2. Real Options in Property-Liability Insurance Robert P. Butsic Fireman’s Fund Insurance CAS Seminar on Enterprise Risk Management April 2-3, 2001

3. 2 Agenda Financial options Introduction to real options Applications to insurance Purpose: to stimulate option thinking

4. 3 Option Basics Option is a right, not an obligation Characterized by asymmetric outcomes, or non-linear payoff Either zero or a positive amount –Can be highly levered Call option example –Buy IBM at $100 a share by May 1 for $7.20 –Payoff is zero or (Stock Price - $100) –Leverage: share goes from $110 to $120

5. 4 Option Asymmetry Value Underlying Asset Value Asset Option

6. 5 Financial Options Traded in highly liquid markets Based on underlying traded financial asset Options are derivatives (futures, swaps)

7. 6 P-L Insurance Features with Financial Option Characteristics Excess coverage (reinsurance) Contingent commissions Employee stock options Insolvency put option

8. 7 Financial Option Pricing Option value = PV of expected outcome Expectation is over all possible outcomes, adjusted for risk –Includes contingent decisions PV is taken at risk-free interest

9. 8 Reinsurance Example Reinsurer pays losses above K Similar in structure to a call option Loss density is f(x) for loss x Density is risk-adjusted (risk-neutral) Value of reinsurance is PV of

10. 9 Real Options Valuation of non-financial assets involving: –Contingent decisions –Non-linear payoff, as in financial options Time element (event sequence) is important –Volatility of outcomes drives the option value Have been used successfully in –Natural resource investment –Technology valuation

11. 10 Components of Firm Value Company value = market value of equity MVE = MV of (Book Assets - Book Liabilities) + Intangible Assets, or MVE = Tangible Equity + Intangible Assets Intangible (soft) assets = PV of future business Intangible Assets are largely real options

12. 11 Value of Renewals Re-pricing option –Multi-year policy is risky –Pricing flexibility is valuable Non-renewal option –Re-underwriting advantage –Offset by cost of new business

13. 12 Other Major Insurance Real Options Acquisition and divestiture Growth Capacity –Staffing level –Capital level Information technology (internet) All these can be valued with Real Option techniques

14. 13 Net Present Value vs. Real Options Why NPV often doesn’t work: an example Pay $10 million for license to sell insurance in Asia; $50 million to develop business if we go ahead 20% chance favorable market with huge success; 80% chance of poor market with dismal failure If favorable, gross profit is $100 million, if not, loss is $70 million Under NPV (0% interest), expected profit is $-96 million = -10 - 50 + 0.2(100) + 0.8(-70)

15. 14 NPV vs. Real Options, Continued As a real option, the value is $15 million = -10 + 0.2(100 - 50) NPV ignores conditional nature of follow-on investments NPV

16. 15 Role of Uncertainty More uncertainty increases the value of real options Recall the Asian investment –Expected gross profit is $-36 million –Standard deviation is $68 million Change payoff to (200 mill, -95 mill) –Expected gross profit remains $-36 million –Standard deviation rises to $118 million –Option value increases to $20 million = -10 + 0.2(200 - 50)

17. 16 General Types of Real Options Growth (Amazon model) Learning (Cisco; failure may have value) Flexibility (getting ahead of competition) Exit (cutting losses) Waiting to invest (watch others fail)

18. 17 Types of Real Option Risk Market Risk –Uses existing market prices of similar investments –Allows accurate valuation of option Private Risk –No direct link to traded assets –Requires explicit probability distribution of outcomes –Difficult to value: uncertainty about demand, competitive responses, regulation, loss costs, interest rates and other macroeconomic conditions

19. 18 Real Options Applications Process –Set the scope of the application –Implement option valuation model –Review results and redesign if necessary Illustrate with insurance example –New venture: Direct marketing of Homeowners insurance

20. 19 Application Scope Map the decisions –Incremental investments and time frames –Decision points –Residual value if abandoned Include sources of uncertainty –Costs (combined ratio) –Evolution of market prices (bad timing)

21. 20 Decision Map Invest $30 M Costs OK ? No Yes Market OK? Go Ahead for $100 M Abandon for $10 M Wait 1 Year Abandon for $5 M 2 Years Yes Go Ahead for $100 M Market OK?

22. 21 Scope, Continued Nature of the uncertainty –Lognormal is often used –Mean-reversion on market prices Set the decision rules –“Loss ratio should be under 90% before market evaluation” –“Market is such that composite market/book ratio on Personal Lines insurers exceeds 120%”

23. 22 Scope, Continued Choose financial market analogy –Portfolio of personal insurance stocks –Used in valuing final investment stage (when market is favorable) Review for transparency and simplicity –Explain the scope to Homeowners managers –Also to disinterested managers with broad experience

24. 23 Implement Valuation Model Establish inputs –Values of assets, cash flows, interest –Volatility of each source of uncertainty –Loss ratio (20%), Personal Lines Co. (15%) Value option with proper model –Black-Scholes is standard –Others: binomial tree, simulation or dynamic programming

25. 24 Review the Results Valuation numbers –Compare to NPV (shows embedded option values) Critical values for strategic decisions –When to abandon vs. asset value Sensitivity to inputs –May lead to redesign Investment risk profile –Shows likelihood of abandonment

26. 25 Redesign Expand/reduce investment alternatives –Additional products (auto) –Joint ventures Add options by staging or creating modules –Rollout by expansion to different territory –Add research phase to gain market knowledge

27. 26 Summary Options are a new and useful way to think about the value of insurance investments Insurance applications of real options are just beginning to unfold Actuaries, as risk experts, are well- positioned to use real-option methods in insurance strategies

28. 27 Further Study Books –Amram, Martha and Nalin Kulatilaka, 1999 Real Options: Managing Strategic Investment in an Uncertain World Harvard Business School Press – Trigeorgis, Lenos, 1996 Managerial Flexibility And Strategy In Resource Allocation MIT Press –Tom Copeland, Vladimir Antikarov, 2001 Real Options: A Practitioner's Guide Texere Websites –http://www.real-options.com –http://www.mbs.umd.edu/finance/atriantis/RealOptions.html