Archive for February 2022

Determining Risk Capital

February 5, 2022

Knowing the amount of surplus an insurer needs to support risk is fundamental to enterprise risk management (ERM) and to the own risk and solvency assessment (ORSA).

With the increasing focus on ERM, regulators, rating agencies, and insurance and reinsurance executives are more focused on risk capital modeling than ever before.

Risk – and the economic capital associated with it – cannot actually be measured as you can measure your height. Risk is about the future.

To measure risk, you must measure it against an idea of the future. A risk model is the most common tool for comparing one idea of the future against others.

Types of Risk Models

There are many ways to create a model of risk to provide quantitative metrics and derive a figure for the economic capital requirement.

Each approach has inherent strengths and weaknesses; the trade-offs are between factors such as implementation cost, complexity, run time, ability to represent reality, and ease of explaining the findings. Different types of models suit different purposes.

Each of the approaches described below can be used for purposes such as determining economic capital need, capital allocation, and making decisions about risk mitigation strategies.

Some methods may fit a particular situation, company, or philosophy of risk better than others.

Factor-Based Models

Here the concept is to define a relatively small number of risk categories; for each category, we require an exposure metric and a measure of riskiness.

The overall risk can then be calculated by multiplying “exposure × riskiness” for each category, and adding up the category scores.

Because factor-based models are transparent and straightforward to apply, they are commonly used by regulators and rating agencies.

The NAIC Risk-Based Capital and the Solvency II Standard Formula are calculated in this way, as is A.M. Best’s BCAR score and S&P’s Insurance Capital Model.

Stress Test Models

Stress tests can provide valuable information about how a company might hold up under adversity. As a stand-alone measure or as an adjunct to factor-based methods, stress tests can provide concrete indications that reflect company-specific features without the need for complex modeling. A robust stress testing regime might reflect, for example:

Worst company results experienced in last 20 years
Worst results observed across peer group in last 20 years
Worst results across peer group in last 50 years (or, 20% worse than stage 2) Magnitude of stress-to-failure

Stress test models focus on the severity of possible adverse scenarios. While the framework used to create the stress scenario may allow rough estimates of likelihood, this is not the primary goal.

High-Level Stochastic Models

Stochastic models enable us to analyze both the severity and likelihood of possible future scenarios. Such models need not be excessively complex. Indeed, a high-level model can provide useful guidance.

Categories of risk used in a high-level stochastic model might reflect the main categories from a factor-based model already in use; for example, the model might reflect risk sources such as underwriting risk, reserve risk, asset risk, and credit risk.

A stochastic model requires a probability distribution for each of these risk sources. This might be constructed in a somewhat ad-hoc way by building on the results of a stress test model, or it might be developed using more complex actuarial analysis.

Ideally, the stochastic model should also reflect any interdependencies among the various sources of risk. Timing of cash flows and present value calculations may also be included.

Detailed Stochastic Models

Some companies prefer to construct a more detailed stochastic model. The level of detail may vary; in order to keep the model practical and facilitate quality control, it may be best to avoid making the model excessively complicated, but rather develop only the level of granularity required to answer key business questions.

Such a model may, for example, sub-divide underwriting risk into several lines of business and/or profit centers, and associate to each of these units a probability distribution for both the frequency and the severity of claims. Naturally, including more granular sources of risk makes the question of interdependency more complicated.

Multi-Year Strategic Models with Active Management

In the real world, business decisions are rarely made in a single-year context. It is possible to create models that simulate multiple, detailed risk distributions over a multi-year time frame.

And it is also possible to build in “management logic,” so that the model responds to evolving circumstances in a way that approximates what management might actually do.

For example, if a company sustained a major catastrophic loss, in the ensuing year management might buy more reinsurance to maintain an adequate A.M. Best rating, rebalance the investment mix, and reassess growth strategy.

Simulation models can approximate this type of decision making, though of course the complexity of the model increases rapidly.

Key Questions and Decisions

Once a type of risk model has been chosen, there are many different ways to use this model to quantify risk capital. To decide how best to proceed, insurer management should consider questions such as:

  • What are the issues to be aware of when creating or refining our model?
  • What software offers the most appropriate platform?
  • What data will we need to collect?
  • What design choices must we make, and which selections are most appropriate for us?
  • How best can we aggregate risk from different sources and deal with interdependency?
  • There are so many risk metrics that can be used to determine risk capital – Value at Risk, Tail Value at Risk, Probability of Ruin, etc. – what are their implications, and how can we choose among them?
  • How should this coordinate with catastrophe modeling?
  • Will our model actually help us to answer the questions most important to our firm?
  • What are best practices for validating our model?
  • How should we allocate risk capital to business units, lines of business, and/or insurance policies?
  • How should we think about the results produced by our model in the context of rating agency capital benchmarks?
  • Introducing a risk capital model may create management issues – how can we anticipate and deal with these?

In answering these questions, it is important to consider the intended applications. Will the model be used to establish or refine risk appetite and risk tolerance?

Will modeled results drive reinsurance decisions, or affect choices about growth and merger opportunities? Does the company intend to use risk capital for performance management, or ratemaking?

Will the model be used to complete the NAIC ORSA, or inform rating agency capital adequacy discussions?

The intended applications, along with the strengths and weaknesses of the various modeling approaches and range of risk metrics, should guide decisions throughout the economic capital model design process.


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