Tag Archives: insurance internal models

Beautiful Models

It has been a while since I posted on dear old Solvency II (here). As highlighted in the previous post on potential losses, the insurance sector is perceived as having robust capital levels that mitigates against the current pricing and investment return headwinds. It is therefore interesting to look at some of detail emerging from the new Solvency II framework in Europe, including the mandatory disclosures in the new Solvency and Financial Condition Report (SFCR).

The June 2017 Financial Stability report from EIOPA, the European insurance regulatory, contains some interesting aggregate data from across the European insurance sector. The graph below shows solvency capital requirement (SCR) ratios, primarily driven by the standard formula, averaging consistently around 200% for non-life, life and composite insurers. The ratio is the regulatory capital requirement, as calculated by a mandated standard formula or a firm’s own internal model, divided by assets excess liabilities (as per Solvency II valuation rules). As the risk profile of each business model would suggest, the variability around the average SCR ratio is largest for the non-life insurers, followed by life insurers, with the least volatile being the composite insurers.

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For some reason, which I can’t completely comprehend, the EIOPA Financial Stability report highlights differences in the SCR breakdown (as per the standard formula, expressed as a % of net basic SCR) across countries, as per the graph below, assumingly due to the different profiles of each country’s insurance sector.

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A review across several SFCRs from the larger European insurers and reinsurers who use internal models to calculate their SCRs highlights the differences in their risk profiles. A health warning on any such comparison should be stressed given the different risk categories and modelling methodologies used by each firm (the varying treatment of asset credit risk or business/operational risk are good examples of the differing approaches). The graph below shows each main risk category as a percentage of the undiversified total SCR.

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By way of putting the internal model components in context, the graph below shows the SCR breakdown as a percentage of total assets (which obviously reflects insurance liabilities and the associated capital held against same). This comparison is also fraught with difficulty as an (re)insurers’ total assets is not necessarily a reliable measure of extreme insurance exposure in the same way as risk weighted assets is for banks (used as the denominator in bank capital ratios). For example, some life insurers can have low insurance related liabilities and associated assets (e.g. for mortality related business) compared to other insurance products (e.g. most non-life exposures).

Notwithstanding that caveat, the graph below shows a marked difference between firms depending upon whether they are a reinsurer or insurer, or whether they are a life, non-life or composite insurer (other items such as retail versus commercial business, local or cross-border, specialty versus homogeneous are also factors).

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Initial reactions by commentators on the insurance sector to the disclosures by European insurers through SFCRs have been mixed. Some have expressed disappointment at the level and consistency of detail being disclosed. Regulators will have their hands full in ensuring that sufficiently robust standards relating to such disclosures are met.

Regulators will also have to ensure a fair and consistent approach across all European jurisdictions is adopted in calculating SCRs, particularly for those calculated using internal models, whilst avoiding the pitfall of forcing everybody to use the same assumptions and methodology. Recent reports suggest that EIOPA is looking for a greater role in approving all internal models across Europe. Systemic model risk under the proposed Basel II banking regulatory rules published in 2004 is arguably one of the contributors to the financial crisis.

Only time will tell if Solvency II has avoided the mistakes of Basel II in the handling of such beautiful models.

Divine Diversification

There have been some interesting developments in the US insurance sector on the issue of systemically important financial institutions (SIFIs). Metlife announced plans to separate some of their US life retail units to avoid the designation whilst shareholder pressure is mounting on AIG to do the same. These events are symptoms of global regulations designed to address the “too big to fail” issue through higher capital requirements. It is interesting however that these regulations are having an impact in the insurance sector rather than the more impactful issue within the banking sector (this may have to do with the situation where the larger banks will retain their SIFI status unless the splits are significant).

The developments also fly in the face of the risk management argument articulated by the insurance industry that diversification is the answer to the ills of failure. This is the case AIG are arguing to counter calls for a breakup. Indeed, the industry uses the diversification of risk in their defences against the sector being deemed of systemic import, as the exhibit below from a report on systemic risk in insurance from an industry group, the Geneva Association, in 2010 illustrates. Although the point is often laboured by the insurance sector (there still remains important correlations between each of the risk types), the graph does make a valid point.

click to enlargeEconomic Capital Breakdown for European Banks and Insurers

The 1st of January this year marked the introduction of the new Solvency II regulatory regime for insurers in Europe, some 15 years after work begun on the new regime. The new risk based solvency regime allows insurers to use their own internal models to calculate their required capital and to direct their risk management framework. A flurry of internal model approvals by EU regulators were announced in the run-up to the new year, although the amount of approvals was far short of that anticipated in the years running up to January 2016. There will no doubt be some messy teething issues as the new regime is introduced. In a recent post, I highlighted the hoped for increased disclosures from European insurers on their risk profiles which will result from Solvency II. It is interesting that Fitch came out his week and stated that “Solvency II metrics are not comparable between insurers due to their different calculation approaches and will therefore not be a direct driver of ratings” citing issues such as the application of transitional measures and different regulator approaches to internal model approvals.

I have written many times on the dangers of overtly generous diversification benefits (here, here, here, and here are just a few!) and this post continues that theme. A number of the large European insurers have already published details of their internal model calculations in annual reports, investor and analyst presentations. The graphic below shows the results from 3 large insurers and 3 large reinsurers which again illustrate the point on diversification between risk types.

click to enlargeInternal Model Breakdown for European Insurers and Reinsurers

The reinsurers show, as one would expect, the largest diversification benefit between risk types (remember there is also significant diversification benefits assumed within risk types, more on that later) ranging from 35% to 40%. The insurers, depending upon business mix, only show between 20% and 30% diversification across risk types. The impact of tax offsets is also interesting with one reinsurer claiming a further 17% benefit! A caveat on these figures is needed, as Fitch points out; as different firms use differing terminology and methodology (credit risk is a good example of significant differences). I compared the diversification benefits assumed by these firms against what the figure would be using the standard formula correlation matrix and the correlations assuming total independence between the risk types (e.g. square root of the sum of squares), as below.

click to enlargeDiversification Levels within European Insurers and Reinsurers

What can be seen clearly is that many of these firms, using their own internal models, are assuming diversification benefits roughly equal to that between those in the standard formula and those if the risk types were totally independent. I also included the diversification levels if 10% and 25% correlations were added to the correlation matrix in the standard formula. A valid question for these firms by investors is whether they are being overgenerous on their assumed diversification. The closer to total independence they are, the more sceptical I would be!

Assumed diversification within each risk type can also be material. Although I can understand arguments on underwriting risk types given different portfolio mixes, it is hard to understand the levels assumed within market risk, as the graph below on the disclosed figures from two firms show. Its hard for individual firms to argue they have material differing expectations of the interaction between interest rates, spreads, property, FX or equities!

click to enlargeDiversification Levels within Market Risk

Diversification within the life underwriting risk module can also be significant (e.g. 40% to 50%) particularly where firms write significant mortality and longevity type exposures. Within the non-life underwriting risk module, diversification between the premium, reserving and catastrophe risks also add-up. The correlations in the standard formula on diversification between business classes vary between 25% and 50%.

By way of a thought experiment, I constructed a non-life portfolio made up of five business classes (X1 to X5) with varying risk profiles (each class set with a return on equity expectation of between 10% and 12% at a capital level of 1 in 500 or 99.8% confidence level for each), as the graph below shows. Although many aggregate profiles may reflect ROEs of 10% to 12%, in my view, business classes in the current market are likely to have a more skewed profile around that range.

click to enlargeSample Insurance Portfolio Profile

I then aggregated the business classes at varying correlations (simple point correlations in the random variable generator before the imposition of the differing distributions) and added a net expense load of 5% across the portfolio (bringing the expected combined ratio from 90% to 95% for the portfolio). The different resulting portfolio ROEs for the different correlation levels shows the impact of each assumption, as below.

click to enlargePortfolio Risk Profile various correlations

The experiment shows that a reasonably diverse portfolio that can be expected to produce a risk adjusted ROE of between 14% and 12% (again at a 1 in 500 level)with correlations assumed at between 25% and 50% amongst the underlying business classes. If however, the correlations are between 75% and 100% then the same portfolio is only producing risk adjusted ROEs of between 10% and 4%.

As correlations tend to increase dramatically in stress situations, it highlights the dangers of overtly generous diversification assumptions and for me it illustrates the need to be wary of firms that claim divine diversification.

Confounding correlation

Nassim Nicholas Taleb, the dark knight or rather the black swan himself, said that “anything that relies on correlation is charlatanism”.  I am currently reading the excellent “The signal and the noise” by Nate Silver. In Chapter 1 of the book he has a nice piece on CDOs as an example of a “catastrophic failure of prediction” where he points to certain CDO AAA tranches which were rated on an assumption of a 0.12% default rate and which eventually resulted in an actual rate of 28%, an error factor of over 200 times!.

Silver cites a simplified CDO example of 5 risks used by his friend Anil Kashyap in the University of Chicago to demonstrate the difference in default rate if the 5 risks are assumed to be totally independent and dependent.  It got me thinking as to how such a simplified example could illustrate the impact of applied correlation assumptions. Correlation between core variables are critical to many financial models and are commonly used in most credit models and will be a core feature in insurance internal models (which under Solvency II will be used to calculate a firms own regulatory solvency requirements).

So I set up a simple model (all of my models are generally so) of 5 risks and looked at the impact of varying correlation from 100% to 0% (i.e. totally dependent to independent) between each risk. The model assumes a 20% probability of default for each risk and the results, based upon 250,000 simulations, are presented in the graph below. What it does show is that even at a high level of correlation (e.g. 90%) the impact is considerable.

click to enlarge5 risk pool with correlations from 100% to 0%

The graph below shows the default probabilities as a percentage of the totally dependent levels (i.e 20% for each of the 5 risks). In effect it shows the level of diversification that will result from varying correlation from 0% to 100%. It underlines how misestimating correlation can confound model results.

click to enlargeDefault probabilities & correlations