Viewing Risk Through the Eyes of the Insured March 12, 2004 Casualty Actuarial Society

2 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

3 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?

4 Is It Better – in Risk Retention, It Depends n How much premium is saved? n What is the difference in expected losses? n How much volatility is added? n What is the value of the added volatility? n What parts of the financial equation are impacted?

5 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?

6 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?

7 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?

8 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

9 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 Test for effectiveness: If the worst case happens, will you still be employed?

10 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

11 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

12 Market Driven During hard market, retentions forced up by insurers Got used to it - the bad thing didn’t happen No reason for exploring - now used to higher level and management understands Problems – Not based on rational decision – Doesn't measure risk reward relationship – Externally controlled – Assumes status quo is OK – Doesn't lead to least cost decision

13 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?

14 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

15 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 – Sounds more scientific - it isn’t

16 " 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 by luck only - rolling the dice

17 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

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

19 Considering Expected Loss Differences Volatility increases as retentions increase

Risk Retention as an Investment Decision

21 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

22 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

23 Equity Option Comparison Put Option on Microsoft Stock price = $25 per share Put option to sell stock at $22.5 expiring January, 2005 Option price on March 11 = $2.25 Option price for $20 strike = $1.35

24 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

25 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

26 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

27 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

28 Example  = $250k  = $1M 99% Confidence = $250k 99% Confidence = $1M Hurdle Rate = 10% (assumed) Premium at $250k retention = $548,000 Premium at $1M retention = $358,000

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

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

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

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

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

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

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

36 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?

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

38 Question Should you set higher retentions in a soft market?

39 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

40 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

41 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 is 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.