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## Interest Rate Risk and Duration Matching

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**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**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.**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.**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.**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.**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).**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.**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?**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).**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.**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”).**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.**VFIC Return Measures**• Statutory Net Income. • GAAP Net Income (adjusted for unrealized capital gains).**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.**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).**Workers Comp (Statutory)Normal Loss Ratio, Increasing**Premium**General Statutory Observations**• When there is no efficient frontier, matching is suboptimal. • Duration matching does not generally appear to be the “best” strategy.**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.**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.**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.**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.**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.**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.**. . . 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.**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.**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