Pitfalls of Capital Allocation

1. Pitfalls of Capital Allocation Donald Mango, FCAS, MAAA American Re-Insurance CAS 2001 Spring Meeting

2. “The Happy Sholom”

3. Step One: A Single Name • We allocate CAPITAL • And we have Premium-to-SURPLUS • And we talk about Return on EQUITY • We need ONE NAME

4. Step One: A Single Name • SQUAPITAL • SURQUITY • EQUITUS • SQUIRTAL • SCRAPITAL

5. Should We Allocate Capital? • Yes • No • Maybe • Splunge • See Monty Python • It isn’t yes, and it isn’t no, but I’m not being indecisive.

6. Look At All the Benefits • Risk-adjusted performance measurements for products • Strategic insights into the efficiency of our capital management • Determine which activities create shareholder value and which destroy it • SOUNDS GOOD !!

7. What Total Amount Should We Use? • Statutory, Economic, GAAP Equity, RBC, BCAR, S&P? • Static or Dynamic? • Top-Down (true allocation) or Bottom-Up (rolled up from “atomic” level)? • Tied to financials or purely theoretical?

8. Do We Want More or Less? • The Home Office allocates capital to our underwriting division • Do we want MORE or LESS? • Depends on what it represents • Underwriting capacity, Vote of Confidence MORE • Return burden (Subject to a “Hurdle Rate”) LESS • MORE on this later …

9. What About the Bathwater? • Everybody likes to assume a single policy, with dedicated assets, and capital that gets released over time in a nice non-increasing manner, … • Then a single IRR falls out !!! :-) • Forget the actual reserves, current asset portfolio, runoff operations, A&E, steady state, … They just cloud the picture.

10. What About the Bathwater? • But for a steady-state, multi-line carrier with substantial casualty reserves, those reserves can carry the majority of the future calendar year risk • Show of hands - who works for a company that has had material adverse development on prior accident years in the last two calendar years?

11. What About the Bathwater? • What should we do with that reserve (or asset or A&E or runoff) risk? • Ignore it Incomplete, misleading overall picture; throwing away the majority of the risk • Allocate to it Less allocation to prospective business; nobody wants that hot potato burden anyway; but it’s an ongoing maintenance nightmare

12. What’s the “R” in “ROE”? • Risk-adjusted profitability ( RAROC / RORAC / ROE ) needs investment income • Allocate actual or develop theoretical? • Use realized or “promised” yield? • Include investment income on Squirtal?

13. Should It Be a Zero Sum Game? • If Total Surquitus decreases, all our LOB ROE’s go up, and vice versa. • We can adjust the hurdle rates, but that sensitivity response doesn’t inspire confidence • We increase our risk assessment of LOB1  LOB1 gets more Capital • But the others get less (zero sum), which increases their ROE’s • Has our view of their profitability changed?

14. What About the Risk Measure? • We want to know each segment’s contributions to “Total RiskTM” • Anybody define “Risk” yet? • First we select one of many fine available measures: • Prob of Ruin, Std Dev, Variance, EPD, VaR, CVaR, TVaR, Tail Conditional Expected Value, Default Loss Rate, … • Which one do we choose?

15. What’s the Relative Contribution? • Each segment’s contribution to “Total RiskTM” • Many marginal methods: • Swap-in-and-out a.k.a. “Last-In” • Stand-alone a.k.a. “First-In” • Build up the portfolio one segment at a time a.k.a. “Need an Entry Order” • Which one to choose? Does it even matter?

16. What About Order Dependency? • Any of the marginal methods, using any of the probabilistic risk measures, will face the same issue: • Each marginal method implies a certain order of entry into the portfolio • And all the risk measures are order-dependent

17. What About Order Dependency? • Fact of life with most popular actuarial risk measures • Many consider it an “annoyance” to be normalized or re-balanced away… • But it is symptomatic of decomposition of an aggregate distribution into its component distributions • Especially problematic when there is a dependency structure

18. What About Order Dependency? • Underneath lie politically loaded issues of ALLOCATION • Covariance SharingTM • How do we split the impact of a dependency relationship between segments? • My Brain Hurts!!

19. Self-Serving Advertisement • “An Application of Game Theory: Property Catastrophe Risk Load” • 1998 Proceedings • Available on the CAS website: www.casact.org/pubs/proceed/proceed98/index.htm • Frames the problem more rigorously and provides a possible solution

20. But The Benefits... • Risk-adjusted performance measurements for products • Strategic insights into the efficiency of our capital management • Determine which activities create shareholder value and which destroy it

21. But The Benefits... • Risk-adjusted performance measurements for products • An ILL-POSED PROBLEMAnybody define “Risk” yet?

22. But The Benefits... • Strategic insights into the efficiency of our capital management • More on this in a minute… • Determine which activities create shareholder value and which destroy it • Russ showed you can get your arms around that without using allocated capital

23. Now It Gets Weird

24. Where Did We Get This Idea? • “Das Kapital” = Means of Production • “Capital” in a “Spend-then-Receive” industry • Costs are current, well known • Revenues are future, unknown • Sink Costs now  hope for Revenues later • Capital “Allocation” means spending available cash for Production (and Distribution) Capacity

25. “Spend-then-Receive” Industry • No issues about whether we want MORE or LESS capital -- We want MORE • No issues about which total amount to use -- it’s CASH ON HAND • No issues about mismatched allocation abstracted over time -- The money funds current production efforts

26. “Receive-then-Spend” Industry • Insurance is a “Receive-then-Spend” industry • Revenues are current, well known • Costs are future, unknown • Take Revenues now  hope Costs aren’t too high/soon • Our business model requires no CAPITAL EXPENDITURE for production - our “production” is revenue collection !!

27. “Receive-then-Spend” Industry • For current underwriting activities, what we are really allocating (spending) is FUTURE CAPITAL • Current Capital is already spoken for by the reserves !! • Given this fundamental difference, should we even attempt insurance capital allocation?

28. Can Capital Be Meaningfully Atomized? • Concept comes from Ancient Greece (Leucippus, Democritus) • Decompose a “Whole” into its component parts--“atoms” • Dangerous mental framework • Becomes the hammer looking for nails • Every thing (!!!) we analyze must be decomposable into meaningful subsets, right? • That’s the road that leads to all the trouble

29. Can Capital Be Meaningfully Atomized? • Quantum Physics pulled down the whole “atomic” framework • Yet 100 years later the full impact of this revolution / evolution in thinking has not soaked in • The Physicists are in line with the Taoists • Gary Zukav, “The Dancing Wu Li Masters” • Fritjof Capra, “The Tao of Physics”

30. Can Capital Be Meaningfully Atomized? • Capital is a FLOW PHENOMENON that only exists at the Portfolio level • We must resist the urge to decompose • We don’t reserve at the policy level • Butsic, 2000 Reinsurance Call Paper, atomizes capital and default …

32. Call Ourselves “Insurings” • Use gerunds to describe flows • Nouns in motion • Many of the problems we have considered here are results of assessing a flow situation using imperfect, mismatched, static measures and practices

33. Call Ourselves “Insurings” • Capital is a living buffer that is fed by current activities and depleted by prior activities • Amounts move in and out of it all the time • It only exists and has meaning in total • “A jar of water is not a river”

34. Allocating Flows? • Do we allocate Life to the various bodily organs? • First-in, Last-in, order dependency… INSANITY • Can we allocate Health to food, drink, rest, warmth, vitamins, exercise, prayer, …? • Dissection  a cut-up frog on a table is not a living frog

35. Yes, I Had an Agenda • I came to BURY capital allocation, not praise it • Nor rehabilitate it • Instigate, yea, even rouse the rabble • “Catalyze discussion”

36. “What I tell you three times is true.”- Nasrudin