Institute and Faculty of Actuaries (IFoA) Exams Actuarial Risk Management and Modelling (CP1, CP2, CP3) Syllabus

State the cost-of-capital formula for the Solvency II risk margin.

$$\text{Risk Margin} = \text{CoC} \times \sum_{t \geq 0} \frac{SCR_t}{(1+r_{t+1})^{t+1}}$$ where CoC is the cost-of-capital rate (6%), $SCR_t$ is the projected Solvency Capital Requirement for non-hedgeable risks at time $t$, and $r_{t+1}$ is the risk-free rate.

What is the difference between the SCR and the MCR under Solvency II?

The SCR (Solvency Capital Requirement) is the capital needed to withstand a 1-in-200-year loss over one year (99.5% VaR). The MCR (Minimum Capital Requirement) is a lower floor; breaching it triggers the most serious regulatory intervention (loss of authorisation).

What confidence level and time horizon define the Solvency II SCR?

A Value-at-Risk over one year calibrated to a 99.5% confidence level, i.e. enough capital to survive a loss expected no more than once in 200 years.

Define Value at Risk (VaR) at confidence level $p$.

VaR is the loss threshold $L$ such that the probability of a loss exceeding it over the chosen horizon is $1-p$: $$P(\text{Loss} > \text{VaR}_p) = 1 - p.$$ It is the $p$-quantile of the loss distribution.

How does Tail Value at Risk (TVaR / Expected Shortfall) differ from VaR?

TVaR is the expected loss given that the loss exceeds the VaR threshold: $$\text{TVaR}_p = E[L \mid L > \text{VaR}_p].$$ Unlike VaR it accounts for the severity of losses in the tail and is a coherent risk measure (sub-additive).

What are the four axioms a coherent risk measure must satisfy?

Monotonicity, sub-additivity, positive homogeneity, and translation invariance. VaR fails sub-additivity in general; Expected Shortfall (TVaR) satisfies all four.

What are the main principles governing the choice of an investment strategy for an institution?

Select assets to match the nature, term, currency and uncertainty of the liabilities, subject to the assets available, the free assets/risk appetite, regulatory and tax constraints, and the objective of maximising return for an acceptable level of risk.

What is meant by 'matching' assets to liabilities?

Selecting assets whose value and cashflows respond to economic and demographic changes in the same way as the liabilities (by nature, term and currency), so that surplus is protected against those changes.

Define immunisation and state Redington's three conditions.

Immunisation protects surplus against small changes in interest rates. Redington's conditions: (1) PV of asset cashflows equals PV of liability cashflows; (2) the (discounted mean term) durations are equal, $\frac{\partial V_A}{\partial i}=\frac{\partial V_L}{\partial i}$; (3) the convexity (spread) of asset cashflows exceeds that of the liabilities.

What is the Macaulay duration of a series of cashflows?

The present-value-weighted mean term of the cashflows: $$D = \frac{\sum_t t\, C_t v^{t}}{\sum_t C_t v^{t}}$$ where $v=(1+i)^{-1}$. It measures sensitivity of value to interest rate changes.

How does effective (modified) duration relate to the change in a bond's price?

Modified duration $D_{mod}=\frac{D}{1+i}$ approximates the proportional price change for a small yield change: $$\frac{\Delta P}{P} \approx -D_{mod}\,\Delta i.$$

What does convexity add to a duration-based price estimate?

Convexity captures the second-order (curvature) effect of yield changes: $$\frac{\Delta P}{P} \approx -D_{mod}\,\Delta i + \tfrac{1}{2}\,C\,(\Delta i)^{2}.$$ It improves accuracy for larger yield movements and explains Redington's third condition.

What are the main approaches to valuing liabilities?

Discounted cashflow / present value of expected future outgo less income (a prospective method), and accumulation of past contributions less benefits (a retrospective method). Market-consistent valuation discounts using risk-free or replicating-portfolio rates.

Contrast a prospective and a retrospective reserve.

A prospective reserve is the present value of future outgo less future income. A retrospective reserve is the accumulated value of past income less past outgo. On the same assumptions and with consistent equation of value they give the same result.

What is a market-consistent valuation of assets and liabilities?

A valuation in which both assets and liabilities are valued at the amount for which they could be exchanged between knowledgeable, willing parties — using market prices where available and market-calibrated models otherwise — so values are consistent with observed market prices.

Define 'solvency' for a financial institution.

The state of having assets at least equal to liabilities (plus any required regulatory capital). An entity is solvent on a given basis if its assets are sufficient to meet its liabilities valued on that basis.

What is meant by 'surplus' and what is surplus management?

Surplus is the excess of the value of assets over the value of liabilities. Surplus management is the process of analysing, controlling and distributing that surplus (e.g. to policyholders via bonuses, to shareholders, or retaining it as capital) in a fair and prudent way.

What are the typical sources of surplus arising in a life insurer?

Differences between actual and assumed experience in mortality/morbidity, investment return, expenses, and withdrawals/persistency, plus the release of margins in the valuation basis and new business contributions.

What is an Analysis of Surplus (AoS)?

A reconciliation that splits the total change in surplus over a period into the contributions from each assumption (investment, mortality, expenses, withdrawals, new business, basis changes), providing a check on data/valuation and feedback on experience.

What is the difference between a going-concern and a break-up (wind-up) valuation?

A going-concern valuation assumes the entity continues to operate and write business. A break-up/wind-up valuation assumes it ceases trading and assets/liabilities are realised/settled, typically using more cautious (discontinuance) assumptions.

In CP2, what are the standard steps for building an actuarial model?

Specify the purpose and scope; collect and check data; choose model structure and assumptions; build the model (with checks); validate/test against expectations; run scenarios and analyse results; document the model; and communicate results to the audience.

In CP2, why is checking the reasonableness of model results essential, and what techniques are used?

To detect errors and ensure outputs are fit for purpose. Techniques include spot-checks, recalculation by an independent method, checking against analytic limits, sensitivity tests, comparison with prior results/experience, and reconciliation of totals.

What should the documentation of a model (CP2) contain?

The purpose and scope, data sources and checks, assumptions and their rationale, the model's structure/methodology, any simplifications and limitations, validation/testing performed, results, and version control so that a suitably skilled person could understand or reproduce it.

In CP2, why is a clear audit trail important when building a model?

It allows the work to be checked, reviewed and reproduced by another actuary, supports peer review and regulatory scrutiny, reduces operational risk, and ensures continuity if the original author is unavailable.

What are the key principles of effective actuarial communication (CP3)?

Identify the audience and their needs/knowledge level; have a clear purpose and structure; use plain, jargon-free language; be accurate, balanced and objective; state assumptions and limitations; and give clear conclusions/recommendations.

In CP3, how should technical jargon and assumptions be handled when writing to a non-technical audience?

Avoid or clearly explain technical terms, replace formulae with plain English, state key assumptions and their implications explicitly, and focus on the practical meaning and uncertainty of the results rather than the underlying mechanics.

In CP3, what is the recommended structure for a piece of professional communication?

An opening that states purpose and context; a clearly organised body addressing the recipient's needs with appropriate signposting; and a close giving conclusions, recommendations and any required actions or next steps.

What is the purpose of an actuarial profession's code of conduct / Actuaries' Code?

To set the ethical and professional standards expected of members, protecting the public interest and the reputation of the profession by requiring integrity, competence, care and proper conduct.

State the core principles of the IFoA's Actuaries' Code.

Integrity, Competence and Care, Impartiality, Compliance, Speaking Up, and Communication. Members must act honestly, work within their competence, manage conflicts of interest, follow relevant law/standards, raise concerns, and communicate clearly.

How should an actuary handle a conflict of interest under professional standards?

Identify and disclose the conflict to affected parties, decline or withdraw if it cannot be properly managed, and put safeguards (e.g. information barriers, separate advisers, informed consent) in place so that the duty to each party and the public interest is not compromised.

What is the difference between the role of professional guidance/standards and the actuary's own judgement?

Standards (e.g. Technical Actuarial Standards and the Actuaries' Code) set the mandatory framework and minimum requirements, while professional judgement is exercised within that framework to choose appropriate methods, assumptions and to interpret results for the specific circumstances.