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

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AgendaAgenda

• Financial options

• Introduction to real options

• Applications to insurance

• Purpose: to stimulate option thinking

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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)

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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

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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