real options in property-liability insurance
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Real Options in Real Options in Property-Liability InsuranceProperty-Liability Insurance
Robert P. Butsic
Fireman’s Fund Insurance
CAS Seminar on
Enterprise Risk Management
April 2-3, 2001
2
AgendaAgenda
• Financial options
• Introduction to real options
• Applications to insurance
• Purpose: to stimulate option thinking
3
Option BasicsOption 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
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Option AsymmetryOption Asymmetry
ValueValue
Underlying Asset ValueUnderlying Asset Value
AssetAssetOptionOption
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Financial OptionsFinancial Options
• Traded in highly liquid markets
• Based on underlying traded financial asset
• Options are derivatives (futures, swaps)
6
P-L Insurance Features with P-L Insurance Features with Financial Option CharacteristicsFinancial Option Characteristics
• Excess coverage (reinsurance)
• Contingent commissions
• Employee stock options
• Insolvency put option
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Financial Option PricingFinancial 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
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Reinsurance ExampleReinsurance 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
dxxfKxK
)()(
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Real OptionsReal 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
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Components of Firm ValueComponents 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
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Value of RenewalsValue 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
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Other Major Insurance Other Major Insurance Real OptionsReal 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. Net Present Value vs. Real OptionsReal 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)
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NPV vs. Real Options, ContinuedNPV 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
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Role of UncertaintyRole 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)
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General Types of Real OptionsGeneral 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)
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Types of Real Option RiskTypes 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
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Real Options Applications 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
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Application ScopeApplication 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)
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Decision MapDecision MapInvest $30 M
CostsOK?
No
No
NoYes
YesMarketOK?
Go Ahead for $100 M
Abandon for $10 M
Wait 1 Year
Abandon for $5 M
2 Years
Yes
Go Ahead for $100 M
MarketOK?
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Scope, ContinuedScope, 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%”
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Scope, ContinuedScope, 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
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Implement Valuation ModelImplement 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
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Review the ResultsReview 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
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RedesignRedesign
• 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
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SummarySummary
• 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
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Further StudyFurther Study• Books
– Amram, Martha and Nalin Kulatilaka, 1999Real Options: Managing Strategic Investment in an Uncertain WorldHarvard 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
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