Rodney Lester gives an opinion on the pitfalls of overreliance on probability and risk models in insurance and how a greater appreciation of uncertainty can improve actuarial thinking.

Leading actuarial bodies are increasingly recognising the limitations of probability-based models in an uncertain world (see Mervyn King’s interview in The Actuary, August 2020, and Gutterman’s article in Contingencies, July/ August 2020). A key theme is that such models fail to properly account for highly uncertain but material events, where setting reasonable probabilities is virtually impossible.  This in some ways represents a reversion to an earlier generation of actuarial thinking, but modified by 21st century realities and technology. Some background may be useful to explain this development.

Until the 1980s, actuarial models tended to be deterministic and assumptions were largely based on curves fitted to historical data and the application of a ‘Bayesian’ approach to changing experience over time: if a new product was being developed, it was priced significantly higher than expectation and adjusted as the experience emerged. This was possible, as at the time market leaders had some pricing power. However, it would not be accurate to say that actuaries ignored the second and third moments implicit in their models; experienced life actuaries just acknowledged the limits of their knowledge by building in substantial safety margins, the so called actuarial black box (epitomised by net premium valuation methods). 

Non-life insurance actuaries effectively did not exist in Australia until the late 1970s/early 1980s when high inflation rates threw the pricing and reserving methods then in use out the window.

Fortunately, the Australian profession had the intellectual firepower (such as Greg Taylor, Bob Buchanan, John Trowbridge and others) to develop new approaches over a short timeframe, building in part on techniques already developed in the US.

Before that, Australian long tail insurers had been surviving through a combination of investment returns, cross cohort subsidies and blissful ignorance of their real positions, sustained (at least for a period) by positive cash flows. Some large-long tail insurers did subsequently fail when reality caught up, although they survived longer than they should have.

Risk management using stochastic models took off after the stagflation era, largely due to ongoing financial sector failures in major markets and the influence of a new group of financial economists, particularly out of the Universities of Chicago and Rochester (progenitors of the so-called ‘Neoliberal revolution’). In the actuarial sphere, we saw the emergence of risk-based capital (RBC) requirements in the US in the 1990s. Efficient markets assumptions[1] led to innovations such as the Black-Scholes model for pricing options, the capital asset pricing model and portfolio insurance. Actuarial liability models assumed that the past is a reasonable guide to the future (including that processes being modelled were at least weakly stationary) while asset pricing was based on short term market signals. 

In Europe, work was begun on Solvency II for insurers in the early 2000s. Within this, Pillar I (capital and other quantitative requirements) was built on the framework of the snapshot-in-time VAR approach originally developed by J.P. Morgan in the late 1980s. Much of this thinking was drawn from banking requirements under Basel II. Even after the GFC and a very evident failure of Basel II, and the earlier failure of portfolio insurance, the short-term VAR approach continued to shape Pillar 1, albeit with the GFC experience incorporated. In addition, some scope for yield curve modification was introduced, as were allowances for weaker assumptions during a long transition period. However, since January 2016 the European central insurance supervisor (EIOPA) has had to promulgate numerous further adjustments, some under political pressure, as the adverse impacts of the solvency rules on capital markets and product development became apparent (although these should have been obvious from day one).

The fundamental faults with Solvency II Pillar I approaches are that they do not recognize that risk and uncertainty are two different things (see the book Radical Uncertainty, by Kay and King, 2020), and do not allow for the superior long term risk return characteristics of equity-style investments (see Parsaud, ‘How Not to Regulate Insurance Markets’, Peterson Institute, 4/15). It assumes a precision that is not accessible in a world of uncertainty, applies a flawed short-term approach, and imposes a responsibility on risk managers and Boards of Directors that is unreasonable. There is no inherent need for solvency balance sheets to reflect a point in time fair value snapshot or a potentially volatile one-year survivability metric – accounting standards should take on this role. By now it should be clear that asset markets can be highly volatile over short periods and asking actuaries to estimate what a transferee will require to take over a liability portfolio in a going concern environment is a theoretical concept at best, particularly where risk margins are formulaic.

In addition, there is plenty of evidence that well-run insurers with strong cash flows can survive even major short-term fluctuations. 

So how can prudential standards for long term contingent contracts, such as many types of insurance, cope with the reality of high levels of uncertainty as global financial, social and physical systems become even more intertwined and complex? Two core realities are that there is a limit to how much capital a privately owned insurer can be asked to hold (either explicitly or in reserves) and secondly that supervisors need to be able to form a reasonable view as to the ultimate survivability of an institution. In addition, long-term insurers need to be able to fulfil their increasingly critical roles as long-term investors (particularly for infrastructure), providing greater scope for product development as a by-product. While the answers need some deep collective thinking some possibilities are as follows:

  • Moving away from a bank style one year, 99.5% survivability VAR solvency approach for long term/ long tail contracts, possibly including the use of moving average asset values and focusing on ultimate shortfall probabilities for long term liabilities.
  • Reducing the current reliance on disclosed capital as ‘the’ solvency guide and increasing emphasis on the largest item in the balance sheet – the technical reserves. Sensitivity analysis does this to some extent by identifying the key assumptions but there could be more focus on ‘out of model’ possibilities. 
  • Stronger government legislative support for pre-emptive risk management, including limits on geographical exposure and enhanced vulnerability management (e.g. stronger building standards).
  • A greater emphasis on medium term cash flow monitoring of insurers – HIH may have been caught earlier if this had been a priority.
  • Building greater recovery and resolution skills and capacities in supervisory bodies.
  • Simplifying risk capital calculations – complex algorithms such as Solvency II Pillar I are not necessarily superior to simpler formulations such as RBC (see Haldayne – The Dog and the Frisbee, ).
  • Giving supervisors (at least in developed markets) greater flexibility in times of crisis. Solvency II does provide some scope in this regard.
  • Most importantly, fostering a mode of actuarial thinking that is not limited by stochastic models that fail to encompass the broad range of uncertainties.

Such changes may be controversial given the historical direction of models and regulation but would create space to consider the big risks and uncertainties faced by an insurer.

Importantly, this does not mean abandoning risk modelling completely, as there is considerable value in modern techniques (although advanced techniques require advanced knowledge). However, it does require a recognition that actuarial work involves a lot more than just being a mathematical technician and that the experienced actuary should not ignore messages from the back of their neck.

[1] Essentially that the future of asset prices is not predictable but follow a definable stochastic process.

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