Go with the Flow: Asset Liquidity and Insurer Solvency

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Cash-Flow Solvency
Leigh J. Halliwell, FCAS, MAAA Consulting
Actuary leigh_at_lhalliwell.com Casualty Loss
Reserve Seminar Boston, MA September 12, 2005
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Financial Solvency

• Latin solvere (generally) to solve, to free, to
  loosen (financially) to pay off or discharge,
  especially a debt
• Solvent (adj) able to pay ones debts or
  liabilities
• Solvency (n) ability to pay ones debts

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Balance-Sheet Solvency

• Balance Sheet, a tabular statement of assets and
  liabilities (Oxford Universal Dictionary)
• With (non-negative) values assigned to each item!
  What values GAAP, SAP, market, fair?
• Surplus as balancing item A L S
• Balance-sheet solvent ? A ? L ? S ? 0
• BS solvency is the ability to pay, to a high
  probability, ones liabilities as they come due
  by liquidating ones assets in their respective
  markets at their current market values.

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BS Solvency Aims and Concerns

• Study historic behavior of asset prices, and how
  asset prices interact (i.e., returns and
  correlations).
• Time the markets, i.e., Buy low and sell high.
• Allocate capital as a solvency cushion against
  plausible market downturns.
• How to treat assets and liabilities that have no
  liquid markets, and hence no market values? Use
  fair value?
• The greatest threat to a BS-solvent entity is an
  adverse revaluation of its assets and
  liabilities. Just get me to the next accounting
  period! Butsic (1994), 667-674.

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BS Solvency and Duration

• Bond income and loss outgo most important to
  insurers
• Interest-rates are the main determinant of the
  market value of high-grade bonds. They and
  underlying inflation can affect loss payments.
  Butsic (1981, 62f.) AD PD models
• Macauley duration theoretically immunizes cash
  flows from interest-rate fluctuations. Cf.
  Feldblum (1989) and Halliwell (1999). DArcy
  (1996) gives caveats (504-509).
• cash inflow from new policies is adequate to
  pay all losses and expenses (DArcy, 505) Cf.
  Bustic (1994) on insurers as going concerns
  (674f).

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Cash Flows and Market Values

• Cash flows fundamental market values derivative.
  Market participants value stochastic cash flows
  (Halliwell, 2003).
• Confusion between the two levels abounds in
  financial theory and practice. Account values
  are not cash flows.
• Example 100 in a bank account paying 4 per
  year
• Incorrect 100 100/1.00 4/1.04 103.85
• Correct 0 -(100)/1.00 (100 4)/1.04
• An account is a wrapper with which cash flows in
  and out. The account merely capitalizes the cash
  flow. Dont double count!

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Cash-Flow Solvency

• CF solvency is the ability to pay, to a high
  probability, ones liabilities as they come due
  from ones current pool of cash mathematically,
  for all t, CumCashIn(t) ? CumCashOut(t).
• Impervious to market valuation solvent on a
  deeper level and to a more stringent standard
• Shifts attention off of investment and onto
  underwriting. For too long the insurance
  industry has been straining out a gnat and
  swallowing a camel. (Mt 23.24)
• Discourages the writing new business to pay old
  claims
• Doable with the present state of actuarial
  science and DFA

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The Major Objection to CF Solvency

• Providing such a cash pool by a portfolio of
  high-quality (even risk-free bonds) unduly
  reduces investment income!
• Four answers (unlikely to convince many,
  especially CFOs)
• Are alternatives, e.g., liquidity capital, any
  better?
• We make money the old-fashioned way. We
  underwrite!
• Regulators and policyholders will appreciate CF
  solvency.
• Ratings agencies might eventually accept it.
• The noble and aesthetic Its right and
  beautiful!

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Example of CF Solvency

• We have 250 equiprobable loss-runoff scenarios
  over a 10-year horizon. Their derivation
  considered all plausible economic and social
  conditions (in good DFA parlance).
• We desire to schedule cash inflows from US
  Treasuries that will fund 225 scenarios, i.e.,
  achieve CF solvency to the 90th percentile.
• From the many possible schedules we will choose
  the least expensive one in terms of current
  Treasury prices.

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Fundamental Theorem of Funding

• A schedule (or funding arrangement) cannot
  discharge runoff scenarios, if its present value
  is less than theirs i.e., less in-PV cannot
  fund greater out-PV. (However, greater in-PV
  in does not necessarily fund less out-PV.)
• Proof To discharge a scenario, income from x to
  xDx must precede outgo. Since v(t) decreases,
  for all Dx, v(tincome) Dx ? v(toutgo) Dx. Hence,
  SDPVincome ? SDPVoutgo.
• Therefore, the cost of funding 225 scenarios is
  at least the 225th order statistic of the present
  values of the scenarios.

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Steepest-Descent Algorithm

• Fund the envelope of the cumulative outflows of
  the 225 lowest-PV scenarios. Envelope(t)
  Max(cumoutflows(t)).
• So PVFund ? PV order statistic 225.
• Are more than 225 scenarios funded?
• If not, the envelope is best. If yes, chip away
  from the envelop the scenario that most reduces
  the PV. Repeat this until 225 scenarios remain.
• Steepest Descent Simple, but may not be
  optimal. Counting down from 250 better for 225,
  but not for 200.
• Excel demonstration Cash-Flow Solvency.xls
• Extra conservatism no reinvestment, no
  mid-interval flows

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References

• Butsic, Robert P., The Effect of Inflation of
  Losses and Premiums for Property-Liability
  Insurers, Inflation Implications for
  Property-Casualty Insurance, CAS 1981 Discussion
  Paper Program, 58-109.
• Solvency Measurement for Property-Liability
  Risk-Based Capital Applications, Journal of Risk
  and Insurance, Vol 61 (Dec 1994), 656-690.
• DArcy, Stephen P., Investment Issues in
  Property-Liability Insurance, Foundations in
  Casualty Actuarial Science (Third Ed., 1996),
  Chapter 8.
• Feldblum, Sholom, Asset-Liability Matching for
  Property/Casualty Insurers, Valuation Issues,
  1989 CAS Special Interest Seminar, 117-154.
• Halliwell, Leigh J., Insights into Present Value
  and Duration, Spring 1999 Forum, 408-437.
• The Valuation of Stochastic Cash Flows,
  Spring 2003 Forum, 1-68.