in that year - The Chartered Insurance Institute

							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
        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
             Average Reserve Errors
               as % Initial Reserve
         1405 company/years, 1985-1996
  1984   1986       1988       1990   1992     1994         1996
 0

 -5

-10

-15

-20

-25

-30

            discounted error                 undiscounted error
         Average (Discounted) Reserve
                    Errors

         Reserve Error %, Balanced Sample
             31 Companies, 1985-1996

 0
  1984   1986   1988   1990   1992   1994   1996
-10
                                                   of Initial
-20                                                Reserve

-30                                                of Capital


-40
Independent Insurance Company
          1985-1994
 Reserve Error as % of initial reserve

 40
 20
   0
   1984    1986    1988    1990   1992   1994   1996
 -20
 -40
 -60
       All companies in sample
       Independent 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
       Chart 2: Reserve Error as % Initial Reserve
       1985 to 1996, Restricted Sample
30 0




20 0




10 0

                                            Std . Dev = 29 .17
                                            Mean = -18 .5
  0                                         N = 128 7.00




         10
         -9
         -8 .0
         -7 .0
         -6 .0
         -5 .0
         -4 .0
         -3 .0
         -2 .0
         -1 .0


          10
          20
          30
          40
          50
          60
          70
          80
          90
          0. .0
           0
           0
           0
           0
           0
           0
           0
           0
           0




            0.
             0

             .0
             .0
             .0
             .0
             .0
             .0
             .0
             .0
             .0

              0
       ERRRES
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.