1. Presenting the Results of a DFA Study to Management Casualty Actuarial Society Seminar on Dynamic Financial Analysis July 17-18, 2000 Gerald S. Kirschner, FCAS, MAAA Liberty Mutual Group LMN

2. 2 DFA Model Structure (2) Invested Assets Accounting and Cashflow (1) Economic Scenarios (4) Underwriting Cashflow (8) Financial Statements (9) Report Generator (6) Reinvest Cashflow (7) Taxes (5) Miscellaneous Cashflow (3) Underwriting Scenarios Loss Expense Other Premiums

3. 3 Framing the Question n “What actions can my organization take to maximize our expected economic net worth* five years from now?” * Economic net worth = all assets at market value, all liabilities at their present value. Present value calculated using a risk-free rate of return -- i.e. no risk loading included in liability valuation.

4. 4 Considerations n Look at influence caused by various possible future states of the world: u Interest rates u Equity returns u Inflation u Volatility in underwriting and company operations n Influence of various portfolio mixes on expected future net worth values and the associated volatility of results n Projected statutory capital versus capital required by NAIC’s Risk Based Capital formula

5. 5 Impact of Stochastic Elements Deterministic Base Case Year 5 Economic Net Worth

6. 6 Impact of Stochastic Elements - an Alternative Way to View Results Fully Deterministic StateStochastic Base Case

7. 7 Drivers of Volatility Variable Interest Rates 10% Time T1 - T5 Loss Ratio Volatility 8% Time T 0 Loss Reserve Volatility 7% Payout Pattern Volatility 2% Variable Inflation Rates 21% Variable Stock Market Returns 36% Variation Not Accounted For 16%

8. 8 Reinvestment Alternatives n Government bonds n Corporate bonds n High yield bonds n Tax-exempt bonds n Cash n Common stocks n Status quo ( = 6% government, 60% corporate, 2% high yield, 14% tax exempt, 5% cash and 13% common stock)

9. 9 Effect of Alternative Investment Strategies on Economic Net Worth

10. 10 Graphical View of the Effect of Alternative Investment Strategies Status Quo100% Comm. Stock100% High Yield BondsFully Deterministic State 1927-19391940-19491950-19591960-19691970-19791980-19891990-1998 Variations in Economic Net Worth Caused by Alternative Asset Reinvestment Strategies

11. 11 Influence of Economic Variables on RBC Calculation n Examined relationships between the calculated RBC ratios and: u average stock market returns u average long term interest rates u average overall inflation rates n Common stock strategy is most heavily influenced by stock market movements, less by interest rate or inflation rate changes

12. 12 Graphical View of Capital Adequacy Variations Fully Deterministic StateStatus Quo100% Comm StockTarget Minimum100% High Yield Bonds Observation Year Five Capital Adequacy 1927 - 19391940 - 19491950 - 19591960 - 19691970 - 19791980 - 19891990 - 1998 % Observations below the Target Minimum 0.0% - Status Quo 7.9% - Common Stock 0.0% - High Yield

13. 13 Revisiting the Impact of Alternative Investment Strategies on Net Worth

14. 14 Efficient Frontiers of Alternative Asset Mixes n Analyze the risk / return tradeoffs associated with varying the % of assets reinvested in: u Common stocks versus high yield bonds u Common stocks versus the relative percentage invested in all other asset classes n Examine each mix’s downside potential

15. 15 “Efficient Frontier” of Common Stock / High Yield Bond mix options Common Stock & High Yield Bond Mix Reinvestment Alternatives - Average of Stochastic Observations Status Quo Reinvestment Alternatives - Average of Stochastic Observations Higher Economic Net Worth, using more Capital: Higher return with more risk Lower Economic Net Worth, using more Capital: Lower return with more risk Higher Economic Net Worth, using less Capital: Higher return with less risk A D C E F G H J I B K Point A: 100% common stock Point K: 100% high yield bonds

16. 16 “Efficient Frontier” of Common Stock / Status Quo mix options Varying % of Common Stock relative to rest of Status Quo portfolio - Average of Stochastic Observations Status Quo Reinvestment Alternatives - Average of Stochastic Observations Higher Economic Net Worth, using more Capital: Higher return with more risk Lower Economic Net Worth, using more Capital: Lower return with more risk Higher Economic Net Worth, using less Capital: Higher return with less risk A D C E F G H J I B K Point A:100% common stock Point K:0% common stock

17. 17 “Downside Potential” of Common Stock / Status Quo mix options Varying Common Stock Reinvestment Percentage - Average of Stochastic Observations Status Quo Reinvestment Alternatives - Average of Stochastic Observations % of Observations Falling Below Targeted Minimum Capital Threshold Recommendation to management