Real Options in Property-Liability Insurance

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

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

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

4. Option Asymmetry Asset Option Value Underlying Asset Value

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

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

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

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

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

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

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

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

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 $-96million = -10 - 50 + 0.2(100) + 0.8(-70)

14. NPV 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

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)

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)

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

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

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)

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

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%”

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

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

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

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

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

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