Interest Rate Risk and Duration Matching

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

2. 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. Milliman USA

3. 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. Milliman USA

4. 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. Milliman USA

5. 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). Milliman USA

6. 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? Milliman USA

7. 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. Milliman USA

8. 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. Milliman USA

9. 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. Milliman USA

10. VFIC Return Measures • Statutory Net Income. • GAAP Net Income (adjusted for UCG). Milliman USA

11. 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. Milliman USA

12. 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). Milliman USA

13. Workers Comp (Statutory)Normal Loss Ratio, Increasing Premium Milliman USA

14. 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. Milliman USA

15. Workers Comp (GAAP)Normal Loss Ratio, Increasing Premium Milliman USA

16. 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. Milliman USA

17. 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. Milliman USA

18. 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. Milliman USA

19. . . . 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.” Milliman USA

20. 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. Milliman USA

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