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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 U t , Ct , Pt 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 PsN ( d1) Xert N ( d 2) d 1 [ln( P s / X ) ( r d 2 d 1 t Pc Ps X r t σ N 1/ 2 = Price of a call option = Current price of the asset = Exercise price = Risk free interest rate = Time to expiration of the option = Standard deviation of returns = Normal distribution function 2 / 2 ) t ] / t 1/ 2 Black-Scholes Problems • Based on lognormal distribution of prices • Fine for at-the-money options • Inappropriate for far in- or out-of-themoney 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?