1. CIA Annual Meeting Assemblée annuelle de l’ICA
June 29 & 30, 2006 Ÿ Les 29 et 30 juin 2006
Ottawa, Ontario

2. Session INV-1
Stochastic Models: Would they ever lead you to a different course of action?

3. Objective Today
The profession is developing complex models for investments, claims, and so on.
Such models are being widely used in setting liabilities and capital.
These are reporting tools than operational tools.
These tools affect operations only to the extent companies set up appropriate liabilities and capital.

4. The Question Is:
With the right stochastic analysis, would you actually make a different operational decision than you would without that model?

5. This session is NOT: Yet more complex formulas
Debate about the 4th decimal place of a result
Debate about CTE vs. Percentile vs. some other risk metric

6. Approach Used
A comprehensive company-wide stochastic model was developed.
That is, seriatim lists of in force and sales along with rates of lapse, mortality, disability, recovery, investment activity were modeled.
The model is run forward to get projected claims, reserves, expenses and profits under thousands of scenarios.

7. Approach Used
A key point is the ‘Stochastic Connectedness’ of key risk drivers
‘Connectedness’ is more than just correlation in the textbook sense of the term
Depending on the form of Connectedness, you get different decisions about the optimal business strategy

8. Connectedness Can include traditional random correlation
Could be a formulaic relationship
Positive or negative
Linear, progressive or regressive
Can involve more than two elements

9. Major Conclusions
The right reinsurance program can give you more capital relief for less cost.
A deliberate investment mismatch can produce better returns and lower CALM reserves.
The right liabilities and capital for Disability Income depends on your view of the relationship between claims and interest rates.

10. Model Overview

11. Model Overview
A more complete description is available in a separate paper.
Many of the connections are admittedly simple-minded.
Despite this, they indicate the importance about the nature of the connectedness.

12. Model Overview
The model serves its purpose because it demonstrates which connections matter and which don’t matter so much.
The next step is therefore further study about the connectednesses that matter.

13. Model Overview This is a two-product company selling:
Conventional whole life with cash values, and
Disability Income insurance.
The next chart shows the connections.

14. Model Overview

15. Model Overview
‘Economic’ generates two random, correlated numbers called InterestDriver and JobDriver.

16. Model Overview
InterestDriver drives Long interest rates, and from there a Yield Curve develops shorter interest rates.
JobDriver drives Employment, which affects Disability Incidence and Recovery, and Life Lapses.

17. Model Overview
DisPlan is a Disability Income product with seriatim policy listings and claims.
LifePlan is a seriatim Whole Life insurance module.

18. Model Overview
DisAssets and LifeAssets are seriatim listings of fixed assets, to be bought and sold according to cash flow requirements.

19. Model Overview
DisStmt and LifeStmt are financial statements from these components.

20. The few formulas:
InterestDriver and JobDriver are two Normal(0,1) random variables with ρ = 0.5
IncidenceMultiplier = x JobDriver
RecoveryMultiplier = 1 / ( x JobDriver)
LapseMultiplier = x JobDriver

21. The few formulas:
Numbers of claims, recoveries, deaths, and lapses are generated with Binomial distributions reflecting:
The seriatim policy lists;
Tables of base rates, which are;
Multiplied by the factors on the previous slide.

22. Life Claims Volatility

23. Life Reinsurance Look at Life Claims volatility
Reflects the mix of sizes in the seriatim data
Reflects volatile lapses as well

25. Life Claims Volatility
Profit on this business is about $50 MM/yr.
A claims swing from the mean to 99%ile is about $40 MM, which is too much.
So, some risk mitigation is probably desired.

26. Life Claims Volatility
Some possible reinsurance approaches:
Excess $1000k per life.
Excess $500k per life.
50% Quota Share.
Stop Loss above 110% of mean.

27. Life Claims Volatility
Ignoring reinsurance costs for the moment, look at the 99% of claims in excess of mean on the different programs.

29. Life Reinsurance All produce a reduction in claims volatility.
Which one to choose?

30. Life Reinsurance
In the modeled-capital world, capital requirement is 99%ile minus mean.
So, “savings” from reinsurance equals your cost of capital times this reduction in capital.
Taking first year only, the comparison is:

31. Life Reinsurance

32. Life Reinsurance The expected claims alone isn’t enough.
Must look at claims volatility and capital.
The Quota Share, Excess $500k and Stop Loss programs produce similar changes in capital.
Yet the premiums run from $3MM to $59MM.
‘More reinsurance’, i.e. the program with the highest reinsurance premium, doesn’t always translate into lower capital.

33. Life Reinsurance
To manage the tail risk and/or capital, you might want a very different type of reinsurance program.
Capital Reduction is near-best; Premium is least by large margin.

34. Life Investment Strategy

35. Life Investment Strategy
As noted, the model has seriatim investments, new investment/divestment, fluctuating yield curves and volatile claims.
Might this affect your investment strategy?
Take two Strategies:
All purchases are Long Bonds
Purchases are a mix of Medium and Long Bonds

36. Comparison of Investment Strategies

37. Comparison of Investment Strategies
The All Long strategy has a better mean AND better percentiles. i.e., no apparent downside,
“So what? Of course All Long has better yields.”, you say. “This is news?”

38. Life Investment Strategy
The All Long strategy is mismatched against liabilities.
CALM testing (not shown) confirms worse CALM liabilities with an All Long strategy.

39. Life Investment Strategy
The point is, by quantifying the impact of the mismatch, you can decide whether to trade off possible higher liability requirements against the possible higher returns.
It might be financially advantageous to hold higher liabilities to get the additional yield.

40. Life Investment Strategy
With deliberate mismatch:
CALM Liabilities are +$40
Investment Income are +$4.1
A Return of 10.2%

41. Life Investment Strategy
Or, do CALM testing with Stochastic Investment Yields.
Result is lower CALM liabilities.
The only ‘downside’ is the additional effort and computer time of additional testing.

42. Disability Income

43. Disability Income
Different reinsurance and investment strategies can be analyzed similarly. Examples are given in the separate paper.
With disability products, can also consider the relationship among the economy, yield rates and employment rates

44. Disability Income – Model A
More Jobs  Low Claims
The Economy is ‘Up’
More Investment  More Borrowing  High Interest
Hence: Low Claims High Interest

45. Disability Income – Model B
High Interest Rates
Less Borrowing
Less Construction and Industrial Investment
Hence: High Interest  High Claims
Less Jobs  More Claims

46. Disability Income So, either:
High interest is correlated with High claims, OR
High interest is correlated with Low claims
What is the impact of these two assumptions?

47. Disability Income To repeat one of the earlier formulas, either: OR
A: IncidenceMultiplier = x JobDriver OR
B: IncidenceMultiplier = 1/ ( x JobDriver)
Recovery Multiplier also inverted.
All distributions have same mean and same volatility.

48. Disability Income
Some Modeling noise, but profit about $2MM/yr different.

49. Disability Income
If all distributions have same mean, why is mean profit different?
Because losses are asymmetric.
That is, the distribution of results is skewed.
Upsides and downsides do not, on average, merely offset.

50. Disability Income
Model B has higher mode and longer tail.

51. Disability Income
Capital is 99%ile of total profit variability – reflects new claims, recoveries, payments, and investment volatility.

52. Disability Income
Some Modeling noise, but Capital about $7MM/yr different.

53. Disability Income So, RESULT: Same means; Same distributions;
Change only the economic relationship.
RESULT:
Mean profit is DOWN about $2MM.
Capital required is UP about $7MM.

54. Disability Income Conclusion:
It is worth some further study to understand the correlation or possible time lags between interest rates and Disability incidence and recovery.

55. Other Observations

56. Other Observations
The paper includes an analysis of whether different Life lapse relationships would change your recommended investment strategy.
The answer is, not much.

57. Other Observations
The paper also looks at how your growth and claims expectations on Disability Income can affect your investment strategy.
Again, the conclusion is, not much.

58. Combined Results

59. Combined Results
The model described above has rational economic relationships.
i.e., lapse and DI claims rates correlated with employment and investment metrics.
Total capital can be determined by looking at percentiles of combined profits.
That total can be compared to stand-alone capital requirements.

60. Combined Results

61. Combined Results
‘Combined Capital’ is determined by looking at percentiles of combined profit across all scenarios.
‘Sum Life + Dis’ is determined by looking at percentiles of Life and Disability profits separately.
Diversification reduces capital required by about $27 million on average.

62. Combined Results If using Claims Model B: Claims Mean is different
Diversification is different

63. Combined Results
Some Modeling noise, but Capital about $4MM/yr different.

64. Combined Results
Per earlier slide, Model B required an additional $7 MM of capital on a stand-alone basis, i.e., in isolation.
Yet requires only $4 MM more capital when diversified with a Life product.
So, not only are claims different, but the diversification benefit is different with different economic models.

65. Recap

66. Recap The Question was:
With the right stochastic analysis, would you actually make a different operational decision than you would without that model?

67. Recap
The answer is, there is certainly potential benefit from doing things differently.

68. Recap Life Reinsurance:
Traditional Excess Per Life and Quota Share reinsurance are probably the least effective ways to manage volatility.
An excess of loss treaty reduces volatility much more at a lower reinsurance price.

69. Recap Investment Strategy:
There are demonstrable benefits from a deliberate mismatch strategy.
Stochastic Modeling can quantify whether this is worth the additional liabilities to be held, or
Stochastic Interest CALM testing can reduce your CALM requirements.

70. Recap Disability Income: Losses are asymmetric.
Average results depend on your view on the connection between interest rates and claims.
Even your benefits of diversification depend on your view of the connection between interest and claims.

71. Discussion