FCAS exams

Exam 9

Risk Management for Actuaries

5 discussions

Study strategy

Exam 9: An ERM recommendation needs a constraint and a management action

Risk measures support decisions such as capital allocation, investment limits and business strategy. A recommendation should connect the measure to the objective and constraints. Listing risk categories alone does not explain how the organisation will act.

Worked example or practice scenario

A toy insurer can reduce market exposure by selling assets, but a stressed market may reduce sale proceeds or create liquidity pressure. A modelled management action needs timing, authority and feasibility assumptions. An instantaneous cost-free action is a material simplification.

Try this next

Write a scenario recommendation with trigger, action, decision maker and limitation. Compare the expected benefit with the trade-off, such as lower return or higher liquidity cost. Keep regulatory requirements distinct from an internal appetite or target.

Reading sources

Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.

0 repliesOct 1

Explanation

Exam 9: A reinsurance layer requires the correct loss basis

An exposure-rating calculation must match the contract’s attachment, limit and underlying loss basis. A ceded payment is not the same variable as a ground-up loss. Inflation and policy limits can change the share of expected loss reaching the layer.

Original layer example

A layer of 500 above 500 pays min(max(X−500,0),500). With an exponential ground-up loss of mean 1,000, expected layer payment is 1,000(e^−.5−e^−1), about 238.65. Multiplying the limit by the attachment exceedance probability overstates payment because not every attaching loss exhausts the layer.

Study check

Draw the payment function, identify the contract basis and explain where an exposure curve or severity assumption enters. Then consider a larger underlying policy limit. Separate distribution assumptions from contract terms and check the current Exam 9 catastrophe and reinsurance readings.

Reading sources

CAS · Exam 9 syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.

0 repliesOct 1

Explanation

Exam 9: Duration and convexity explain a local bond-price approximation

Duration provides a first-order yield sensitivity; convexity adds a second-order term under a specified yield change. Cash-flow timing and yield conventions matter. A local approximation does not capture every investment or insurance risk.

Worked example or practice scenario

With modified duration 6 and convexity 50, a +.01 yield move gives approximate ΔP/P = −6×.01 + .5×50×(.01)² = −5.75%. Omitting convexity gives −6%. These assumed sensitivities are for an original illustration.

Try this next

Compare with exact repricing of a simple bond. State whether convexity uses the matching rate convention. Explain why non-parallel curve changes, credit spread changes or options can require more than a single duration-and-convexity pair.

Reading sources

Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.

0 repliesOct 1

Explanation

Exam 9: Diversification depends on dependence, not only marginal risk

Aggregating risks requires a dependence assumption. Summing stand-alone capital numbers ignores diversification, while assuming independence can understate joint stress. Correlation alone may also miss tail dependence.

Worked example or practice scenario

Two toy zero-mean risks each have standard deviation 10. With correlation zero, the standard deviation of their sum is √200≈14.14. With correlation .8, it is √360≈18.97. Summing standard deviations to 20 is a different limiting assumption.

Try this next

Write the covariance term explicitly. Then describe a common catastrophe or market factor that could alter dependence during stress. Do not call a standard-deviation calculation a complete regulatory capital model.

Reading sources

Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.

0 repliesOct 1

Explanation

Exam 9: VaR identifies a quantile, while tail measures look beyond it

For a stated loss distribution, VaR is a quantile. A tail measure such as expected shortfall describes losses beyond a specified tail threshold under its definition. Neither is a universal synonym for “worst possible loss.”

Worked example or practice scenario

For a continuous uniform loss on 0 to 100, 95% VaR is 95. Expected shortfall at 95% is the mean of the upper 5%, or 97.5. For discrete distributions, the treatment of probability mass at the boundary requires care.

Try this next

Draw the distribution and shade the tail. Explain what information each measure discards. State the confidence level, horizon and loss definition before comparing two capital measures.

Reading sources

Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.

0 repliesOct 1