Interest Rate Risk and Duration Matching

1. CASUALTY ACTUARIAL SOCIETY Valuation, Finance and Investments Committee Interest Rate Riskand Duration Matching Presented by: Ken Quintilian MLMIC (New York) Presented to: CAS Risk and Capital Management Seminar July 8, 2002 Toronto, ON

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.

3. 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. 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. 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.

6. 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. Surplus Duration • VFIC modeled duration of liabilities and related assets, but not surplus. • Excess (“surplus”) asset duration can be modeled separately; different risk profile probably appropriate. • Using duration matching to directly immunize surplus yields illogical investment decision criteria.

8. 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. VFIC’s Analysis • Two hypothetical companies. • Workers’ Compensation insurer. • Homeowners insurer. • Selected alternative loss ratios. WCHO • Typical 80% 72.5% • Adverse 110% 87.5% • Constant expense ratio of 30%. • Varying underwriting environments. • Increasing premium (+5% per year). • Decreasing premium (-5% per year).

10. 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 scenarios. • Summarize results graphically for comparison.

11. Hypothetical Risk / Return Curve

12. 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”).

13. Hypothetical Risk / Return Curve

14. 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. Hypothetical Risk / Return Curve

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

17. 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. 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. Workers Comp (Statutory)Normal Loss Ratio, Increasing Premium

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

21. 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. 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. Workers Comp (GAAP)Normal Loss Ratio, Increasing Premium

24. 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. 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. 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. 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. . . . 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. 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. CASUALTY ACTUARIAL SOCIETY Valuation, Finance and Investments Committee Interest Rate Riskand Duration Matching Presented by: Ken Quintilian MLMIC (New York) Presented to: CAS Risk and Capital Management Seminar July 8, 2002 Toronto, ON