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### Real Options in Property-Liability Insurance

Robert P. Butsic

Fireman’s Fund Insurance

CAS Seminar on

Enterprise Risk Management

April 2-3, 2001

Agenda

- Financial options
- Introduction to real options
- Applications to insurance
- Purpose: to stimulate option thinking

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

Traded in highly liquid markets

Based on underlying traded financial asset

Options are derivatives (futures, swaps)

Financial OptionsP-L Insurance Features with Financial Option Characteristics

- Excess coverage (reinsurance)
- Contingent commissions
- Employee stock options
- Insolvency put option

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

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

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

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

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

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

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)

NPVNPV 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

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)

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)

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

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

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)

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 MapInvest $30 M

No

Yes

Market

OK?

Costs

OK?

No

Yes

Yes

No

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%”

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

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

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

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

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

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

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