Apr 08 1(ii) the EEV in the report is PVIF + Free Surplus. We're told FS is zero. What about the required capital minus the cost of capital component of EEV? The company has reserves. Does reserves here mean only that to cover liabilities? No solvency capital requirement on top- why not? Seems a very unreal situation for a recently established UK proprietary. How is there no free surplus when it only writes term assurance where £102m premiums came in January and only £1.2m reserves are held & no solvency capital held?
Yes, the figures given here are not very realistic. This is already a very hard question, so its good that the examiners have chosen to simplify it by ignoring free surplus and the capital components. For most contracts you'd perhaps expect reserves and premiums to be consistent, but not for term assurance. Often term assurances have negative reserves (because the future premiums outweigh the future cliams and expenses), especially early on in the term which would apply to these contracts. So having reserves which are tiny compared to premiums is perfectly reasonable. Best wishes Mark
OK, but how can an insurance company charge £102m premium when reserves required only £1.2m? That's an enormous margin. Doesn't this imply an enormous initial expense & commission? I don't see why.
Yes, this probably does imply lots of expenses, commission and a profit loading too. But that's quite likely for term assurance. Consider the following simplified example (eg I've ignored investment and lapses and assumed constant mortality). 10 year annual premium TA. Expected claims are 40 per annum. Expected regular expenses are 5 per annum. Initial expenses are 120. Total costs are 120 + 10 x (40 + 5) = 570 So insurer charges 60 (giving an expected profit of about 30 if we assume that almost all the policyholders pay the premiums until the end). Note, we have very high initial expenses (due to lots of underwriting) and relatively high renewal expenses (as premiums are much lower for protection contracts than saving contracts). Assuming that the reserving basis is fairly close to the pricing basis we have (just after the payment of premium and expenses) t=0, V = 10 x 40 + 9 x 5 - 9 x 60 = -95 t=5, V = 5 x 40 + 4 x 5 - 4 x 60 = -20 In reality mortality rates increase over time. Lets assume that average claims are 30 for the first 5 years and 50 for the last 5 years. The premium and reserve at time zero are unchanged. But t=5, V = 5 x 50 + 4 x 5 - 4 x 60 = 30 We can see that reserves can be less than the premium. Indeed reserves can be negative early on (because we spread the initial expenses using a level premium). Using more accurate assumptions won't change the overall pattern. So for a new company, I'm not surprised that the average reserve is a small fraction of the average premium. I hope the numerical example helps. Best wishes Mark
