Hi, The solution to Question 14.2 (i) (page 27) mentions several specific quantitative assertions: "Suppose that the distribution of liability outgo approximates a normal distribution (or something with similar dispersion). We would therefore be very sure that the liability outgo will not exceed $130 million, ie three standard deviations above the expected value (around 99.9% sure). We have no measure of the uncertainty of the premium income. However, it would be imprudent to rely upon the full $100 million. Assuming that the company’s trading policy for the next year was not under threat of some radical plan (eg to stop writing business) then it would probably be safe to rely upon, say, $80 million. On the basis of these figures, we would be exceedingly surprised if $50 million in money market investments was insufficient." Where do these assertions (3 standard deviations, $80mn, $50mn) come from and are they a subjective example view or a reliable actuarial judgement which should be used in other questions?
Hi Bill, It’s a bit of both (subjectivity and actuarial judgement), but they are not definitive numbers and other answers would have been acceptable. The relative positions and justification for them is most important here. Addressing the assertions in isolation: 3 standard deviations: this is to coincide with a very high level of certainty that the liabilities will not exceed the calculated number (3 standard deviations corresponds to >99% certainty). Other acceptable answers might have been eg 2 or 2.5 standard deviations, resulting in >95% certainty. Whereas 1 standard deviation only represents 68% certainty, or in other words more than a 30% chance of exceeding the calculated number, which doesn’t feel sufficient. $80mn: the key here was to recognise that an insurance company cannot expect to be able to estimate its premium volume completely accurately for the following year, as the actual amount it receives will depend on how much new business it manages to attract and how many of its existing customers choose to renew. If this were an exam question, I’d expect any number under $100mn, and above perhaps $70mn, to be acceptable, if accompanied by the correct justification. $50mn: this number does result from the previous two, ie if we think liabilities won’t be above 130 and reliable premium income might be 80, we are $130mn - $80mn = $50mn short. Thanks Richie
