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

high?

Stephen Diacon, Paul Fenn and Chris O’Brien Nottingham University Business SchoolCentre for Risk and Insurance Studies

Copies can be obtained from stephen.diacon@nottingham.ac.uk

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.

Outline

• Introduction• Accuracy: over- or under-reserving,

time patterns• Loss reserves and loss errors (= ‘actual’

– ‘expected’)• Reserve error motivation• Data and evidence • Conclusions

Introduction

The research has two main tasks:1. 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

2. To investigate why reserve errors differ between companies and over time.

Note: Reserve errort = actual-expectedt, so a negative figure represents over-reserving

-30

-25

-20

-15

-10

-5

0

1984 1986 1988 1990 1992 1994 1996

discounted error undiscounted error

Average Reserve Errors as % Initial Reserve

1405 company/years, 1985-1996

Average (Discounted) Reserve Errors

Reserve Error %, Balanced Sample31 Companies, 1985-1996

-40

-30

-20

-10

01984 1986 1988 1990 1992 1994 1996

of InitialReserve

of Capital

Independent Insurance Company1985-1994

Reserve Error as % of initial reserve

-60

-40

-20

0

20

40

1984 1986 1988 1990 1992 1994 1996

All companies in sampleIndependent Insurance

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.

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

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

Histogram of discounted reserve errors % by company/year

ERRRES

Chart 2: Reserve Error as % Initial Reserve

1985 to 1996, Restricted Sample300

200

100

0

Std. Dev = 29.17

Mean = -18.5

N = 1287.00

Histogram of discounted reserve errors % by company

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%

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

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.