1. Interest Rate Risk and Duration Matching Presented by: Ken Quintilian MLMIC (New York) Presented to: CAS Loss Reserve Seminar September 23, 2002 Crystal Gateway Marriott, Arlington, VA CASUALTY ACTUARIAL SOCIETY Valuation, Finance and Investments Committee

2. - 1 - 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.

3. - 2 - Previous CAS Work CAS conducted work in 80’s and early 90’s. Less computing power led to non-dynamic analyses, less compelling results. VFIC wanted to bring a more detailed stochastic model to bear on the problem.

4. - 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. Many analysts today use the empirical “effective duration;” such distinctions did not affect VFIC’s research.

5. - 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 economic value (assets, liabilities, surplus) due to random interest rate shifts.

6. - 5 - What is Duration Matching? Both liability and asset cash flows have durations. They react similarly to interest rate changes, hedging each other. 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).

7. - 6 - Surplus Duration VFIC modeled duration of liabilities and their supporting assets, but not surplus. Excess (“surplus”) asset duration can be modeled separately; different (more risky?) profile probably appropriate. Using duration matching to directly immunize surplus yields illogical investment decision criteria.

8. - 7 - Importance of Duration Matching to Insurers Interest rate is a source of risk to surplus. Duration matching can reduce this risk. Regulators have long seen this as a desirable goal, at least for life insurers. Life insurers must perform cash flow tests and monitor duration. The question has often been raised: Should P/C insurers be encouraged to match durations?

9. - 8 - VFIC’s Analysis Two hypothetical companies. – Workers’ Compensation insurer. – Homeowners insurer. Selected alternative loss ratios. WC HO – Typical 80%72.5% – Adverse110%87.5% Constant expense ratio of 30%. Varying underwriting environments. – Increasing premium (+5% per year). – Decreasing premium (-5% per year).

10. - 9 - VFIC’s Analysis Alternative investment scenarios (all investments in government bonds). – Short (duration = 1 year). – Matched (4 years [WC] or 2 years [HO]). – Long (> 7 years). 1000 randomly generated iterations. Summarize results graphically for comparison.

11. - 10 - Hypothetical Risk / Return Curve

12. - 11 - Risk / Return Framework Compared outcomes by plotting risk against return. Sought to rank outcomes by comparing risk to return. More risk – more return: – A tradeoff (“efficient frontier”).

13. - 12 - Hypothetical Risk / Return Curve

14. - 13 - Risk / Return Framework To compare outcomes, plot risk against return. Seek to 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.

15. - 14 - Hypothetical Risk / Return Curve

16. - 15 - VFIC Return Measures Statutory Net Income. GAAP Net Income (adjusted for unrealized capital gains).

17. - 16 - VFIC Risk Measures Each measure was calculated for Statutory and GAAP. Downside measures. – 5% Value at Risk (VaR). – Probability substantial (25%) surplus decline. – Probability of ruin. – Others tested (TVaR): little difference in results. Two-sided measures. – Standard deviation of net income.

18. - 17 - Statutory Results Longer average asset duration results in higher yield / return. Bonds recorded at amortized cost. When interest rates change, bonds respond only as coupons shift at maturity or liquidation. Longer bonds therefore 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).

19. - 18 - Workers Comp (Statutory) Normal Loss Ratio, Increasing Premium

20. - 19 - General Statutory Observations When there is no efficient frontier, matching is suboptimal. Duration matching does not generally appear to be the “best” strategy.

21. - 20 - Other Statutory Observations Liquidation (e.g., homeowners cats or adverse results) can cause risk from long strategy to increase. Cash flow can protect the risk profile, esp. with a long tail – if new funds cover current payments, revaluation to market never required even when results are poor.

22. - 21 - 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.

23. - 22 - Workers Comp (GAAP) Normal Loss Ratio, Increasing Premium

24. - 23 - General GAAP Observations Many GAAP scenarios yielded direct risk / return relationship (“efficient frontier”). When duration matching is on the “efficient frontier,” it is one of many optimal strategies. Companies must choose their level of risk.

25. - 24 - Other GAAP Observations Downside measures such as VaR sometimes yielded inverse risk-return relationship (no efficient frontier). For these measures, more income = less risk. This effect can override the effect of greater variability.

26. - 25 - Additional Observations Variability of return is not sole source of risk. 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.

27. - 26 - 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. Less opportunity cost.

28. - 27 -... 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). Risk / return tradeoff: matched is not “better” or “worse.” Matching causes more opportunity cost.

29. - 28 - 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.

30. Interest Rate Risk and Duration Matching Presented by: Ken Quintilian MLMIC (New York) Presented to: CAS Loss Reserve Seminar September 23, 2002 Crystal Gateway Marriott, Arlington, VA CASUALTY ACTUARIAL SOCIETY Valuation, Finance and Investments Committee