potential outcomes in assessing a course of action.

One lesson of this investigation into non-quantifiable hazards is that uncertainty is not unitary but plural. Former Secretary of Defense Donald Rumsfeld famously distinguished between known knowns, known unknowns and unknown unknowns, with the latter being the most worrisome. The “known knowns” correspond not merely to certainties but to probability distributions that are well understood – risks, rather than uncertainties, in the lexicon of this article.

But the known unknowns fall into several categories. Some are known in the sense that we have a grasp on the shape of the probability distribution but not key parameters – and in some cases, the key parameters turn out to be difficult to determine or even unknowable. There are also risks that we know are unknowable, such as the evolution of human society over future millennia. These known unknowables merge into the Rumsfeld’s category of unknown unknowns.

Yet, in some cases we may have a handle on even the unknown unknowns. For instance, we may not have a good understanding of which particular future shocks might affect a system. Nevertheless, understanding the feedbacks in the system and the statistical distribution of outcomes might enable us to understand how the system will respond even to unknown shocks. Uncertainty, then, is a multidimensional concept.

It would certainly be nice if economics were to provide a foolproof way of making decisions under conditions of uncertainty, given the importance of those decisions for society. The prospects for such a development are themselves – there is no other way to put this – highly uncertain, and they are all the more so because uncertainty takes so many forms. Certainly, no such methodology now exists, and one might well question whether it is even possible. But an analytical tool need not be decisive to still be useful.

Complicated but potentially catastrophic problems like global climate change or financial crashes will always present difficult choices, once we at least get to the point of acknowledging that these threats are real and must be dealt with. There is no easy recipe for divining the right solution to problems whose parameters involve so much uncertainty. We cannot afford to ignore perils simply because their probability is uncertain, nor can we safely proceed on the basis of speculative numerical estimates. But we can gain some much-needed clarity with the tools discussed in this article.

For the full article, click here.

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