Category Archives: Actuarial and Risk

The worst insurance policy in the world

Aviva in France is still dealing with having written the worst insurance policy in the world. From the sounds of things, they weren’t alone in this foible. It’s also hard to say as an outsider what the right or reasonable resolution to their current problem is, but here is the policy that they wrote.

  • Buy a policy
  • Choose what funds you want to invest in
  • Unit prices calculated each Friday
  • Allow policyholders to switch funds on old prices until the next week
  • Hope like hell policyholders don’t switch out of poorly performing funds into well performing funds with perfect information based on backwards, stale prices.

Inconceivable – and since I don’t know more than I read on this blog post, maybe the reality and liability is really quite different.

See the post from FT Alphaville on the man who could own Aviva France.

Summary of November links

These are some of the stories I’ve followed or commented on in November:

  • Pro-cyclical fiscal policy from Nigeria. Knee-jerk reactions are usually not the right answer
  • eVoting seems error-prone and fraud-suspect around the world. Good luck Namibia…
  • IASB: re-deliberations will extend into 2015. Performance measurement, participating contracts still unresolved
  • Namibia has the second highest house-price inflation in the world of 29% every year – second to Dubai
  • Please stop using SA85-90 “combined” as your base mortality table
  • 2014 mid-year EV analysis
  • MG digs dirt, eventually, on 2002 Zimbabwe elections. Asks some thought provoking questions about election monitoring
  • Consolidation in Kenyan life insurance sector. More needed, more to come surely.
  • Doing business on our continent isn’t always easy.
  • Selective lapse impacting mortality?
  • Why model structure matters, not just passing the calibration tests
  • The inevitable growth of solar energy. Declining prices help emerging markets with plenty of sunshine. #Africa…
  • The Beveridge curve and long term unemployment.


SA85-90 “combined” and more actuarial sloppiness

I know of far too many actuaries who think that the “average” SA85/90 table is an appropriate base for their insured lives mortality assumption.

It’s not.

It’s also a good example of “actuarial sloppiness”.

To be specific, it is equally inappropriate if your current experience is a reasonable fit for the combined SA85/90 table.

SA85/90 was graduated based on South African insured lives data from 1985 to 1990. This period is important because it’s generally felt to be the last period in South Africa where HIV/AIDS would not have had a significant impact on mortality. (Estimates differ, but 1985 is often taken as the starting point for the HIV epidemic in South Africa and even though there might have been some deaths within the first five years, it is inconceivable to have affected a significant portion of the population.)

SA85/90 came in two version, “light” and “heavy”. Somewhat disappointingly, no distinction was made between males and females. Light mortality reflected the typical, historical, insured life characteristics which was pretty much white males. If I recall correctly, “Coloured” and “Indian” males were also combined into the light table. “Heavy” mortality reflected the growing black policyholder base in South Africa.

For all the awkwardness of this racial classification, the light and heavy tables reflect the dramatically different mortality in South Africa based on wealth, education, nutrition and access to healthcare. Combining the results into a single table wasn’t reliable since there were significant differences in mortality AND expected changes in the proportions of the heavy and light populations in the insured populations into the future.

A combined table was still created at the time. I suspect Rob Dorrington may have some regrets at having created this in the first place or at least in not having included a clearer health warning directly in the table name. The combined table reflects the weighted experience of light and heavy based on the relative sizes of the light and heavy sub-populations during the 1985 to 1990 period. I think a safer name would have been “SA85/90 arbitrary point in time combined table not to be used in practice”.

There is no particular reason to believe that the sub-population that you are modelling reflects these same weights. Even for the South African population as a whole these weights are no longer representative. The groups, at least in the superficial sense we view any particular citizen as coming from distinctly one group, will fairly obviously have experienced different mortality but will also have experience different fertility and immigration rates.

Our actuarial pursuit of separating groups of people into smaller, homogenous groups should also indicate that in most cases the sub-population you are modelling will more closely reflect one or the other of these groups rather than both of them.

But even if, just for the sake of argument, your sub-population of interest does reflect the same mix at each and every age as baked into the combined SA85/90 table, then it would still be entirely inappropriate to use the table for all but the crudest of tasks. After all, there a reason for our penchant for homogenous groups. If you model your sub-population for any length of time, the mix will surely change as those exposed to higher mortality die at a faster rate than those with low mortality.

The first order impact would be that you would be modelling higher mortality over time than truly expected. Due to the relative mortality between the two populations differing by age, the actual outcome will be somewhat more complex than that and more difficult to estimate in advance. This is particularly important with insurance products where the timing of death is critically important to profitability.

So, just because you can get a reasonable fit to your experience of an age- or percentage-adjusted SA85/90 combined table does not mean you have an appropriate basis for modelling future mortality. It may not vastly different from a more robust approach, but it’s just sloppy.

Selective lapsation – where it does happen

A few years ago, as South African life insurers were experiencing sharp spikes in lapse rates as a result of the GFC, some analysts and actuaries raised concerns about the impact of selective lapsation on mortality experience.

The principle is sound: Policyholders who know their health is very poor are less likely to lapse than policyholders who have no concerns about their health. Thus, those who lapse are likely to be healthier than those who remain. The mortality (and morbidity and disability) experience of those who remain will be worse than expected based on past experience.

The higher the lapses, the more significant this impact becomes. As an example, let’ say we have the following mix of policyholders by underwriting class (best to worst)

underwriting class Mix of population mortality experience as % of best
1 80% 100%
2 10% 150%
3 5% 200%
4 5% 400%


I’ve approximated the experience here based on some past CSI presentations on mortality experience – could definitely be fine-tuned.

This would give rise to experience on average of 125% of “best underwriting class experience”. If 10% of policyholders lapse and we assume these are all “best class” lives, the average experience increases by just 2.8% to 127.8%.  A pretty modest impact even assuming 100% of lapses are very healthy.

In practice, some lapses would be driven by affordability and other issues so it wouldn’t be as dramatic as this. If only half the lapses were selective, the impact drops to 1.4%.

If lapses rise to 25%, then experience might be 8.3% worse, which is only just larger than the compulsory margin. And again, this is likely a worst case scenario. The “50% selective impact” is still only 4.2%.

So where does all the fuss come from? At a recent conference in the US I discovered some products where lapse rates at certain durations are as high as 90%. This relates to points where the premiums jump up dramatically after an extended period of being level and continue to rise from thereon out.

With a 90% lapse rate, assuming the best 90% of policyholders lapse, results in future mortality experience of 175% higher than before or 300% of the best class mortality experience. The impact is still a nearly doubling of experience under the 50% selective scenario.

So yes, selective lapsation can be a genuine risk, but the lapse rates where this becomes a major issue are higher than most insurers will experience under normal scenarios.

Last postscript here is that none of this would have an impact if the insured population were completely homogenous – I’ll have another post on the need to dig into populations and understand how combining heterogeneous populations is dangerous when I discuss the misuse of SA85/90 “combined”.

Actuarial sloppiness

An actuary I know once made me cringe by saying “It doesn’t matter how an Economic Scenario Generator is constructed, if it meets all the calibration tests then it’s fine. A machine learning black box is as good as any other model with the same scores.” The idea being that if the model outputs correctly reflect the calibration inputs, the martingale test worked and the number of simulations generated produced an acceptably low standard error then the model is fit for purpose and is as good as any other model with the same “test scores”.

This is an example of actuarial sloppiness and is of course quite wrong.

There are at least three clear reasons why the model could still be dangerously specified and inferior to a more coherently structured model with worse “test scores”.

The least concerning of the three is probably interpolation. We rarely have a complete set of calibration inputs. We might have equity volatility at 1 year, 3 year, 5 year and an assumed long-term point of 30 years as calibration inputs to our model. We will be using the model outputs for many other points and just because we confirmed that the output results are consistent with the calibration inputs says nothing about whether the 2 year or 10 year volatility are appropriate.

The second reason is related – extrapolation. We may well be using model outputs beyond the 30 year point for which we have a specific calibration. A second example would be the volatility skew implied by the model even if none were specified – a more subtle form of extrapolation

A typical counter to these first two concerns is to use a more comprehensive set of calibration tests. Consider the smoothness of the volatility surface and ensure that extrapolations beyond the last calibration point are sensible. Good ideas both, but already we are veering away from a simplified calibration test score world and introducing judgment (a good thing!) into the evaluation.

There are limits to the “expanded test” solution. A truly comprehensive set of tests might well be impossibly large if not infinite with increasing cost to this brute force approach.

The third is a function of how the ESG is used. Most likely, the model is being used to value a complex guarantee or exotic derivative with a set of pay-offs based on the results of the ESG. Two ESGs could have the same calibration test results, even calculating similar at-the-money option values but value path-dependent or otherwise more exotic or products very differently due to different serial correlations or untested higher moments.

It is unlikely that a far out-of-the-money binary option was part of the calibration inputs and tests. If it were, it is certain that another instrument with information to add from a complete market was excluded. The set of calibration inputs and tests can never be exhaustive.

It turns out there is an easier way to decreasing the risk that the interpolated and extrapolated financial outcomes of using the ESG are nonsense: Start with a coherent model structure for the ESG. By using a logical underlying model incorporating drivers and interactions that reflect what we know of the market, we bring much of what we would need to add in that enormous set of calibration tests into the model and increase the likelihood of usable ESG results.

Argentina teetering towards default

I’ve been working with a few insurers and reinsurers on credit risk recently. We’ve had plenty of reasons to think about it, what with new regulations (SAM, Basel III) and South African government downgrades. However, sometimes I get the impression that credit risk is viewed as an academic risk, as something that happens to others, micro lenders and maybe banks.

In South Africa, we’ve had incredibly few corporate bond defaults and most market participants don’t even know that the South African government “restructured” some of its debt in 1984 and so has, in fact, defaulted on contractual bond obligations.

In a recent credit risk and capital workshop, I raised the issue of Russia defaulting on Ruble-denominated debt in 1998, a big part of what led to the collapse of LTCM. Again, these events are often figured as “exceptionally unlikely” and not even worth holding capital.

Well, in the news, Argentina is about to default. Again. They have been one of the most regular defaulters on sovereign debt in the last couple of centuries. They’re also an example I often use of “currency pegs” doing precious little to mitigate currency risk except on a day to day basis.

More on that in another post (yes, I’m hoping to post a little more regularly in the coming months.)