The Risk of Change
In insurance it is customary to distinguish between three types of risk: volatility (random), change and error.1 To visualize the differences, consider 10 tosses of a coin with heads on one side and tails on the reverse. Asked to predict the number of times heads will appear, you may say “five,” but the actual result could be four or six. Random deviation from the expected number represents volatility.
The risk of change is that the coin becomes worn, shifting its centre of gravity and resulting in a systematically higher number of heads. In the end, we are all subject to the risk of error. An example is the “gambler’s fallacy”: after nine heads in a row, people with no basic knowledge of probability theory would erroneously expect the chance of tails on the tenth coin toss to be higher than 50%.2
While the relative impact of the volatility risk decreases with the number of coin tosses (the law of large numbers), the risks of change and error cannot be mitigated by increasing the number of tosses (read: the size of a portfolio of insured risks) because they affect all risks alike.
The manifestations of the risks of change and error are difficult to disentangle whenever predictions are involved.3
Who is to decide with hindsight whether an incorrect forecast was due to a change that was unforeseeable at the time the forecast was made? For this reason further reference to the risk of change in this article is also meant to encompass the risk of error. Past experience shows that insurers have reason to be mostly worried about the risk of change. This has amongst others been highlighted in numerous publications on Solvency II.4
Unlike volatility risk, the risk of change cannot be captured by stochastic models. In the following sections, we examine in more detail why this is the case. We will also explore whether or not there are ways to learn from past experience. Moreover, we take a brief look at how the risk of change is dealt with in non-insurance business and provide a number of valuable clues for the role that reinsurers can play in risk mitigation. This approach we then contrast with an alternative, in which reinsurance is replaced by higher amounts of retained capital.
Unlike gamblers, insurers derive probabilities from empirical data – the annual number of death cases or the annual number of car accidents. Their objective is to condense the available data into subgroups containing homogeneous and independent risks. This way insurers hope to minimize as much as possible their exposure to sampling error, i.e. the deviation of the composition of the insured portfolio from the composition of the population on which the claims data is based.5
The classification into subgroups is carried out by means of risk factors.6
It is known, for example, that people have a significantly higher mortality at age 80 than at age 20. Therefore, two separate age groups will each contain more homogeneous risks than one risk group of octogenarians and 20-year-olds together. Next to age, gender is known to be a relevant risk factor in mortality, as is smoking. Figure 1 illustrates the fact that the frequency of an insured event depends on various risk factors.
The classification of empirical data by means of (a combination of) risk factors – for example, all 30-year-old female non-smokers – increases the degree of uniformity within each risk group. In practice we cannot expect to achieve perfect uniformity, nor should we; otherwise, each risk group during a given period of time would either remain claim-free or the totality of its individual risks would claim. In this deterministic world, insurance would lose its purpose.7 Even gambling is far from perfect uniformity. If it were perfect, there would be no volatility and “dice made alike and thrown alike [would] fall alike, and that [would be] the end of it.”8
Risk of change
Unknown or accidental risk factors are all-pervasive, for example a falling roof tile or a blood clot in the brain. Such risk factors, which we cannot, or do not, statistically control for, are the cause of random fluctuation (volatility). In contrast, the risk of change can be described as the unforeseen and loss-making change of one or more of the risk factors (e.g. occupation or security standards in factories) used for the classification of the entities to be insured (underwriting factors).9
Claims frequency is also influenced by environmental factors. Some examples include the effect of the economy on disability incidence rates, snow-packed roads on the loss frequency of motor insurers or the absence of extremely rare catastrophic events, such as a major pandemic or catastrophic factors.10
Although known, they are not used in the classification of risks because they are assumed to indiscriminately affect the entire (data) population alike.
The risk of change also pertains to claims “severity” expressed as the total amount to be paid. This is the case whenever the latter depends on additional pricing parameters that are in turn subject to risk factors. For example, consider the termination rates in disability and long-term care products as well as the prices and wages pertaining to repair costs in third-party liability.
In summary, the risk factors underlying the risk of change include factors in the following subdivisions:
- Underwriting (e.g. occupation or safety standards)
- Environmental (e.g. lifestyle habits or weather conditions)
- Catastrophic (e.g. a pandemic or a terrorist attack)
Changes in risk factors can have an impact on both the claims frequency and the claims severity. They can occur irregularly and over time may also develop a cyclical pattern or a trend.11 Figure 2 provides an illustration including underwriting factors and environmental factors.
The rectangular block to the left represents a set of empirical data – for example, all new disability claims from a total population of self-employed persons during a certain observation period. The data are condensed into risk groups according to underwriting factors (UF), such as occupation or age, that exhibit a high positive correlation with the insured event. The incidence rates derived are used as a basis for pricing disability products in future years until updated evidence becomes available.
It is tacitly assumed the environmental factors (EF) that prevailed during the observation period will remain constant in future. However, they may not if the composition of the relevant population changes, for example, or if there is an economic downturn or if work pressures lead self-employed workers to suffer more stress-related disability.
In the Netherlands, for example, the number of single-person companies rose markedly during the past decade – typically as former employees are outsourced along with their functions. Self-employed individuals who work on their own find it much more difficult to make ends meet than do self-employed people with a workforce. Unsurprisingly they are at significantly higher risk of becoming disabled than the latter group.
The change of environmental factors is represented in Figure 2 by an upwards diagonal movement of the block. Had environmental factors remained constant, the block would have moved horizontally (along the dotted arrows). Unless the intermediate change of environmental factors since the time of the investigation is taken into account, the pricing will likely be off the mark. This is illustrated in Figure 2 by the risk group that lies outside the dotted rectangle.
Box 1: Five Methods of Dealing With Risk of Change
1. Continuous analysis
Sometimes uncertainty regarding relevant risk factors can be attributed to a lack of available information (epistemic uncertainty) rather than to irreducible unpredictability.12 To see this, consider the coin toss analogy.
We can content ourselves with the knowledge that in 50% of the tosses, a coin with heads on both sides is used. But we can also invest additional time and effort in order to find out on exactly which tosses the double-headed coin comes into play. This knowledge would then allow us to increase the credibility of our unchanged prediction (75% heads) by cutting the standard error (volatility) in half.
In situations involving epistemic uncertainty, experience suggests an inclination to avoid thoroughgoing research in favour of makeshift stochastic models.
2. Limited exposure
The exposure regarding a certain risk should always be inversely proportional to the uncertainty surrounding possible adverse changes of its risk factors. In practice, however, one frequently encounters instances that appear to violate this rule. A typical example would be an insurer/reinsurer that prides itself on the expertise and competitive advantage it has acquired in a particular product line. As a result, it is rewarded with a significantly higher market share but eventually ends up with an unhealthy, disproportionate risk exposure.
We have seen above that it is impossible to put a probability tag on the risk of change. The possible changes of the risk factors are virtually unique and therefore do not allow for any classification of similar recurring instances or any learning experience for that matter.13 On closer inspection, however, the question arises whether we can benefit from diversification by expanding both the product range and the geographical scope. As mentioned above, volatility is caused by unknown risk factors, and experience suggests that they cancel each other out, provided that the risks are uncorrelated (independent) or negatively correlated.
The benefits of specialization are twofold: On the one hand, specialization implies concentration on a large number of equal or similar cases. It can therefore be considered as “an application of the insurance principle.”14 On the other hand, the specialist has more expert knowledge. Since the risk of change can be seen as varying in magnitude according to the quality of judgment on the part of those dealing with it, chances are that it will be significantly reduced by specialization.
In cases for which the above methods are unlikely to lead to any satisfactory results, avoidance remains the only viable solution.
Is the risk of change quantifiable?
If the probabilities for changes in risk factors were known, the risk of change would merge into the volatility risk. It would cease to exist because the problem of the predictability of change would find a stochastic solution. Only its variability – the volatility risk – would remain to be addressed.
Consider the following example: In the first round, a fair coin is tossed 10 times. In the second round, the setting is changed; in 50% of the tosses the fair coin is exchanged for a coin with heads on both sides (risk of change). The introduction of the quantifiable risk of change would merely change the probability distribution and the standard error (volatility) as follows:
Round 1: Heads (50%), Tails (50%); standard error = 16%
Round 2: Heads (75%), Tails (25%); standard error = 14%
The risk of change is necessarily confined to instances for which no probabilities are available. Only irregular events, trends or cyclical patterns that cannot be specified in terms of probability remain.15
To estimate the total claim amount for various changes in risk factors, we require an exploration of what-if scenarios and notably the worst-case variant. In the recent past, such investigations were conducted to assess pandemic threat. The objective was to derive a plausible mortality increase, partly based on the data available from previous pandemics (most prominently the “Spanish” influenza outbreak of 1918-1919). However, the probability of a major pandemic itself continues to remain pure guesswork.
Can we learn from past experience?
An element of ad hoc learning is involved when it comes to the risk of change. This is mainly confined to singular changes, trends and sometimes cyclical patterns. Irregular changes and rare events do not allow for any successful adaptation of our predictions.
Examples of singular changes include a sudden and politically motivated leniency of state authorities in the assessment of public disability claims or a major improvement in cancer diagnostics.
Trend parameters also play an important role in the calculation of longevity risk. We have seen attempts at modelling cyclical incidence rates which, in many markets, appear to be characteristic for the disability risk.16 However, such cyclical models introduce additional economic and/or behavioural parameters, which are in turn difficult to predict.
Overall, we must live with the fact that no matter how much experience was gathered in the past, we will always have significant, unquantifiable risk of change in the future. It is difficult enough to make sense of past experience and tell systematic change from volatility; more importantly, perhaps, the world is changing at an accelerating pace so whatever learning experience we already have is far from being able to protect us from the vagaries of the future.17
The risk of change places us outside the actuarial realm where probability distributions can be consulted or constructed. It is equal in scope to entrepreneurial risk. Essentially, there is no difference between a car manufacturer worrying about the future demand for gasoline-fuelled vehicles in the face of rising ecological awareness and an insurer fearfully anticipating a major improvement in cancer diagnostics that is likely to increase the future number of Critical Illness claims.
Pointers may be taken from how economists have dealt with entrepreneurial risk. One of the first comprehensive treatments of the role of risk in economic decision-making is attributed to the American economist Frank Knight almost a hundred years ago.
Knight made a distinction between measurable and unmeasurable risk. The first he called “risk”, the second “uncertainty”. How can we deal with (unmeasurable) uncertainty in a business environment? Knight came up with five methods that seem equally useful for dealing with the risk of change (see Box 1).18
Benefits from reinsurance
A closer look at Knight’s proposed safeguards reveals they are all inherent in reinsurance. Participating in the business written by the cedant, the reinsurer is the ideal partner in analysing and monitoring the risk. Unlike non-participating external consultants, the interests of the reinsurer and the cedant are perfectly aligned.19 Thanks to its various forms of risk-sharing, reinsurance tailors a cedant’s exposure to its risk appetite, benefitting them in two additional ways. On the one hand, the reinsurer can support developing new insurance covers that expand a cedant’s product range. On the other hand, a cedant can benefit from lower reinsurance premiums resulting from the reinsurer’s diversified portfolio in terms of product and region.
The worldwide activity of an international reinsurer implies a wealth of experience across many markets that is not available to the typical locally-oriented cedant. The reinsurer knows where the pitfalls are, what is promising and what is likely to cause a loss. The cedant can learn from the exploits of other markets.
The alternative, to replace reinsurance with higher amounts of retained capital, shuts the cedant out from the advantages of a long-term reinsurance partnership in managing the risk of change. By randomizing the latter, and treating it like volatility, Solvency II implies that reinsurance and capital are more or less perfect substitutes in containing the risk of change.
Yet the risk of change is essentially unmeasurable. Quantifying a phenomenon that is arguably characterized by its inherent unquantifiability may therefore imply a deceptive degree of certainty that can be abused to promote other interests.
Insurance is all about predicting the future on the basis of past experience. Unlike natural scientists who can manipulate nature to make it conform to the assumptions of their theoretical models, insurers cannot operate in a controlled experimental setting.
With the help of statistical methods, insurers can structure empirical data into homogeneous risk groups on the basis of a number of explanatory underwriting factors. However, they cannot anticipate or control the future development of factors, notably environmental ones, in the same way as a natural scientist can conduct subsequent experiments in an unchanged setting (such as a vacuum).
Success in insurance depends on close monitoring of risk factors. If changes remain unnoticed, pricing models will quickly get out of touch with reality. The monitoring task requires experience, expertise and good judgment. These three indispensable properties are external to the models themselves and cannot be substituted by capital alone. They form the backbone of the services reinsurers should ideally continue to offer their customers.
For more articles in this publication, view the Table of Contents.