Every answer and its explanation appears here once you have finished the path. Each one then links to the matching glossary entry, where the concept is set out in full with its worked example.
1. A group holds assets in eight countries and has its captive carry each one. Where is the error of reasoning?
In a misapplied analogy: it believes it holds eight risks and holds one in eight versions, so the captive does not pool, it concentrates
The error does not come from ignorance of statistics but from an analogy carried over from numerous, repetitive risks, motor fleets, employers' liability, where the law of large numbers works inside the group. Here hostile measures spread by political imitation, financial contagion, membership of one regional bloc: frequency is low, severity high, and the events are correlated at the very moment they occur. The underestimated frequency answer looks for a calibration flaw where the flaw is structural, and a model better calibrated on frequency would concentrate just as much. An industry pool would gather members exposed to the same waves, so would solve nothing. And reinsurance placed line by line would leave the accumulation whole, since it does not respond to several lines hit together.
Glossary entry →2. The captive's model treats simultaneous triggering of its eight lines as near impossible. What is that judgment based on, and why is it wrong?
On correlations measured in ordinary conditions, whereas what correlates in the tail is not what correlates in normal times
Two countries whose economies have nothing in common in normal times become joined when one political movement crosses the region, or when one commodity price collapses and strains their budgets in the same quarter. A correlation measured in ordinary conditions therefore describes precisely the regime where it is of no use. The calculation error answer is the most instructive because it assumes the figure was wrongly obtained: it was rightly obtained, on the wrong years. And a longer history measured the same way would reproduce the same flaw, the question being not the quantity of data but the regime in which it was gathered.
Glossary entry →3. A group sets up a captive to save an insurer's margin. What does it discover on strongly correlated commitments?
That it must hold more regulatory capital than a captive of the same volume carrying independent risks, reducing the apparent saving accordingly
A captive is a real insurance company, subject to a solvency requirement computed on the distribution of the claims it carries, and the additional capital is exactly the prudential sanction of concentration. A group that thought it was saving an insurer's margin funds regulatory capital instead. The answer keeping the margin in full forgets that a risk carrier ties up capital whoever owns it. The one imagining an exemption for group captives is the most tempting because it looks logical, a group insuring only with itself, and it overlooks that the regulator also protects the solvency of the entity carrying the risk. Management costs exist and weigh less than capital.
Glossary entry →4. What does the retention level get set on, if expected loss is a poor guide?
On cash: what simultaneous loss across several lines the group can absorb without breaching a banking covenant, abandoning an investment or damaging its rating
On a low frequency, high severity distribution, expected loss describes an average the group will never experience, since it will suffer neither an eighth of a loss each year nor the average of a population it does not constitute. The useful test is cash, and the retention is set below that threshold, whatever exceeds it being transferred whatever the apparent price. The answer comparing premium with expected loss is an actuary's and is right on a portfolio, wrong on a single carrier. Available capacity is a real constraint and a market constraint, not a decision criterion. And a sector average is the same expected loss, borrowed from a population the group is not part of.
Glossary entry →5. Eight lines each carrying five million of retention look reasonable taken separately. What calculation is missing, and why is it missing?
Consolidation of the retentions, forty million of simultaneous exposure appearing nowhere if the analysis was done line by line, which is the usual way of doing it
It is a three minute calculation few groups keep current, and it is the only one that says what is actually carried: the error is common and invisible precisely because each line, taken alone, is reasonable. The module draws from it the first of its four steps, consolidate before judging. The probability weighting answer is the most instructive: it would remake the module's error exactly, by assuming the eight lines independent, which tail correlation forbids. A break even premium per line still reasons line by line. And discounting refines a figure whose flaw is not its precision but its absence.
Glossary entry →