Using Dynamic Financial Analysis

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Using Dynamic Financial Analysis to Structure
Reinsurance Session Using DFA to Optimize the
Value of Reinsurance 2001 CAS Special Interest
Seminar on Dynamic Financial Analysis, June 6-8,
2001, Boston Reto Angliker, Martin Melchior
and Markus Stricker, Swiss Re
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Underlying Data Set DFA Insurance Company

• This case study for the DFA Insurance Company is
  based on the data available on the CAS web-site
• The DFA Insurance Company is a fictional
  insurance company with two lines of business
• Property Gross written premium 1.29 Bio USD
  (short tail business)
• Casualty Gross written premium 1.26 Bio USD
  (long tail business)
• (for the payout patterns see appendix)
• Each line of business has only non-proportional
  reinsurance Working excess of loss with one
  layer and an infinite number of reinstatements

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DFA Model

• We have selected a relatively simple DFA model
  for this case study.
• The level of detail of the data provided for the
  DFA Insurance Company is not enough to initialize
  a sophisticated DFA model. Hence, by analyzing
  with a sophisticated DFA model, we would have to
  introduce additional assumptions which may divert
  the focus away from our primary objective.
  Consequently, we work with a simple DFA model to
  produce the following case studies.

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Result for the Base Scenario

• The key figures such as underwriting result,
  annual result, underwriting cash flow, GAAP RoE
  and solvency ratio are stable.
• Due to the conservative asset allocation (71
  Bonds, 11 Equities, 11 Cash), the main
  contribution of the volatility of the annual
  results stems from insurance business and not
  from investments.
• Due to claims inflation (assuming 3 on average)
  the reserves for outstanding claims payments and
  total claims paid increase.
• The book value of the investments increases
  although any earning is paid out to the
  shareholders. This stems from the increase of
  reserves and premium due to claims inflation.

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DFA Insurance Company Case Study 1

• The set-up We study the effect of two different
  reinsurance programs with an equal amount of risk
  transfer, i.e. the programs have the same
  volatility of the net-loss ratio and the same
  technical result distribution.
• The two reinsurance programs as of beginning of
  2001Most of the risk transfer ceded to
  reinsurance stems from property business.Most
  of the risk transfer ceded to reinsurance stems
  from casualty business.
• Pricing assumptionsThe net present value (based
  on a fixed interest rate used for pricing) of the
  gross insurance business and the reinsurance
  business is chosen to be equal to zero.

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Outstanding Claims Provisions DFA Insurance
Company

• Yellow More casualty (long-tail) business is
  retained, thus more reserves for outstanding
  claims are built up.
• Magenta More property (short-tail) business is
  retained such that the reserves for outstanding
  claims are not equally large.

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Time Limited Effects DFA Insurance Company

• For a transitional period the two different
  reinsurance programs have a significant effect on
  net claims paid and underwriting cash flows.
• On long term average, retaining more casualty
  business leads to slightly lower underwriting
  cash flows. This is caused by the pricing
  assumptions.

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Other Key Figures DFA Insurance Company

• The two different reinsurance programs have only
  marginal effects on the following key figures
• annual result
• surplus
• solvency ratio
• GAAP RoE

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Case Study 1 Conclusion

• Reinsurance programs with an equal amount of risk
  transfer can still have a significantly different
  impact on the total reserves and claims payments
  of an insurance company.
• When switching between such reinsurance programs,
  the effect on underwriting cash flows and change
  in reserves usually is time limited. After a
  transition period these effects almost vanish,
  depending on the assumed pricing.
• Question How can one exploit these effects to
  create value?

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DFA Insurance Company Case study 2

• We consider the same reinsurance structures as in
  case study 1,ie, more reinsurance on property
  versus more on casualty such that the risk
  transfer is the same.
• We attempt to exploit the effects created by the
  change in reinsurance by applying a more
  aggressive asset mix as of 1st January 2001.
• The more aggressive asset mix is
• 51 bonds (71)
• 31 equity (11)
• 11 cash
• 7 other investments

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Investments DFA Insurance Company

• Since the new asset mix encompasses a larger
  proportion of equity, the volatility and the
  average growth rate of the investments (book
  value) is much higher.
• The same qualitative effects appear under both
  asset allocation strategies When more business
  is retained in the long tail LoB, more reserves
  have to be held, and hence the volume of
  investments increases.

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Investment Income Realized Gains DFA Insurance
Company

• A slightly higher investment income is achieved
  if more casualty business is retained since the
  investment volume is larger.
• Since dividend yields in our framework are chosen
  to be smaller than the yields from fixed income
  securities, the investment income drops after
  implementing the more aggressive asset allocation
  strategy.
• The drop becomes only visible in 2002, since in
  2001 - when the new asset mix is implemented -
  the realized gains from the sale of the bonds
  offset the smaller yield due to the new asset mix.

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Revaluation Reserves DFA Insurance Company

• The change in unrealized capital gains is
  excluded from the statutory income statement and
  contributes to the revaluation reserve.Because
  we assume a low turn-over of the portfolio, the
  major contribution to the income statement comes
  from investment income cash flow.
• Revaluation reserves and its volatility increases
  dramatically under the more aggressive asset mix

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RoE and Solvency DFA Insurance Company

• The more aggressive asset mix affects income
  marginally, but increases revaluation reserves
  and surplus significantly
• Consequently the solvency ratio is increased and
  return on equity is lowered by the more
  aggressive asset allocation strategy. The
  volatility of solvency ratio and RoE is largely
  increased.

Aggressive asset strategy, more casualty retained
Aggressive asset strategy, more property retained
Conservative asset strategy, more casualty
retained
Conservative asset strategy, more property
retained
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Case Study 2 Conclusion

• A more aggressive asset mix affects merely the
  balance sheet and only marginally the income
  statement, as long as the capital gains are not
  realized, consequently profitability (RoE) and
  solvency ratios are affected by a more aggressive
  asset strategy.
• The change in investment income due to a
  different asset allocation kicks in only with a
  time delay of at least one year due to realized
  gains associated with the reallocation.
• Qualitatively, this picture results under both
  reinsurance programs.

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Appendix Representation of the Data Set

• The loss ratio of each line of business is the
  sum of a log-normally distributed ground up loss
  ratio and a ratio for large losses (Compound
  Poisson-Pareto Process). The ratios are stated as
  percentage of the gross earned premium income.
• The mean and the standard deviation of the
  individual gross loss ratios is given as
• The non-proportional reinsurance program applies
  only to the compound Poisson-Pareto-Processes

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Appendix Payout Patterns for Property Casualty

• Property represents insurance business with short
  tail loss development whereas Casualty represents
  insurance business with long tail loss
  development.
• The claims development payout pattern (lag
  factors) have been determined as follows

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Appendix Presentation of the Simulation Outputs

• 60 of the sample data fall within this range
• 90 of the sample data fall within this range

95
80
50
20
5

• We work with the 5, 20, 50, 80 and 95
  percentiles
• percentiles can give an intuition for the shape
  of the distribution of the key figures

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Output Technical Annual Result DFA Insurance
Company

• The technical result is rather stable. The
  little bump in year 2002 is mainly due to
  inflation which affects premiums and claims after
  different time lags and which has no influence on
  the expenses.
• The main proportion of the volatility of the
  annual results stems from insurance and not from
  investments
• The volatility of the annual result - which is
  reported after tax - is smaller than the
  volatility of the technical result, which is
  reported before tax.

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Output Investments Claims Provisions DFA
Insurance Company

• The book value of total assets is about 5.3 Bio.
  USD
• 71 Bonds
• 11 Equity
• 7 Other investment
• 11 Cash
• It is assumed that this asset mix is also the
  target asset mix for future years
• Due to claims inflation the reserves for
  outstanding claims payments increase accordingly

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Output Cash Flow DFA Insurance Company

• The technical cash flow is rather stable and the
  median (50 percentile) lies in the positive area
• Total payments for claims increase due to claims
  inflation

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Output GAAP ROE Solvency DFA Insurance Company

• The median of the return on equity distribution
  is rather stable at about 8 - slightly
  increasing
• Solvency is rather stable, however a slight
  downward trend is visible