UK General Insurance Companies – are their reserves too low or too high?

1. UK General Insurance Companies – are their reserves too low or too high? Stephen Diacon, Paul Fenn and Chris O’Brien Nottingham University Business School Centre for Risk and Insurance Studies Copies can be obtained from stephen.diacon@nottingham.ac.uk

2. Acknowledgement • This work is part of a project on loss reserve errors undertaken at the Centre for Risk and Insurance Studies • Financial support from the Research Committee of the Faculty and Institute of Actuaries is gratefully acknowledged.

3. Outline • Introduction • Accuracy: over- or under-reserving, time patterns • Loss reserves and loss errors (= ‘actual’ – ‘expected’) • Reserve error motivation • Data and evidence • Conclusions

4. Introduction The research has two main tasks: • To estimate calendar-year net reserve errors for UK ‘one year’ general business in year t, based on discounted net claims paid in years t+1 to t+5 and claims o/s in t+5 • To investigate why reserve errors differ between companies and over time. Note: Reserve errort = actual-expectedt, so a negative figure represents over-reserving

5. Average Reserve Errors as % Initial Reserve1405 company/years, 1985-1996

6. Average (Discounted) Reserve Errors

7. Independent Insurance Company1985-1994

8. Loss reserves and reserve errors • Loss reserves = OCR + IBNR • Focus on loss reserves in calendar year t generated from accident years t, t-1, …t-4 • Reserve error = PV(cash settlement on these accident years in t+1 to t+5, plus reserve @ calendar year t+5) – (current estimate @ calendar year t). Discounted using return on British Government 5-year gilt stock • Element of subjectivity in the estimation. Depends on information available in year t.

9. Reserve error motivation • Estimation error and prudence • To smooth performance over time • To improve current or future performance and reduce taxes • To improve solvency picture • Managerial factors

10. Data • Data from the Regulatory Returns for general business of UK-licensed insurers (net) for 5 most recent accident years (ie t, t-1, .., t-4) • So methodology ‘looks forward’ for up to 10 years after the initial accident year, but cannot detect reserve errors arising after t+10 • Focus is on aggregate calendar year net reserve for all lines, not accident year gross reserve by line • Sample selection: positive gross premium in year t, and no restructuring t+1 to t+5 • Unbalanced panel data for 202 different companies, 1985-1996

11. Histogram of discounted reserve errors % by company/year

12. Histogram of discounted reserve errors % by company

13. Evidence, 1985-1996 • Average discounted reserve error approximately -22% of initial estimated reserve and -17% of capital • Average undiscounted reserve errors approximately -8% of initial reserve • The distribution is skewed, with 79% of companies over-reserving (ie negative errors) • Almost half of all companies over-reserved by at least 20%

14. Further Evidence • First-order autocorrelation in reserve errors– this year’s errors depend on last year’s! • Positive short-run relationship between net profits and reserve errors, ie high profits in year t are associated with under-reserving in that year • Positive short-run relationship between current solvency and reserve errors, ie high capital levels in year t are associated with under-reserving in that year

15. Conclusions • Weighted average reserve error –22.3% of initial estimated reserve • Two-thirds of over-reserving arises from non-discounting • Autocorrelation of reserve errors (what does this imply for estimating efficiency?) • In the short run, under-reserving is associated with higher net profits and higher solvency margins.