Interest Rate Risk and Duration Matching

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Interest Rate Riskand Duration Matching
Ken Quintilian CAS Spring Meeting May 20,
2002 San Diego, CA
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Nature of Project

• Interest rate risk has been discussed for years.
• Duration matching has been held out as a risk
  reduction tool.
• VFIC undertook a paper on duration matching Is
  it optimal?
• Goal was to apply DFA techniques to quantify
  pros/cons of matching asset liability duration.

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What is Duration?

• Any set of cash flows has duration.
• A convenient definition (Macaulay duration)
• Weighted average time to maturity.
• Discounted cash flows are the weights.
• More refined definitions are available such
  distinctions did not affect VFICs research.

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Why is Duration Important?

• Duration is a source of interest rate risk.
• Duration (D) is expressed in years.
• If interest rates increase 1, present value of
  cash flows decrease about D.
• This gives rise to a risk of loss/gain in value
  (assets, liabilities, surplus) due to random
  interest rate shifts.

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What is Duration Matching?

• Both liability and asset cash flows have
  durations.
• They react similarly to interest rate changes.
• If duration for assets and liabilities are equal,
  the surplus will not be subjected to interest
  rate risk from the liabilities (or their
  supporting assets).

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Importance of Duration Matching to Insurers

• Interest rate is a source of balance sheet risk.
• Duration matching can reduce this risk.
• Regulators have long seen this as a desirable
  goal, at least for life insurers.
• Life insurers are required to perform cash flow
  tests.
• The question has often been raised Should P/C
  insurers be required to match durations?

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VFICs Analysis

• Performed a DFA analysis.
• Formulated hypothetical companies.
• Workers Compensation insurer.
• Homeowners insurer.
• Alternative loss ratios.
• Typical.
• Adverse.
• Varying underwriting environments.
• Increasing premium.
• Decreasing premium.

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VFICs Analysis

• Alternative investment scenarios (all investments
  in government bonds).
• Short investments (duration 1 year).
• Matched investments (4 years or 2 years).
• Long investments (gt 7 years).
• 1000 randomly generated scenarios.
• Summarize results graphically for comparison.

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Risk / Return Framework

• To compare outcomes, plot risk against return.
• Rank outcomes by comparing risk to return.
• More risk more return
• A tradeoff (efficient frontier).
• Less risk more return
• A best option can be selected.

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VFIC Return Measures

• Statutory Net Income.
• GAAP Net Income (adjusted for UCG).

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VFIC Risk Measures

• Each measure was calculated for Statutory and
  GAAP.
• Downside measures.
• 5 Statutory Value at Risk (VaR).
• Probability substantial surplus decline.
• Probability of ruin.
• Two-sided measures.
• Standard deviation.

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Statutory Results

• Longer duration results in higher yield/return.
• Bonds recorded at amortized cost.
• Bonds respond to interest rate only as coupons
  shift.
• Longer bonds respond more slowly to interest rate
  movements opposite of market pattern.
• Result Longer duration yields lower risk.
• Outcome Higher return, lower risk.
• Invest long (matching is suboptimal).

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Workers Comp (Statutory)Normal Loss Ratio,
Increasing Premium
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GAAP Results

• Bonds are marked to market.
• Asset values respond to interest rate
  fluctuations.
• Outcome Higher return, higher risk.
• Risk / return tradeoff (many optimal
  outcomes).
• Duration matching just one consideration in
  profiling corporate risk strategy.

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Workers Comp (GAAP)Normal Loss Ratio, Increasing
Premium
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Observations

• When duration matching is on the efficient
  frontier, it is one of many optimal strategies.
• Companies must choose their level of risk.
• When there is no efficient frontier, matching is
  suboptimal.
• Duration matching does not generally appear to be
  the best strategy.

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Additional Observations

• Risk is not solely variability of return.
• Lower average return is also a form of risk.
• VFICs one-sided risk measures consider that.
• This increases the range of circumstances in
  which increased return can result in decreased
  risk, regardless of accounting.
• Reinforces the finding against matching.

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Whats Good for the Goose . . . .

• Life Insurers
• Longer liabilities.
• Shorter (than matched) assets was the norm.
• Matching meant lengthening the investment
  strategy.
• Result Longer investments (higher return)
• Matched duration (lower risk).
• Qualitative risk improvement over previous
  strategy.

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. . . may not be Good for the Gander

• P/C Insurers
• Shorter liabilities.
• Longer than matched assets is the norm.
• Matching means shortening the investment
  strategy.
• Result Shorter investments (lower return)
• Matched duration (lower risk).
• Efficient frontier outcome Risk / return
  tradeoff matched is not better or worse.

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Future / Ongoing Research

• Reserves do not respond to interest rates.
• GAAP, Statutory No discounting.
• Model not parameterized to make losses vary with
  inflation.
• Future modeling efforts will utilize economic
  value (discounted losses).
• Will integrate inflation-sensitive loss
  projections.
• Although patterns will differ, issues discussed
  above may lead to similar conclusions.

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Interest Rate Riskand Duration Matching
Ken Quintilian CAS Spring Meeting May 20,
2002 San Diego, CA