Introduction
In our previous lesson, we focused on establishing "best-estimate" assumptions for expenses, which represent our most likely forecast of future costs. As a statistician, you can think of a best estimate as the mean or median of a probability distribution—it's the point where the actual outcome is equally likely to be higher or lower. However, for many actuarial purposes, particularly when setting aside money to pay future claims, a 50/50 chance of being sufficient is not prudent enough. We need a greater degree of confidence.
This brings us to the topic of this lesson: adding an explicit layer of caution to our assumptions. We will explore the role of Margins for Adverse Deviation (MADs), which are buffers built into actuarial calculations to absorb the impact of uncertainty. By the end of this session, you will be able to describe what MADs are, why they are used for different purposes like valuation and capital assessment, and the frameworks actuaries use to determine their size.
Part 1: From Best Estimate to Prudent Provision
A Margin for Adverse Deviation (MAD) is a deliberate, explicit adjustment made to a best-estimate assumption to allow for uncertainty. The resulting dollar-value impact on the liability is called the Provision for Adverse Deviations (PAD).
To understand this better, let's clarify the terminology using an example from the Canadian Institute of Actuaries.
[PDF] Margins for Adverse Deviations for P&C insurance (209138) - PUB
This educational note provides clear definitions and examples of MADs and PADs.
Please read the section on "Terminology." Focus on the distinction made between a margin and a provision. You will see it can be expressed in a few ways: An adjustment to an assumption, like reducing an expected interest rate from 10% to 8%. The 2% is the margin, and the resulting $20 million increase in liabilities is the provision. A direct multiplier on the liability itself.
The core idea is to move from a "best estimate," where we aim for the most accurate prediction, to a "prudent estimate," where we build in a safety buffer. The following video gives an excellent real-world perspective on why this is crucial in practice.
Actuarial Pricing vs Reserving: Something no one talks about
This video from Actuary Elle distinguishes between the work of a pricing actuary and a reserving actuary, providing great intuition for the role of prudence in financial reporting.
Please watch the segment from this clip. The speaker explains that a reserving actuary impacts the perception of profit. Pay close attention to her example of a true underlying claims cost of $100 million. Notice how reporting a reserve of $80 million (under-reserved), $110 million (prudently reserved), or $200 million (overly conservative) affects reported profits, share prices, and strategic decisions, even though the ultimate cost remains the same. This highlights that the margin doesn't change reality, but it manages how the company absorbs and reports it over time.
This concept of building prudence into liabilities is so fundamental that it is a cornerstone of modern insurance accounting standards like IFRS 17. The liability for an insurance contract is calculated using a "building block" approach, and one of those blocks is an explicit allowance for risk.
Part 2: Deconstructing Uncertainty - A Framework for Setting MADs
A MAD is fundamentally a compensation for uncertainty. To set an appropriate margin, we must first understand the sources of that uncertainty. A powerful way to structure this thinking is to separate uncertainty into two broad categories: independent risk and systemic risk.
[PDF] A Framework for Assessing Risk Margins - Casualty Actuarial Society
This paper from the Australian actuarial community proposes a comprehensive framework for thinking about risk margins by dissecting the sources of uncertainty.
Please read the section on "Sources of uncertainty," from this paragraph. This section introduces a key conceptual split: Independent Risk: This is the inherent statistical randomness in the insurance process. Given your background in probability theory, you can think of this as the natural variance or "noise" in a well-specified stochastic process (e.g., the random fluctuation in the number of claims from year to year). It consists of: Process risk: Even if our model parameters were perfect, the real world won't match the expectation perfectly. Parameter risk (random component): The statistical error in estimating parameters from a finite data sample. Systemic Risk: This captures risks that are common across claims or business lines and are often harder to model. The paper splits this further: Internal Systemic Risk: This is essentially model risk—the risk that our actuarial models, data, or processes are flawed. For example, using an inappropriate valuation method or having undetected errors in our data. External Systemic Risk: This is the risk of future changes in the environment that our models, based on historical data, cannot foresee. This includes things like sudden legislative changes, unexpected economic shifts, or new social trends that alter claim patterns (often called "superimposed inflation").
This framework is incredibly useful because it forces the actuary to consider not just the statistical volatility in the data (independent risk) but also the limitations of their own models (internal systemic risk) and the unpredictability of the future world (external systemic risk). A comprehensive MAD should implicitly or explicitly cover all three.
Part 3: Determining the Size of the Margin
Now that we have a framework for what the margin needs to cover, how do we determine its size? Broadly, there are two approaches: a qualitative, judgment-based approach and a quantitative, model-based one.
1. The Deterministic / Judgmental Approach
In this approach, the actuary uses professional judgment to select margins based on a structured assessment of various risk factors. The Canadian educational note provides a fantastic, detailed example of this. It sets out ranges for margins and provides extensive checklists of factors to consider.
[PDF] Margins for Adverse Deviations for P&C insurance (209138) - PUB
This resource details the practical application of setting margins based on qualitative factors.
First, read the section on the three categories of margins for P&C insurance: for claims development, reinsurance, and investment returns. Next, review the section on explicit assumptions, which gives prescribed low and high ranges for these margins. Finally, spend some time reviewing the detailed checklists of considerations that influence the margin selection. You don't need to memorize them all, but appreciate the level of detail involved. Skim Table 5.1 (Claims Development): Notice how factors like "high turnover of personnel" or "significant changes in coding procedures" (internal systemic risks) lead to a higher required margin. Factors like "length of tail" (inherent product risk) also demand a higher margin. Skim Table 5.2 (Reinsurance Recovery): Factors like dealing with reinsurers in poor financial condition increase the risk and thus the margin. Skim Table 5.3 (Investment Returns): A significant mismatch between asset and liability cash flows would warrant a higher margin on the discount rate.
This qualitative approach translates an actuary's expert understanding of the business, its processes, and its environment into a quantitative risk margin.
2. The Stochastic / Quantitative Approach
This approach uses statistical models to quantify the probability distribution of future outcomes and derive a margin based on a desired level of confidence. This will resonate with your statistical background. The goal is typically to set a provision that is adequate to a certain probability level.
Common methods, or "quantile approaches," include:
- Multiples of Standard Deviation: A simple approach, e.g., setting the provision equal to the mean plus half a standard deviation. This works well for symmetric, normal-like distributions but is less reliable for skewed risks.
- Value at Risk (VaR): This sets the provision at a specific percentile of the distribution. For example, a 75% VaR means selecting a provision that is expected to be sufficient 75% of the time. It is intuitive but ignores the severity of losses beyond the threshold.
- Conditional Tail Expectation (CTE): Also known as Tail Value at Risk (TVaR), this measures the average of all outcomes beyond a certain percentile. For example, CTE(75%) is the average of the worst 25% of outcomes. Because it considers the magnitude of tail events, it is a more robust measure for skewed distributions, which are common in insurance.
The following reading compares these approaches and highlights their strengths and weaknesses.
[PDF] Margins for Adverse Deviations for P&C insurance (209138) - PUB
This section uses your existing statistical knowledge of quantiles to explain how MADs are calculated in a stochastic framework.
Please read the section on Quantile Approaches. Focus on: The definitions of VaR (confidence levels) and CTE. The comparison tables (9.1 and 9.2), which show how for a highly skewed risk (Product C), a 65% confidence level can bizarrely result in a negative risk margin, whereas CTE behaves more intuitively. The final evaluation, which concludes that CTE is more risk-sensitive and often a better measure for skewed risks than VaR or standard deviation multiples.
It is crucial to remember that even stochastic models require significant judgment. The choice of model, its parameters, and the allowance for risks not captured in the historical data (i.e., systemic risks) are all judgmental calls that feed into the final margin.
Part 4: The Role of MADs for Different Purposes
The size of the margin depends critically on its purpose. An actuary does not use a single MAD for everything.
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Financial Reporting (Statutory Valuation): The goal is to present a prudent view of the company's liabilities on its balance sheet. Regulators often prescribe a minimum level of prudence, for example, requiring liabilities to be adequate at a 75% confidence level. The focus is on ensuring policyholder protection and preventing the overstatement of profit.
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Pricing: When pricing a product, actuaries need to cover the best-estimate cost plus a charge for the risks being taken on. This charge contributes to profit and provides the capital needed to support the business. While a margin for uncertainty is included, it is constrained by market competition. A price that is too prudent will not be competitive.
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Capital Assessment: This typically requires the most conservative margins. Regulatory regimes like Solvency II require insurers to hold capital sufficient to withstand a 1-in-200-year adverse event, which corresponds to a 99.5% confidence level over one year. The liability used for this calculation (the "technical provisions") includes a best estimate plus a risk margin, but the total capital requirement is set at a much higher level of confidence than is used for day-to-day financial reporting.
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Management Information: Analyzing results with and without margins allows management to understand the underlying profitability of the business (from the best estimate) versus the reported profitability (including margins). This informs strategic decisions about which business lines are generating true economic value versus which are simply releasing built-in prudence.
Conclusion
We have moved beyond the world of best estimates to incorporate a structured and explicit allowance for uncertainty. Margins for Adverse Deviation are not arbitrary additions; they are carefully considered buffers designed to ensure provisions are adequate for their intended purpose.
We saw that a robust margin should account for all sources of uncertainty—from statistical noise (independent risk) to model deficiencies (internal systemic risk) and unforeseen future events (external systemic risk). Actuaries determine the size of these margins using either structured professional judgment or quantitative models based on probabilistic concepts like VaR and CTE, with the latter being more suitable for the skewed risks inherent in insurance. Ultimately, the level of prudence is tailored to the task at hand, whether it be cautious financial reporting, competitive pricing, or rigorous capital assessment.
In our next lesson, we will close the loop on the assumption-setting process by examining how actuaries monitor experience as it unfolds, comparing actual outcomes to both best-estimate assumptions and provisions that include MADs.
Key Takeaways & Cheatsheet
This framework summarizes the key aspects of Margins for Adverse Deviation.
| Aspect | Description |
|---|---|
| What is a MAD? | An explicit, prudent adjustment to a best-estimate assumption to allow for uncertainty. The resulting change in liability value is the Provision for Adverse Deviations (PAD). |
| Why add a MAD? (Purpose) | - Valuation: To ensure liabilities are adequate with a high degree of confidence (e.g., 75%), protecting policyholders and preventing overstatement of profit. - Pricing: To cover the cost of risk and generate profit, balanced against market competitiveness. - Capital: To determine the assets required to survive extreme events (e.g., 99.5% confidence), which is a much higher standard of prudence. - Management: To distinguish between underlying and reported profitability. |
| What does a MAD cover? (Framework) | A structured way to think about uncertainty is to split it into: 1. Independent Risk: Random statistical fluctuations (process & parameter risk). 2. Systemic Risk: - Internal: Model risk, data errors, flaws in the actuarial process. - External: Future changes in the economic, legal, or social environment. |
| How is a MAD set? (Methods) | - Judgmental/Deterministic: Using checklists and expert judgment to select a margin within a range based on qualitative risk factors (e.g., quality of data, complexity of business). - Quantitative/Stochastic: Using models to derive a probability distribution of outcomes and selecting a margin based on a quantile. Key measures include: - VaR (Value at Risk): A percentile threshold (e.g., 75th percentile). - CTE (Conditional Tail Expectation): The average of the worst outcomes in the tail (e.g., average of the worst 25%). Generally preferred for skewed risks. |