Assumption Types and Their Uses

From a Point Estimate to a Spectrum

While the best estimate is our neutral starting point, it is just one point in a wide distribution of possible future outcomes. For many actuarial tasks, particularly those related to ensuring a company's financial stability, we are fundamentally more concerned with the adverse "tail" of this distribution than with its center. This leads us to adopt different sets of assumptions depending on the goal.

The actuarial profession uses specific terminology to describe this spectrum. Let's start by formally defining these terms.

As the text explains, we can think of assumptions along a continuum:

• Average / Best-Estimate / Realistic: This is the neutral, 50/50 basis we discussed in the last lesson.
• Pessimistic / Prudent / Strong / Cautious: This basis deliberately builds in a layer of conservatism to protect against adverse outcomes.
• Optimistic / Weak: This basis is deliberately favorable and is used to explore potential upside.

For the remainder of this lesson, we will focus on understanding the "prudent" basis, as it is central to regulatory valuation and capital management.

Prudent Assumptions and the Margin for Adverse Deviation

A prudent assumption is not simply a guess on the pessimistic side. It is a calculated, deliberate choice to be cautious. The key mechanism for achieving this is the Margin for Adverse Deviation (MAD).

A MAD is an explicit buffer added to a best-estimate assumption to provide a higher level of confidence that an obligation can be met.

Let's look at a concise definition that makes this clear.

As highlighted, a prudent assumption is the Best Estimate + MAD. The purpose of this MAD is to increase the probability that the resulting liability figure is sufficient. For instance, instead of being 50% sure our reserves are adequate (the best-estimate level), a prudent basis might aim for 75%, 90%, or even 99.5% confidence, depending on the regulatory regime and the purpose of the calculation.

The direction of the MAD depends on the nature of the assumption:

• For cash outflows (like insurance claims or expenses), the MAD is positive, leading to a higher prudent estimate.
• For cash inflows or positive drivers (like investment returns or mortality improvements for an annuity provider), the MAD is negative, leading to a lower prudent estimate.

In essence, prudence always means adjusting the assumption to produce a financially worse outcome for the company, thereby increasing its stated liabilities or reducing its stated assets.

This concept is best understood visually.

Let's focus on the left graph, "Distribution of potential fulfilment cash flows."

• The x-axis represents the possible total value of insurance claims.
• The curve is a probability distribution of these outcomes. The peak represents the most likely outcome.
• The line labeled "Unbiased probability weighted expected claims" is the mean of this distribution—our best estimate.
• The line to the right, labeled "Expected claims after including a prudent bias," is the prudent estimate. It is deliberately set higher than the best estimate.
• The distance between these two lines is the Margin for Adverse Deviation (MAD).

By setting the liability at the prudent level, the insurer has a buffer against the risk that claims turn out to be higher than the expected value. The size of this buffer determines the level of confidence the insurer has in its reserves.

When to Use Each Type of Assumption

The choice between a best-estimate, prudent, or optimistic basis is not arbitrary; it is dictated entirely by the purpose of the actuarial work. An actuary will often use all three for the same block of business, but for different applications.

Use Case 1: Best-Estimate Assumptions

A best-estimate basis provides the most realistic picture of expected outcomes.

• Pricing: To set a competitive premium, a company needs to know the expected cost of a policy. Using a heavily prudent basis would lead to uncompetitively high prices. The company might add a profit margin on top of the best-estimate cost.
• Business Planning: When forecasting future profitability or making strategic decisions, management needs a realistic, unbiased view.
• IFRS 17 Reporting: The international accounting standard IFRS 17 explicitly requires the starting point for valuing insurance liabilities (the "Fulfilment Cash Flows") to be based on unbiased, probability-weighted best estimates. Prudence is then added separately and explicitly as a "Risk Adjustment."

Use Case 2: Prudent Assumptions

A prudent basis is used whenever the primary goal is to ensure solvency and protect stakeholders from adverse events.

• Regulatory Reserving (Valuation): This is the most common use. Regulators require insurance companies and pension funds to hold sufficient reserves to meet their obligations to policyholders and members. These calculations are almost always performed on a prudent basis to provide a high degree of confidence that promises can be met.
• Capital Calculation: Prudence is fundamental to determining how much capital a company needs to hold. Economic or regulatory capital models often use assumptions calibrated to a very high confidence level (e.g., a 1-in-200-year adverse event) to ensure the company can survive extreme scenarios.

Use Case 3: Optimistic Assumptions

An optimistic (or "weak") basis is used less frequently in formal reporting but is valuable for specific analytical exercises.

• Scenario Analysis: Management might ask, "What is our best-case scenario for profit next year?" This helps understand the potential upside and the range of possible outcomes.
• Assessing Future Surplus: When considering how much profit might be available to distribute to shareholders or invest in new projects, a company might run forecasts on an optimistic basis to supplement the main best-estimate view.
• Business Case Development: When evaluating a new project or product, an optimistic scenario can be used to model the potential rewards if everything goes well, providing a counterpoint to the more realistic base case.

Conclusion

We have now moved beyond the single point of the best estimate to appreciate the full spectrum of assumptions available to an actuary. The key distinction is intent. A best estimate is our most objective attempt to predict the average outcome. A prudent assumption is a deliberate, calculated move away from that average by including a Margin for Adverse Deviation (MAD). This is not about being arbitrarily pessimistic; it is a risk management tool used to ensure financial soundness and protect policyholders, primarily for regulatory valuation and capital setting. Finally, optimistic assumptions serve to explore upside potential and test best-case scenarios.

The critical takeaway is that there is no single "correct" basis. The right choice of assumptions is always relative to the purpose of the task at hand.

In our next lesson, we will begin to explore the practicalities of deriving the numbers that underpin these assumptions. We will investigate the various sources of data actuaries use—from a company's own history to broad population statistics—and discuss how we determine if that data is credible enough to be used.

Key Takeaways & Cheatsheet

This table summarizes the key differences and applications of the three types of assumption bases.