CIA Annual Meeting Assemble annuelle de lICA CIA
CIA Annual Meeting - Assemblée annuelle de l’ICA CIA Annual Meeting Assemblée annuelle de l’ICA June 29 & 30, 2006 ŸLes 29 et 30 juin 2006 Ottawa, Ontario Session INV-1 Stochastic Models 1
CIA Annual Meeting - Assemblée annuelle de l’ICA Session INV-1 Stochastic Models: Would they ever lead you to a different course of action? Session INV-1 Stochastic Models 2
CIA Annual Meeting - Assemblée annuelle de l’ICA 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. Session INV-1 Stochastic Models 3
CIA Annual Meeting - Assemblée annuelle de l’ICA The Question Is: • With the right stochastic analysis, would you actually make a different operational decision than you would without that model? Session INV-1 Stochastic Models 4
CIA Annual Meeting - Assemblée annuelle de l’ICA This session is NOT: • Yet more complex formulas • Debate about the 4 th decimal place of a result • Debate about CTE vs. Percentile vs. some other risk metric Session INV-1 Stochastic Models 5
CIA Annual Meeting - Assemblée annuelle de l’ICA 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. Session INV-1 Stochastic Models 6
CIA Annual Meeting - Assemblée annuelle de l’ICA 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 Session INV-1 Stochastic Models 7
CIA Annual Meeting - Assemblée annuelle de l’ICA Connectedness • Can include traditional random correlation • Could be a formulaic relationship – Positive or negative – Linear, progressive or regressive • Can involve more than two elements Session INV-1 Stochastic Models 8
CIA Annual Meeting - Assemblée annuelle de l’ICA 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. Session INV-1 Stochastic Models 9
CIA Annual Meeting - Assemblée annuelle de l’ICA Model Overview Session INV-1 Stochastic Models 10
CIA Annual Meeting - Assemblée annuelle de l’ICA 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. Session INV-1 Stochastic Models 11
CIA Annual Meeting - Assemblée annuelle de l’ICA 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. Session INV-1 Stochastic Models 12
CIA Annual Meeting - Assemblée annuelle de l’ICA 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. Session INV-1 Stochastic Models 13
CIA Annual Meeting - Assemblée annuelle de l’ICA Model Overview Session INV-1 Stochastic Models 14
CIA Annual Meeting - Assemblée annuelle de l’ICA Model Overview ‘Economic’ generates two random, correlated numbers called Interest. Driver and Job. Driver. Session INV-1 Stochastic Models 15
CIA Annual Meeting - Assemblée annuelle de l’ICA Model Overview Interest. Driver drives Long interest rates, and from there a Yield Curve develops shorter interest rates. Job. Driver drives Employment, which affects Disability Incidence and Recovery, and Life Lapses. Session INV-1 Stochastic Models 16
CIA Annual Meeting - Assemblée annuelle de l’ICA Model Overview Dis. Plan is a Disability Income product with seriatim policy listings and claims. Life. Plan is a seriatim Whole Life insurance module. Session INV-1 Stochastic Models 17
CIA Annual Meeting - Assemblée annuelle de l’ICA Model Overview Dis. Assets and Life. Assets are seriatim listings of fixed assets, to be bought and sold according to cash flow requirements. Session INV-1 Stochastic Models 18
CIA Annual Meeting - Assemblée annuelle de l’ICA Model Overview Dis. Stmt and Life. Stmt are financial statements from these components. Session INV-1 Stochastic Models 19
CIA Annual Meeting - Assemblée annuelle de l’ICA The few formulas: • Interest. Driver and Job. Driver are two Normal(0, 1) random variables with ρ = 0. 5 • Incidence. Multiplier = 1 + 0. 05 x Job. Driver • Recovery. Multiplier = 1 / (1 + 0. 025 x Job. Driver) • Lapse. Multiplier = 1 + 0. 10 x Job. Driver Session INV-1 Stochastic Models 20
CIA Annual Meeting - Assemblée annuelle de l’ICA 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. Session INV-1 Stochastic Models 21
CIA Annual Meeting - Assemblée annuelle de l’ICA Life Claims Volatility Session INV-1 Stochastic Models 22
CIA Annual Meeting - Assemblée annuelle de l’ICA Life Reinsurance • Look at Life Claims volatility • Reflects the mix of sizes in the seriatim data • Reflects volatile lapses as well Session INV-1 Stochastic Models 23
CIA Annual Meeting - Assemblée annuelle de l’ICA Session INV-1 Stochastic Models 24
CIA Annual Meeting - Assemblée annuelle de l’ICA 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. Session INV-1 Stochastic Models 25
CIA Annual Meeting - Assemblée annuelle de l’ICA Life Claims Volatility Some possible reinsurance approaches: 1. 2. 3. 4. Excess $1000 k per life. Excess $500 k per life. 50% Quota Share. Stop Loss above 110% of mean. Session INV-1 Stochastic Models 26
CIA Annual Meeting - Assemblée annuelle de l’ICA Life Claims Volatility • Ignoring reinsurance costs for the moment, look at the 99% of claims in excess of mean on the different programs. Session INV-1 Stochastic Models 27
CIA Annual Meeting - Assemblée annuelle de l’ICA Session INV-1 Stochastic Models 28
CIA Annual Meeting - Assemblée annuelle de l’ICA Life Reinsurance • All produce a reduction in claims volatility. • Which one to choose? Session INV-1 Stochastic Models 29
CIA Annual Meeting - Assemblée annuelle de l’ICA 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: Session INV-1 Stochastic Models 30
CIA Annual Meeting - Assemblée annuelle de l’ICA Life Reinsurance Session INV-1 Stochastic Models 31
CIA Annual Meeting - Assemblée annuelle de l’ICA Life Reinsurance • The expected claims alone isn’t enough. • Must look at claims volatility and capital. • The Quota Share, Excess $500 k and Stop Loss programs produce similar changes in capital. • Yet the premiums run from $3 MM to $59 MM. • ‘More reinsurance’, i. e. the program with the highest reinsurance premium, doesn’t always translate into lower capital. Session INV-1 Stochastic Models 32
CIA Annual Meeting - Assemblée annuelle de l’ICA 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. Session INV-1 Stochastic Models 33
CIA Annual Meeting - Assemblée annuelle de l’ICA Life Investment Strategy Session INV-1 Stochastic Models 34
CIA Annual Meeting - Assemblée annuelle de l’ICA 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 Session INV-1 Stochastic Models 35
CIA Annual Meeting - Assemblée annuelle de l’ICA Comparison of Investment Strategies Session INV-1 Stochastic Models 36
CIA Annual Meeting - Assemblée annuelle de l’ICA 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? ” Session INV-1 Stochastic Models 37
CIA Annual Meeting - Assemblée annuelle de l’ICA Life Investment Strategy • The All Long strategy is mismatched against liabilities. • CALM testing (not shown) confirms worse CALM liabilities with an All Long strategy. Session INV-1 Stochastic Models 38
CIA Annual Meeting - Assemblée annuelle de l’ICA 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. Session INV-1 Stochastic Models 39
CIA Annual Meeting - Assemblée annuelle de l’ICA Life Investment Strategy • With deliberate mismatch: – CALM Liabilities are +$40 – Investment Income are +$4. 1 • A Return of 10. 2% Session INV-1 Stochastic Models 40
CIA Annual Meeting - Assemblée annuelle de l’ICA 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. Session INV-1 Stochastic Models 41
CIA Annual Meeting - Assemblée annuelle de l’ICA Disability Income Session INV-1 Stochastic Models 42
CIA Annual Meeting - Assemblée annuelle de l’ICA 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 Session INV-1 Stochastic Models 43
CIA Annual Meeting - Assemblée annuelle de l’ICA Disability Income – Model A The Economy is ‘Up’ Hence: Low Claims High Interest Session INV-1 Stochastic Models More Jobs Low Claims More Investment More Borrowing High Interest 44
CIA Annual Meeting - Assemblée annuelle de l’ICA Disability Income – Model B High Interest Rates Hence: High Interest High Claims Session INV-1 Stochastic Models Less Borrowing Less Construction and Industrial Investment Less Jobs More Claims 45
CIA Annual Meeting - Assemblée annuelle de l’ICA 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? Session INV-1 Stochastic Models 46
CIA Annual Meeting - Assemblée annuelle de l’ICA Disability Income • To repeat one of the earlier formulas, either: A: Incidence. Multiplier = 1 + 0. 05 x Job. Driver OR B: Incidence. Multiplier = 1/ (1 + 0. 05 x Job. Driver) • Recovery Multiplier also inverted. • All distributions have same mean and same volatility. Session INV-1 Stochastic Models 47
CIA Annual Meeting - Assemblée annuelle de l’ICA Disability Income Some Modeling noise, but profit about $2 MM/yr different. Session INV-1 Stochastic Models 48
CIA Annual Meeting - Assemblée annuelle de l’ICA 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. Session INV-1 Stochastic Models 49
CIA Annual Meeting - Assemblée annuelle de l’ICA Disability Income Model B has higher mode and longer tail. Session INV-1 Stochastic Models 50
CIA Annual Meeting - Assemblée annuelle de l’ICA Disability Income • Capital is 99%ile of total profit variability – reflects new claims, recoveries, payments, and investment volatility. Session INV-1 Stochastic Models 51
CIA Annual Meeting - Assemblée annuelle de l’ICA Disability Income Some Modeling noise, but Capital about $7 MM/yr different. Session INV-1 Stochastic Models 52
CIA Annual Meeting - Assemblée annuelle de l’ICA Disability Income • So, – Same means; – Same distributions; – Change only the economic relationship. • RESULT: – Mean profit is DOWN about $2 MM. – Capital required is UP about $7 MM. Session INV-1 Stochastic Models 53
CIA Annual Meeting - Assemblée annuelle de l’ICA 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. Session INV-1 Stochastic Models 54
CIA Annual Meeting - Assemblée annuelle de l’ICA Other Observations Session INV-1 Stochastic Models 55
CIA Annual Meeting - Assemblée annuelle de l’ICA Other Observations • The paper includes an analysis of whether different Life lapse relationships would change your recommended investment strategy. • The answer is, not much. Session INV-1 Stochastic Models 56
CIA Annual Meeting - Assemblée annuelle de l’ICA 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. Session INV-1 Stochastic Models 57
CIA Annual Meeting - Assemblée annuelle de l’ICA Combined Results Session INV-1 Stochastic Models 58
CIA Annual Meeting - Assemblée annuelle de l’ICA 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. Session INV-1 Stochastic Models 59
CIA Annual Meeting - Assemblée annuelle de l’ICA Combined Results Session INV-1 Stochastic Models 60
CIA Annual Meeting - Assemblée annuelle de l’ICA 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. Session INV-1 Stochastic Models 61
CIA Annual Meeting - Assemblée annuelle de l’ICA Combined Results • If using Claims Model B: – Claims Mean is different – Diversification is different Session INV-1 Stochastic Models 62
CIA Annual Meeting - Assemblée annuelle de l’ICA Combined Results Some Modeling noise, but Capital about $4 MM/yr different. Session INV-1 Stochastic Models 63
CIA Annual Meeting - Assemblée annuelle de l’ICA 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. Session INV-1 Stochastic Models 64
CIA Annual Meeting - Assemblée annuelle de l’ICA Recap Session INV-1 Stochastic Models 65
CIA Annual Meeting - Assemblée annuelle de l’ICA Recap The Question was: With the right stochastic analysis, would you actually make a different operational decision than you would without that model? Session INV-1 Stochastic Models 66
CIA Annual Meeting - Assemblée annuelle de l’ICA Recap • The answer is, there is certainly potential benefit from doing things differently. Session INV-1 Stochastic Models 67
CIA Annual Meeting - Assemblée annuelle de l’ICA 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. Session INV-1 Stochastic Models 68
CIA Annual Meeting - Assemblée annuelle de l’ICA 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. Session INV-1 Stochastic Models 69
CIA Annual Meeting - Assemblée annuelle de l’ICA 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. Session INV-1 Stochastic Models 70
CIA Annual Meeting - Assemblée annuelle de l’ICA Discussion Session INV-1 Stochastic Models 71
- Slides: 71