The article ‘Alert to black swan-song?’ (‘Soapbox’, September) is based on a curious “traditional view of black swan risk”. Prior to Nassim Nicholas Taleb’s use of the phrase, references to black swans were most commonly found in the philosophy of induction. Taleb uses “black swans” to mean events that have a major impact but could not realistically have been predicted or modelled. He contrasts them – quite emphatically – with the kind of risks reflected in the VaR models that the authors seem to have in mind when they write about 1-in-200-year events. (Examples of Taleb’s variety of black swans might be the outbreak of World War II or, on the upside, the invention of the internet.)

While the authors discuss natural disasters, these are not really black swans in Taleb’s sense and indeed the authors go on to tell us that natural disasters are not really what they have in mind. But what kind of risk are they referring to? I reached the end of the article without feeling I had found out. Perhaps that reflects a healthy recognition on the part of the authors that black swans are “unknown unknowns”.

Nevertheless, I was reminded that Taleb uses an actuary as his archetype of a naive financial modeller. I do not think that this is a fair reflection of our profession, but I do believe it contains more than a grain of truth.

Many of the processes that actuaries consider submit to nice models over a relatively short term, but shocks – black swans – can occur and will. I was pleased to see, later in the same issue, Dr Tsanakas’ thoughtful feature (The elephant in the room) discussing model risk and the dangers of failing to communicate the limitations of our models. It is tempting, as actuaries, to try to extend our success with models from the generally uniform randomness of, say, mortality rates to the unstructured randomness that applies elsewhere. We should not do so because our models simply do not apply.

Risk transfer more generally may better mitigate black swans, but must certainly have limits. I would have been interested to know, for example, what kind of risk transfer could have protected HMV from obsolescence in the face of the internet.

Unfortunately, the authors of ‘Alert to black swan-song?’ did not explain what kind of product they are proposing. I hope, for the reputation of our profession, that it is not simply insurance.

Anonymous 17 September

Model conundrum

Andreas Tsanakas’ feature ‘The elephant in the room’, (September) is a timely reminder of both positive and negative aspects of models.  It reminds me of Lord Turner’s review of the global financial crisis (2009) when he referred to “misplaced reliance on sophisticated maths”, with the question “Fixable deficiencies or inherent limitations?”.

Understanding what it is sensible to do in modelling insurance companies is a challenge to the actuarial profession. Solvency II and the ability of insurers to use internal models in a way that reduces capital requirements is naturally an incentive to more modelling, and supervisors may be keen to see attention to fix perceived deficiencies.

But complexities may themselves be a problem. Andrew Haldane’s recent speech, entitled ‘The dog and the Frisbee’, to the Jackson Hole conference demonstrated that there were some advantages in using simple as opposed to complex rules in measuring banks’ ability to meet their obligations. He concluded that because complexity generates uncertainty, it requires a regulatory response grounded in simplicity, not complexity.

Managing an insurance company is different from regulating companies, and may produce different answers: but it is right to consider how sophisticated we want our maths to be.

Chris O’Brien 19 September

Muddling one’s means?

Roy Colbran drew attention to the geometrical mean component of the consumer prices index model  (Letters, August). One property of a geometrical mean is that if one element tends to zero, the whole thing tends to zero.  That property is not replicated by price movements of consumer goods.  I, too, would welcome an explanation of the justification of the use of geometric means in the CPI.

Trevor Sibbett 1 September

How many actuaries does it take to ...

My wife Elizabeth Treherne and I were both working as volunteers at the Olympics and discovered that Rebecca Porter, an actuarial student, was in the same team as us – printing and distributing results for the handball competitions in the Copper Box.  We wondered what the odds of there being three actuaries in the same team (of about eight people) and also how many other members of the profession have been volunteers at the Olympics and/or the Paralympics.

Simon St Leger-Harris 20 August

Bottom of the barrel: oil overload

I’m sure no one doubts that oil prices are an important factor in the world economy – but Gail Tverborg’s broad predications of economic change being shaped by changing oil supplies (Features, September) seem one-dimensional in the actuarial context, to say the least. For example: Rising oil prices = declining GPD in oil importing countries = rises in unemployment = increasing property damage. Really? There are quite a lot of other things that affect employment, and GDP growth.

Peter Baker 7 September