Valuation, Finance and

Investments Committee

Interest Rate Risk

and Duration Matching

Ken QuintilianCAS Spring Meeting

May 20, 2002San 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 VFIC’s 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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VFIC’s 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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VFIC’s Analysis

Alternative investment scenarios (all investments in government bonds).

– Short investments (duration = 1 year).

– Matched investments (4 years or 2 years).

– Long investments (> 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

6%

7%

8%

9%

10%

1% 2% 3% 4% 5%

Standard Deviation of Net Income as a Percentage of Stat Surplus

Net

Inco

me

Aft

er T

axes

as

a P

erce

ntag

e of

Sta

t Sur

plus

Short Duration Matched Long

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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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7%

8%

9%

10%

11%

12%

13%

4% 6% 8% 10% 12% 14% 16% 18%

Value at Risk 5% (Percent Change in Adjusted Equity in Year 5 Only)

Tot

al R

etur

n as

a P

erce

ntag

e of

GA

AP

Equ

ity

Short Duration Matched Long

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. VFIC’s 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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What’s 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.

Valuation, Finance and

Investments Committee

Interest Rate Risk

and Duration Matching

Ken QuintilianCAS Spring Meeting

May 20, 2002San Diego, CA