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A risk manager argues that relying solely on a single VaR figure for board reporting is dangerous. The strongest supporting reason is that a single VaR:
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2026 Statistics
Key Facts: IFoA SP9 Exam
3h20m
Exam Duration
IFoA SP9 syllabus
~200
Study Hours
IFoA curriculum
Written
Open-Book Paper
IFoA SP9 syllabus
~20%
Quantitative Marks
IFoA SP9 syllabus
99.5%
Solvency II SCR Level
Solvency II framework
CERA
Leads To Credential
IFoA CERA route
IFoA SP9 is the Enterprise Risk Management Specialist Principles subject and the examined component on the route to the Chartered Enterprise Risk Actuary (CERA) credential. It is assessed by a single 3 hour 20 minute online, open-book written paper answered in Microsoft Word, using short-answer and long-answer questions rather than multiple choice. The IFoA recommends around 200 study hours and does not publish a fixed pass mark, fee or question count on the syllabus; the pass standard is set each session. The syllabus spans ERM frameworks and governance, risk appetite, quantitative measurement (VaR, TVaR, copulas, extreme value theory), economic capital and allocation, and Solvency II, Basel and ORSA. This free set provides 100 MCQ technical-knowledge questions to reinforce the underlying concepts.
Sample IFoA SP9 Practice Questions
Try these sample questions to test your IFoA SP9 exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.
1Within an enterprise risk management (ERM) framework, what best describes the primary purpose of taking an 'enterprise-wide' view of risk rather than managing risks in separate silos?
A.It captures diversification and concentration effects across the whole organisation that silo management misses
B.It removes the need for any quantitative modelling of individual risks
C.It guarantees that aggregate risk is always lower than the sum of individual risks
D.It transfers all responsibility for risk to the board's audit committee
Explanation: ERM's defining feature is treating the enterprise as a whole, so that interactions, correlations, concentrations and diversification between risks are recognised and managed centrally. Silo management can hide aggregate exposures and misses offsetting or compounding effects.
2A general insurer is mapping the stages of its ERM control cycle. Which sequence best represents a typical ERM process?
A.Risk reporting, then risk financing, then risk identification, then risk appetite
B.Risk identification, risk measurement, risk management/response, and monitoring/reporting
C.Capital allocation, regulatory filing, audit, then identification
D.Hedging, then identification, then measurement, then appetite-setting
Explanation: A standard ERM cycle runs from identifying risks, to measuring/assessing them, to deciding a response (retain, reduce, transfer, avoid), to ongoing monitoring and reporting, feeding back into identification. The cycle is iterative.
3In the 'three lines of defence' model of risk governance, which function typically constitutes the SECOND line of defence?
A.Business units and operational management that own and take the risk
B.Internal audit providing independent assurance to the board
C.The risk management and compliance functions that oversee and challenge the first line
D.External auditors appointed by shareholders
Explanation: In the three-lines model, the first line is the business that owns the risk, the second line is risk management and compliance providing oversight and challenge, and the third line is internal audit giving independent assurance. External auditors sit outside the three lines.
4An organisation distinguishes between risk appetite, risk capacity and risk tolerance. Which statement correctly relates these three concepts?
A.Risk appetite always exceeds risk capacity by a fixed regulatory margin
B.Risk tolerance is the total resources available, while appetite is purely qualitative
C.Risk capacity and risk appetite are identical and the terms are interchangeable
D.Risk capacity is the maximum risk the organisation can absorb, risk appetite is the amount it chooses to take, and tolerances set acceptable variation around appetite
Explanation: Risk capacity is the absolute maximum risk an organisation could bear given its resources; risk appetite is the level it actually chooses to accept in pursuit of objectives; risk tolerances are the boundaries of acceptable deviation around that appetite, often set per risk type.
5A bank computes a one-day 99% Value at Risk (VaR) of £4 million on its trading book. Which interpretation is correct?
A.With 99% confidence, the one-day loss is not expected to exceed £4 million, i.e. losses exceed it on about 1 day in 100
B.The maximum possible one-day loss is £4 million
C.The portfolio will lose exactly £4 million tomorrow
D.There is a 99% probability that the loss over one day will exceed £4 million
Explanation: A 99% one-day VaR of £4m means that on roughly 1% of days (about 1 in 100) the loss is expected to exceed £4m; equivalently there is 99% confidence the loss will not exceed that figure. VaR says nothing about how large losses are once the threshold is breached.
6Why is Tail Value at Risk (TVaR), also called expected shortfall, often preferred to VaR as a risk measure?
A.TVaR ignores the tail of the loss distribution entirely
B.TVaR is a coherent risk measure that accounts for the severity of losses beyond the VaR threshold and respects sub-additivity
C.TVaR requires no assumption about the loss distribution
D.TVaR is always smaller than VaR at the same confidence level
Explanation: TVaR (expected shortfall) is the expected loss given that the loss exceeds VaR, so it reflects tail severity that VaR ignores. Unlike VaR, TVaR satisfies sub-additivity and is therefore a coherent risk measure, rewarding diversification.
7Artzner et al. define a coherent risk measure by four axioms. Which property of VaR can FAIL, making VaR non-coherent?
A.Translation invariance
B.Positive homogeneity
C.Sub-additivity
D.Monotonicity
Explanation: A coherent risk measure must satisfy monotonicity, sub-additivity, positive homogeneity and translation invariance. VaR generally satisfies the first, third and fourth but can violate sub-additivity, meaning the VaR of a combined portfolio can exceed the sum of the individual VaRs, penalising diversification.
8A copula is used in risk aggregation primarily because it allows the modeller to do what?
A.Force all risks to be perfectly positively correlated
B.Eliminate the need to estimate marginal distributions
C.Convert any distribution into a normal distribution
D.Separate the modelling of each risk's marginal distribution from the modelling of their dependence structure
Explanation: By Sklar's theorem, a joint distribution can be decomposed into its marginals and a copula that captures the dependence structure. This lets the actuary model each marginal separately, then choose a copula to describe how the risks move together, including tail dependence.
9An actuary aggregating catastrophe and credit losses wants a copula that captures the tendency of both risks to produce extreme losses simultaneously (strong lower-tail dependence). Which copula is most appropriate?
A.Clayton copula, which exhibits strong lower-tail dependence
B.Independence copula
C.Frank copula, which has symmetric and zero tail dependence
D.Gaussian (normal) copula, which has zero tail dependence
Explanation: The Clayton copula has strong lower-tail dependence, making it well suited to modelling simultaneous extreme losses. The Gaussian copula has zero tail dependence (a key criticism after 2008), the Frank copula has no tail dependence, and the independence copula assumes no co-movement.
10Extreme value theory (EVT) is used in ERM mainly to model which feature of a loss distribution?
A.The central body of the distribution around the mean
B.The behaviour of low-frequency, high-severity losses in the tail
C.The correlation between two normally distributed risks
D.The seasonality of claim frequencies
Explanation: EVT provides a rigorous framework for modelling the tail of a distribution, i.e. rare but severe events, where ordinary distributional assumptions fit poorly. It helps quantify the size of losses beyond the range of observed data.
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