ASTIN’s Next Greatest Contributions

Stephen P. D’Arcy, Ph. D., FCAS

Professor of Finance

University of Illinois

ASTIN 2007

Orlando, Florida

Objective

• Provide a presentation to facilitate valuable research on risk– Identify potential technical tools that could be

productively applied to risk analysis– List critical practical problems in need of

additional research– Encourage researchers to apply their skills in these

areas

Short Version• Tools

– Data mining and predictive modeling– Neuroscience

• Neuroeconomics• Neurofinance, behavioral finance

• Key practical problems– Enterprise Risk Management – Unified theory of risk– Risk metric– Extreme event probabilities

Data Mining and Predictive Modeling

• Finding patterns in data that were not previously recognized

• Current applications– Risk classification – Ratemaking– Credit scoring– Fraud detection

• Next step, apply to loss reserving

Loss Reserving• Need to move beyond the Chain Ladder Method• Bring predictive modeling approach to reserving

– Technology now allows transactional data analysis– Analyze individual claim histories– Determine correlations across line, lines of business– No longer have to work with aggregate data

• Better approach to loss reserve models– Systematic, statistically driven methodology– Consistent probabilistic models of ultimate losses, case

reserves and paid loss processes akin to interest rate and equity return models of finance

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Loss Reserving (2)

• Economic value of loss reserves• Reserve ranges

– Standard actuarial approach– Communicated effectively to our publics

Neuroscience of Risk

• How are decisions relating to risk made?

• Chemistry of decision making

• Effect of framing

• Impact of recent events

• Cascade behavior

• What factors improve decisions?

Applications of Neuroscience to Insurance

• Optimal policy design

• Sales process

• Pricing

• Default options

• Claim negotiations

• Relationship between risk taking behavior and credit scoring (Brockett, et al)

The Problem With “Risk Management”• Risk Management

– Developed in 1960s– Focus was on pure risk (insurable, hazard)

• Financial Risk Management– Developed independently in 1980s– Value-at-Risk – measure of certain percentile loss

• Asset Liability Management– Impact of interest rate changes on surplus– Duration and convexity – at least two sided metrics

• Enterprise Risk Management– Incorporates all risks facing an organization– Name suggests focus still on managing downside risk

Need for New Emphasis(and Perhaps a New Name)

• ERM is not just managing downside risk

• More on the lines of risk-return tradeoff

• Incorporate portfolio theory

• Combine risk reduction (insuring, traditional risk management) with investing for expected gain

• Need consistent approach for addressing both aspects of financial decision making

Unified Theory of Risk• Unified Theory in Physics – as yet unattained

– Gravitation – Electromagnetism– Strong force (holds atomic nuclei together)– Weak force (responsible for slow nuclear processes)

• Unified Theory of Risk– Speculative risk– Pure risk

• Expand on Friedman-Savage utility function– Concave below current wealth level– Convex above

Current State of Corporate Finance

• For investment decisions– Net present value – invest if positive– Risk adjusted cost of capital

• For reducing risk– Insuring– Hedging– Options to abandon or convert

• If considered by themselves, risk reducing steps would often have a negative NPV

Problems with Risk Measures Used for Adjusted Cost of Capital

• Variance or standard deviation of returns– Treats upside deviation the same as downside– Squares the difference between observation and

expected value

• Semi-variance and semi-standard deviation– Still squares the difference between observation and

expected value

• Portfolio theory– Linear correlation issues

Need an Effective Risk Metric• Metric will be multi-dimensional

– Return (mean, conditional expected)– Variability

• Overall

• Downside

– Probability of particular negative outcome• Amount willing to lose

• Risk of ruin (insolvency)

• Risk of meltdown (adverse external impact)

– Consider qualitative effects (especially for operational risk)

Need for Different Risk Metrics – Corporation

• For a corporation as a whole and rating agencies– Maximum loss would be the stockholders’ equity– Size of any loss larger than that is irrelevant– Portfolio effect is important

• For capital allocation within an organization– Need to consider spillover effects– Loss in one division could consume capital from rest

of organization• Mango’s Capital Hotel example• Rent depends on likelihood of needing capital and amount

Need for Different Risk Metrics –Regulators

• Need to consider all possible losses• What impact would a loss have on external

parties– Counterparties – Long Term Capital Management– Policyholders– Financial market structure

• Loss of confidence• Elimination of segment of market

– Savings and Loan industry– Subprime lenders– Hedge funds

Extreme Event Probabilities• Catastrophic losses impact many areas simultaneously

– Monetary loss itself– Impact on financial markets

• Interest rates• Equity values• Foreign exchange rates

– Can alter market structure• Complex systems• Correlation

– Not a constant– Varies over time– Varies based on position on probability distribution

Copulas• Recognize that correlation varies

across a distribution• Separates joint distribution into

– Marginal distribution of the individual variables

– Interdependency of the probabilities– Venter (2002)

• Many standard copulas• Reality may be more complex than

the mathematics

Black-Scholes Option Pricing Model

Pc = Price of a call option

Ps = Current price of the asset

X = Exercise price

r = Risk free interest rate

t = Time to expiration of the option

σ = Standard deviation of returns

N = Normal distribution function

P P N d Xe rt N dc s ( ) ( )1 2

d P X r t t

d d t

s12 1 2

2 11 2

2

[ln( / ) ( / ) ] / /

/

Black-Scholes Problems

• Based on lognormal distribution of prices• Fine for at-the-money options• Inappropriate for far in- or out-of-the-

money options

Extreme Event Probabilities (2)

• Regime switching approach– Hardy – Equity returns

• Nassim Nicholas Taleb’s work– Fooled by Randomness: The Hidden Role of Chance in the

Markets and Life– The Black Swan: The Impact of the Highly Improbable

Some Other Critical Issues

• What is the value of liquidity?

• Much of finance is based on arbitrage free arguments– What impact do incomplete markets create?– How do we place a value on non-hedgeable risks

• Capital markets for insurance risks

Need for Actuaries and Financial Economists to Work Together on

Next Breakthroughs Both Actuaries and Financial Economists:

Are mathematically inclined

Address monetary issues

Incorporate risk into calculations

Use specialized languages

Each can learn from each other

What Do You Think Will be ASTIN’s Next Greatest

Contributions?