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Premium Earning Patterns

Premium Earning Patterns. Tom Struppeck Scottsdale, AZ September 14, 1999. Company A Assets Cash $1000 Liabilities UEPR $400 Surplus $600. Company B Assets Cash $1000 Liabilities UEPR $400 Surplus $600. Two Companies at 12/31/xx. Which of these would you rather own?.

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Premium Earning Patterns

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  1. Premium Earning Patterns Tom Struppeck Scottsdale, AZ September 14, 1999

  2. Company A Assets Cash $1000 Liabilities UEPR $400 Surplus $600 Company B Assets Cash $1000 Liabilities UEPR $400 Surplus $600 Two Companies at 12/31/xx

  3. Which of these would you rather own? • These two companies look quite similar; the difference, if any, is what risks the UEPR covers. • Each company has written exactly one policy • That policy expires on 12/31/xx+1 • other details on the next slide

  4. Company A Pays $900 if there is a storm of a certain size during the next year Company B Pays $900 if there is a storm of a certain size during the next year AND there is an earthquake of a certain magnitude during the next year The two policies

  5. Now which one would you choose? • You certainly would rather own company B since its policy is less likely to pay (it only pays in a subset of the cases that Company A’s policy pays). • The balance sheets are misleading --- perhaps Company B (or Company A) has mispriced its product.

  6. Actually, this is year 2 of a two year policy period. • Company A’s policy and Company B’s policy were identical except that the quake zones were different (and Company A got hit). • No loss was paid (or incurred) because it is a dual trigger policy. • It seems that some reserve is in order. (Is it premium or loss?)

  7. Mark-to-Market • “Mark-to-market” is a term used for valuing securities at current market prices. • In fast-moving futures exchanges, positions get marked to market twice a day. • How can we mark-to-market the UEPR?

  8. The friendly reinsurer • Reinsurer will accept any risk at its expected loss. • Mark-to-market by computing how much the reinsurer would charge to assume the risk covered by the UEPR. This is the pure premium portion of the UEPR. • Company A would get charged more than Company B.

  9. Company A Will assume the unexpired portion of the UEPR for a premium of $700 Company B Will assume the unexpired portion of the UEPR for a premium of $250 Reinsurer’s Pricing

  10. Company A Assets Cash $1000 Liabilities UEPR $700 Surplus $300 Company B Assets Cash $1000 Liabilities UEPR $250 Surplus $750 Resulting B/S’s

  11. What about the income statement? • Suppose that the original premium was $800 (the loss amount is only $900, so maybe this isn’t realistic, but then most quake companies write more than 1 policy). • Under the pro-rata earning method, both companies earned $400 last year.

  12. Company A BOY-UEPR 800 EOY-UEPR 700 WP 0 So: EP = 100 Company B BOY-UEPR 800 EOY-UEPR 250 WP 0 So: EP = 550 Income Statements

  13. No loss yet! • Observe that Company A has not lost any money yet; it simply has a much riskier book (and, as such, will earn much more next year). • In all cases, the total premium earned during the two years will be $800, the written premium. It all gets earned; the only thing that changes is the timing.

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