Viewing Risk Through the Eyes of the Insured

Casualty Actuarial Society March 28, 2003 Viewing Risk Through theEyes of the Insured

Client Considerations on Risk • Traditional, non-analytic approaches • Difference between a claim and a risk are cloudy • Claims in a normal year are a normal expense • Aggregation of annual claims are considered “risk” • Risk is negative variability from expected • Higher retention = higher expected losses retained • Assuming higher levels of retention increases volatility, but it may not be material • Retaining risk and avoiding premium is the reward for accepting the chance of higher claim expense

Client Considerations on Risk • Traditional, non-analytic approaches • Difference between a claim and a risk are cloudy • Claims in a normal year are a normal expense • Aggregation of annual claims are considered “risk” • Risk is negative variability from expected • Higher retention = higher expected losses retained • Assuming higher levels of retention increases volatility, but it may not be material • Retaining risk and avoiding premium is the reward for accepting the chance of higher claim expense Question - Is it a good deal?

Is it Better - in Risk Retention, it Depends • How much premium is saved? • How much the added expected losses? • How much is the added volatility? • What is the value of the added volatility?

Example General Liability $250k Attachment Forecasted retained losses (unlimited) = $5,000,000 Premium = $1,000,000 General Liability $750k Attachment Premium = $500,000 Which is the better deal?

It Depends • What are the losses expected at $250,000 loss limitation? • What are the losses expected at $750,000 loss limitation • What is the relative timing of the loss payments on the differential? • What is the impact of the tax deduction timing?

Example General Liability $250k Attachment Forecasted retained losses (limited) = $3,000,000 Premium = $1,000,000 General Liability $750k Attachment Forecasted retained losses (limited) = $4,000,000 Premium = $500,000 Which is the better deal?

Why Retain Risk? • Avoiding frictional costs • Premium taxes • Insurance company profit/overhead • Risk pooling cost • Risk may be immaterial • Many losses are predictable • Difference in perception of risk

Conventional Wisdom - Bigger is Better • Higher retentions results in lower cost • Higher retentions improve control • Large retentions are good • Buying risk transfer is bad • Problems • Based on different times • Assumes that risk transfer cost avoided results in lower cost • May be true, but objective analysis is required to know

Most Common Ways an Insured Views Retention and Limits Needed • Ratio rules of thumb • Market driven • Premium too high • Management decision based on feel • "Threshold of pain" • "Not a problem - couldn't happen to us" logic • Peer benchmarks

Ratio Rules of Thumb • Various ratios to financial statements added provide an overall risk retention capacity in excess of expected • Problems • Aggregate capacity figure has little practical use • Overly broad • No relationship to premium avoided • Ratios are subjectively set

Market Driven • During hard market, retentions forced up by insurers • Got used to it • No reason for exploring - now used to higher level • Problems • Not based on rational decision • Doesn't measure risk reward • Externally controlled • Assumes status quo is OK • Doesn't lead to least cost decision

Premium Too High • Premium expense not in budget • Quotes too high for perceived benefit • Problems • No objective consideration of risk/reward • Unanticipated claim isn't in the budget • Will stockholders consider the premium too high after a loss?

Management Decision Based on Feel • Decision based on management comfort • Risk Manager can't have a problem based on a directive • Problems • Decision based on reaction rather than objective analysis • Management looks to risk management for input, shouldn't be forced to decide without information • No rational decision can result

Threshold of Pain • Much like decision on feel, just masked as an EPS decision • Same issues as management decision on feel, modified by how the stockholders might react, based on EPS • Problems • Same as prior slide • Ignores transfer savings or expense in the equation

"Not a Problem - Couldn't Happen to us" Logic • Common human response to unlikely event • Ignores probability of losses • Assumes losses happening to others won't occur to me • Assumes past adverse loss experience will not repeat itself • Problems • Irrational • Least cost decision only if lucky

Peer benchmarks • Blind leading the blind? • Assumes others are efficient • Easy fallback - can't be faulted • Problems • Statistically not comparable • Assumes your risks are identical • Accuracy/interpretation of responses • Doesn't measure risk reward relationship

Considering Expected Loss Differences • Retained loss expectancy increases as retention levels increase

Considering Expected Loss Differences • Volatility increases as retentions increase

Risk Retention as an Investment Decision

How can Retaining Risk be an Investment? • When risk is retained, capital is contingently exposed • If losses occur beyond expected, income and net worth both decrease • When net worth decreases, there is an impact to ongoing interest expense • Retaining risk results in a immediate reward - the premium saved • Retention decisions impact other investment opportunities

How can Retaining Risk be an Investment? • When risk is retained, capital is contingently exposed • If losses occur beyond expected, income and net worth both decrease • When net worth decreases, there is an impact to ongoing interest expense • Retaining risk results in a immediate reward - the premium saved • Retention decisions impact other investment opportunities Result - Much like an equity option decision

Equity Option Comparison Put Option on Microsoft Stock price = $25 per share Put option to sell stock at $22.5 expiring January, 2004 Option price on March 25 = $2.25 Option price for $20 strike = $1.35

What Happens? • If stock remains the same or increases, put has no value at expiration, buyer loses $2.25 • Seller of option makes $2.25 • Buyer of option received protection against MSFT decreasing to $20.25 instead of selling it now and losing the upside potential • On the expiration date, coverage expires

Why is this like Retention Decisions? • Owner of stock purchased "protection" for a premium • Covers a defined period • If no loss, the premium is lost • If a loss, buyer of coverage is made whole • Seller of the option contingently exposes their capital to gain the premium in the same way as one who retains risk to avoid premium payment • Over time neither buyer or seller "win", as rational pricing models take into account stock volatility • Credit for $20 strike recognizes lower probability of attaching

Valuing Volatility by Line • Each exposure has its inherent volatility • The more volatile the exposure, the higher the amount of avoided premium needed to assume the exposure • Unlike options, insurance market pricing is individual risk based, and may be more imperfect • Markets may lead to purchasing coverage or avoiding coverage in a non-traditional way

How do you Calculate the Investment Return on Retention? • Calculate the expected losses (the mean) at alternative retentions • Calculate the difference between the 99% confidence interval and the mean • Multiply the difference times a hurdle rate for an investment with a similar risk profile ("risk margin") • Add the expected increase plus the risk margin to calculate the value of the retention • Present value to take into account claim payment and tax deduction timing • Compare to premium difference

Example • m = $7.795M @ $250k • m = $8.123M @ $1M • 99% Confidence = $9.912M @ $250k • 99% Confidence = $10.902M @ $1M • Hurdle Rate = 10% (assumed) • Premium at $250k retention = $548,000 • Premium at $1M retention = $358,000

Step 1 Calculate the expected losses (the mean) at alternative retentions $8.123M - $7.795M .328M

Step 2 Calculate the difference between the 99% confidence interval and the mean $10.902M - $9.912M .990M

Step 3 Multiply the difference times a hurdle rate for an investment with a similar risk profile ("risk margin") $.990M * 10% $.090M

Step 4 Add the expected increase plus the risk margin to calculate the value of the retention $.328M + .090M $.418M

Step 5 Present value to take into account claim payment and tax deduction timing $.418M * .78% $.326M

Step 6 Compare to premium difference $548,000 - $358,000 $190,000

Step 6 Compare to premium difference $548,000 - $358,000 $190,000 Not Good Enough! Must be at Least $326,000

What Rate of Return is Needed? • Internal rate of return? • What if its negative? • Uncertainty of timing • Does the business have the same risk profile? • Short term cost of money? • Borrowing, not investment rate • Debt has no risk profile • Cost of Capital • Investment decision process • Payback period • Impact on stock price?

Question If you have a very profitable organization with numerous investment possibilities, should you retain more or less risk?

Question Should you set higher retentions in a soft market?

It Depends Entirely on Risk - Reward Relationship • If premium avoided is more than the additional loss expectation and a risk margin, then yes • If an insurer is willing to put up their capital at a lower price than your firm, then no

What About Limits Insured? • Much more complex decision • Modeling is less certain in the tail of the distribution • Less (or no) losses in the extremes • Modeling less helpful, as the outcomes are random and wide • Still useful as a guide • Most risk managers revert to the traditional approaches • Most difficult question to answer and may not be answerable in an analytic way

Summation • Retaining more or less risk is not a qualitative decision, its economic • Contingently exposing corporate resources to volatility without a return is irrational • Care must be taken to avoid losing control or decreasing loss and claim control efforts • Must be willing to accept year to year changes in retentions (inconsistent?) • Limits purchased also a risk-reward relationship, but with fewer tools to assess, unlikely to occur and more catastrophic if it does • If you don't consider all possibilities, your replacement will.

Viewing Risk Through the Eyes of the Insured