Session 71 PD, Actuarial Risk for Deferred and Indexed Annuities — Considering Dynamic Policyholder Behavior

Moderator:

John L. Blocher, FSA, MAAA

Presenters: John L. Blocher, FSA, MAAA Michael Kwan Yu Chan, FSA

Karthik M. Yadatore, ASA, MAAA

71PD Actuarial Risks for Deferred and Indexed Annuities - Considering Dynamic Policyholder Behavior

John L. Blocher, FSA MAAAKarthik M. Yadatore, ASA MAAA

Michael Chan, FSA

1. Statutory View: Reserve Assumptions

2. Key Risk Drivers and Risk Management

3. Research on Policyholder Behavior

Agenda

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John L. Blocher, FSA MAAA

• Originally, fixed deferred annuities had limited additional benefits. Contract owner received interest credits, eventually taking withdrawals or annuitizing for retirement income.

1. Added Waiver-of-surrender-charges and Return of Premium (ROP) on withdrawal.

2. Added Guaranteed Lifetime Income Benefits (GLIBs) and Guaranteed Minimum Death Benefits (GMDBs).

Historical Background

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• Waiver makes available the account value by waiving surrender charges after an incidence defined in the contract form.

Common Waivers: Disability, Nursing Home Confinement, Critical Illness, Terminal Illness, Inability to perform enough Activities of Daily Living.

• Contract owner may take none, some or all the account value (contract may have limitations).

• It is assumed the available benefit is collected.

Waiver-of-Surrender-Charges

6

• ROP pays on a full surrender purchase payments less any prior withdrawals.

• Created when it would not take long to credit the remaining surrender charge. Effect extends during a low interest rate environment.

Provides a clue that we may have to rethink annuities when external conditions change.

• ROP can also act as a “downgrade trigger” for liquidity planning purposes.

Return of Premium (ROP)

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• GLIB may be a rider or built-in to a fixed annuity contract with explicit or implicit charges.

• Benefit Base may increase annually based on a set percentage (x%) or addition (x% + i) or a multiplier to credited interest (m*i, m=>100%).

• Payout Factors vary by single or joint and are not necessarily actuarially equivalent.

• Lifetime income amount at exercise is set as Benefit Base multiplied by a Payout Factor.

Guaranteed Lifetime Income (GLIB)

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• GMDB may be a rider or built-in to a fixed annuity contract with explicit or implicit charges.

• Benefit Base may increase annually based on a set percentage (x%) or addition (x% + i) or a multiplier to credited interest (m*i, m=>100%).

• Benefit Base may be capped or grow slower compared to a GLIB Benefit Base and usually decreases proportionately on withdrawals.

• Death Benefit amount is the Benefit Base.

Guaranteed Minimum Death (GMDB)

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• To avoid having a death benefit active after the account value is depleted the GMDB Benefit Base proportionately decreases on any withdrawal including withdrawals from GLIB exercise if both benefits are present.

Providing a clue that extra care is required when GLIBs and GMDBs are combined in a contract.

• Positive GMDB after AV is depleted might be viewed as a paid-up life insurance policy.

GMDB – Proportional Decrease

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• We’ve seen how the ROP effect extends during low interest compared to high interest rates.

• We’ve seen how a GMDB has to be carefully designed to work with a GLIB.

• What about Waiver and a GLIB and/or GMDB in the same contract? Waiver is a small benefit and relatively tame so mixing these benefits couldn’t possibly cause a reserve issue, right?

Bolting to the Reserve Chassis

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• If account value is depleted no contract owner will collect a waiver benefit after an incidence.

Nothing to collect. • If account value and cash value are the same

few contract owners will collect a waiver benefit after an incidence due to required forms.

Nothing extra to collect compared to surrender.See the “AG33 Non-Elective Incidence Reserve Proposal” report from the AAA for a full discussion.

Waiver and a GLIB and/or GMDB

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In simplified and approximate terms to illustrate:• Reserve = γ * AV + (1–γ) * Max PV Elective,

where γ = incidence rate 1. AV=0: Reserve = γ*0 + (1-γ) * Max PV Elective2. AV<Max PV Elective: Reserve = γ * (< Max PV

Elective) + (1-γ) * Max PV Elective3. In both situations, Reserve < Max PV Elective.

• Waiver may also affect optimal GLIB exercise year and corresponding annual GLIB payment.

Why the Effect in AG33?

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• Current revised proposal is that non-elective non-mortality benefits are split into two benefits.

• First is non-elective (use incidence table) representing probability incidence occurs (γ).

• Second is conditional on the first, treated as elective (test 0-100%) representing probability benefit is actually paid (ω). Benefit is assumed paid only when its PV => than Max PV Elective.

In practice either 0% or 100% will occur.

Subsequent Discussion

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• AV n < Max PV Elective n , therefore ωn = 0• Reserve = γ*ω*AV + (1–γ*ω)*Max PV Elective,

where γ = incidence rate, ω = benefit paid rate• Reserve = 100 = .05*0*99 + (1-.05*0)*100

Illustrative Example 1

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Variable Values Max

Waiver Incidence n = γn 5% ‐‐‐‐‐‐

Cash Value n 95

PV (Non‐Elective Non‐Mortality Benefit) = AV n 99

Max PV (Elective) n Ignoring non‐elective non‐mortality benefits 100 <<<

• AV n => Max PV Elective n , therefore ωn = 1• Reserve = γ*ω*AV + (1–γ*ω)*Max PV Elective,

where γ = incidence rate, ω = benefit paid rate• Reserve = 101 =.05*1*120 + (1-.05*1)*100

Illustrative Example 2

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Variable Values Max

Waiver Incidence n = γn 5% ‐‐‐‐‐‐

Cash Value n 95

PV (Non‐Elective Non‐Mortality Benefit) = AV n 120 <<<

Max PV (Elective) n Ignoring non‐elective non‐mortality benefits 100

• Current assumption is contract owner alwayshas another qualified source from which to take Required Minimum Distributions (RMDs) beginning at attained age 70.5.

Implicitly assumes annuity is “stacked” last for withdrawal and never touched for RMD purposes.

• It may be more accurate to assume pro-rata RMD withdrawals from all qualified sources.

Current plan is to address this issue in VM-22.

Other Issues: Qualified Contracts

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• Joint GLIB is frequently more favorable to the single contract owner than a single GLIB and usually available for single ownership contracts.

Assuming they have someone for a joint payout• Most actuaries “follow the ownership” ignoring

the unexercised joint GLIB when the contract has a single owner. To calculate, make an assumption for a second person in a joint GLIB.

Current plan is to address this issue in VM-22.

Other Issues: Joint GLIB

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• Don’t let building a statutory reserve become a lost art! Actuaries sometimes “code-up” all the benefits at once and then perform valuation run.

It is easy for a reserve to look reasonable that isn’t.• Start with the most basic product possible to

calculate and add benefits checking whether reserves change as expected on each one.

Investigate anomalies. Sometimes an effect won’t be obvious without some digging.

Building a Statutory Reserve (Static)

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• Tendency to focus on time 0 (at issue) reserves attempting to reduce initial surplus strain. Projecting reserves throughout the contract lifecycle can be enlightening.

These different effects become visible with analysis.• To perform a simple analysis you need:

1. Ability to calculate reserves at future time points.2. Assumption for interest credited.3. Other assumptions depending on purpose.

Lifecycle Reserves (Dynamic)

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Karthik M. Yadatore, ASA MAAA

1. Primary Risk and Value Drivers

2. Policyholder Behavior

3. Risk Management Strategies

4. Valuation Topics

Main Talking points

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• Minimum guarantee credited ratesCap, participation and spread rates

• GLB FeaturesLessons learned from VA space, Roll-up rate, roll-up period, payout rates, $ for $ or pro rata reduction to GLB face upon discretionary withdrawals

• Additional Options provided to policy holderAdditional income due to confinement, spousal continuation, extension options, DB options, reset and step-up to rider face amount

• Policyholder behavior assumptionsInteraction between interest credited on base contract and rider benefits, GLWB utilization assumptions

• Statutory Reserve LevelsFormulaic reserves without any provision for lapses, utilization rates and realistic index growth levels, extremely onerous as richness of benefits and options provided to policy holder increase

Key Risk and Value Drivers

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• Common / Prevalent assumptions for lapseFunction of SC, MVA, Credited Rate vs. Competitor Rate, ITM of GLB and DB benefits

• Credited Rate vs. Competitor RateDoes policyholder compare declared cap rate to those prevalent in market, or to actual index performance

• GLB utilization assumptionsCommon practice is based on ITM of GLB and DBs, however policyholder don’t always make rational decisions

• Alternatives methodsBased on experience arrive at cumulative probability distribution based on attained age etc. and perform random draw based on attained age in projection period

Policyholder Behavior

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Consider Predictive Modeling as an alternative method

• Instead of traditional techniques, use more rigorous statistical methods

• Companies are either outsourcing this work or building their own staff for this purpose. Such staff typically have statistical and/or data mining credentials.

• With ORSA around the corner, rigorous treatment of PHB will be required in order to further justify that capital is sufficient, both now and in the future. Predictive modeling is one technique that companies can use in order to get further rigor around the modeling process.

• Lack of experience during rising interest rate environment or for GLB utilization means directly reaching out to policyholders via surveys etc. Use answers from the survey to further tweak the predictive model.

Policyholder Behavior Continued…

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• Product DesignAdditional fees for additional options and rider benefits will not suffice to fund benefits since it is a drain on account value. Dial down richness of benefits.

• ReinsuranceA possible solution to pursue a more aggressive investment strategy and hence increase expected return.

• HedgingCurrent practice is to hedge only the base indexed annuity contract for credited rate. Very few companies hedge the GLB rider benefits.

• ALMIn the absence of hedging, ALM plays a key role in GLB rider costs funding. Duration matching is most commonly employed. However based on policyholder behavior assumptions used, liability cash flows can be very convex, there by duration matching may not be sufficient. Hence importance of policyholder behavior assumptions is again highlighted.

Risk Management Strategies

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Hedging for index based interest credited: • Some companies use static, others use dynamic. • Typically, larger and more sophisticated companies are more open to using dynamic hedging. • There’s probably not much value in dynamically hedging vanilla option types, but in some of the

more exotic types, dynamic hedging offers the opportunity to save some costs relative to OTC pricing.

Why hedging of indexed annuity GLB exposure is not prevalent: • In VA world, most companies use delta hedging with some amount rho and vega hedging. This is

appropriate since most of the risk is equity driven.• Less equity risk exposure in indexed annuity since credited rate is floored at zero.• Cost of funding is primarily driven by the available option budget and resulting index participation

levels. Hence interest rate risk is key which is addressed via ALM.• Index annuity GLB rider reserve need to be on a fair value which will result in a mismatch between

hedge income and reserve released.

Risk Management Strategies Cont..

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Statutory reserving and accounting: Already addressed by John

GAAP Accounting:• Option budget method is most prevalent when calculating FAS133 reserves on base

contract.• Are policyholder behavior assumptions incorporated when calculating host interest

rate?• Are rider charges deducted from account value projections when calculating VED?• Are funds in the fixed bucket treated separately on an FAS97 basis?• What is the reserving basis for rider benefits? Most companies employ SOP03-1 since

benefits levels are driven by account value. Account value growth is greatly influenced by management actions / credited rate strategy as opposed to purely driven by index levels.

Valuation Topics:

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Michael Chan, FSA

SOA research on policyholder behavior

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The purpose of this research is to educate actuaries and other interested parties on current actuarial practices around setting and applying dynamic policyholder behavior assumptions by:

1. Surveying and evaluating current practice in light of recent available research on the subject; and

2. Assessing the methods and application of setting dynamic policyholder behavior assumptions.

Another important purpose of this research was to identify new approaches or techniques used in other industries that:

1. Might be applied to insurers; and

2. Provide insights into enhancing current actuarial practice.

“…Dynamic policyholder behavior is becoming an important aspect of modeling life insurance and annuity cash flows.”

Request For Proposal, Society of Actuaries, 2012

https://www.soa.org/Research/Research‐Projects/Life‐Insurance/research‐2014‐modeling‐policy.aspx(or search “SOA modeling of policyholder behavior”)

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Reviewed over 100 articles, papers and books in the following general areas:

1. Academic2. Actuarial3. Industry

An electronic survey with over fifty questions was sent to over 100 life & annuity companies

Conducted in-depth qualitative interviews with:1. 9 Life insurance companies2. 3 P&C insurance companies3. 3 Non-insurance companies

Literature Review

1

Quantitative Questionnaire

2

Qualitative Interviews

3

Survey design

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46 Participants

46 Participants

40Life Insurance

Companies

40Life Insurance

Companies

6Non-Life Insurance

Companies

6Non-Life Insurance

Companies

8Large Size Companies

8Large Size Companies

12 Medium Size Companies

12 Medium Size Companies

20Small Size Companies

20Small Size Companies

3P&C Insurance

Companies

3P&C Insurance

Companies

3Non-Insurance

Companies

3Non-Insurance

Companies

Total Life direct premiums and Annuity asset under management:

Less than $9 billion

Total Life direct premiums and Annuity asset under management:

Greater than $9 billion and less than $50 billion

Total Life direct premiums and Annuity asset under management:

Greater than $50 billion

Top 10 P & C insurance companies as measured by premium Focus was on personal lines (i.e.,

home owners and auto)

Large bank

Large industrial company

Large consumer staples

12 with EIAs12 with EIAs

Profile of Survey Participants

1. The life insurance industry is behind the P&C insurance industry and other industries in using advanced analytical techniques to understand their customers (i.e., policyholders).

2. Actuaries have a very good quantitative understanding of policyholder behavior using traditional actuarial techniques, but often only a second-hand qualitative understanding.

3. Significant movement has been made in recent years toward a formal assumption setting process across a broad range of insurer functions, in some cases including those outside the actuarial area.

4. Data quality and credibility are a primary source of impediment to implementing greater dynamism in assumption setting and modeling.

5. Data sources are nearly universally limited to insurer experience data whether internal, industry or reinsurer sourced.

6. Level of financial efficiency of the policyholder is considered by nearly all companies in assumption development.

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Survey Key Findings

Note: The following results are based company responses around their EIA products. There were not enough responses received for EIA products with GLWB riders for us to disclose those results.

Overview• Dynamic assumptions were mostly commonly used for modeling surrenders• Other dynamic assumptions include renewals/future deposits, and utilization. • Overall, static assumptions are much more prevalent, but the introduction of GLWB riders has led

to more dynamic modeling.• For surrenders, companies were evenly divided between using static assumptions, dynamic

assumptions, or both. This decision is often driven by the purposes (e.g. pricing versus valuation) and resource/data constraints.

Drivers of dynamic behavior• For surrenders, often it’s ‘moneyness’: account value to benefit base or guaranteed payments. • Another factor is interest rates, with various of credited rates versus competitor rates, and external

interest rates and comparisons to fixed payout policies. • Recent returns may impact policyholders’ fund transfer and election decisions?

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EIA Key Findings

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0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

16.0%

1980 1990 2000 2010

U.S. Ten Year Treasury RatesEIA products have become increasinglycomplex, and have given policyholders moreflexibility in making choices.

To complicate the situation further, theseproducts have been sold during a prolongedperiod of steadily declining interest rates andinflation rates.

Thus, a significant challenge confronting theactuarial profession is how policyholders willbehave under different environments:

• Surrenders under rapidly increasing interestrates? Or prolonged low interest rates?

• When will policyholders begin withdrawals?

• Behavioral differences between buyers ofGLWB riders versus traditional contracts?

• Where do EIAs stand in terms of a source ofliquidity, relative to other assets?

Addressing a challenge

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“I’m curious how assumptions have been developed for situations where there is absolutely no experience (including industry experience) at all”.

Data credibility

“… we’ve got a fair bit of data on actual lapses during a level and falling rate environment. Rapidly increasing rates are more what we’re keyed on at the moment.”

Data credibility

“We’ve heard a fair bit about predictive modeling… On the surface this would seem hard to model in a stochastic environment?”

More sophisticated methods

“What should actuaries do in situations where we believe a variable will be a predictor of behavior, but we have limited or no experience? ” 

Getting to the real drivers

Quotes used with permission. Thank you to Glen Reineke, Thad Dawson and Daniel Van Gerpen for raising the questions.

SOA Assumption Discussion Group

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What are the limitations of our current practice?

• Companies have put a lot of reliance on historical averages, and many failed to anticipate how policyholders behave under different circumstances;

• At the same time, data credibility is often cited as a limiting factor – we often don’t even have the data.

How does predictive analytics fit in?

• Predictive modeling can make better use of the data by accounting for more variables than traditional modeling.

• It can also be useful in determining the interaction effects between variables.

• However, predictive modeling relies on historical correlations to predict future results, without including the actual drivers behind a policyholder's decisions.

• The predictive power of statistical models significantly decreases when there is a broad shift in the environment, and over longer time horizons (3-5 years).

“[Predictive modeling] is designed to rank individuals by their relative risk, but not to adjust the absolute measurement of risk when a broad shift in the economic environment is nigh.”

Eric Siegel, Predictive Analytics: The Power to Predict Who Will Click, Buy, Lie or Die, Wiley (2013).

Predictive Analytics

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Viewing our customers as a member of society and part of a household switches the focus on:

• The composition of that household and how it changes over time;

• The life events that take place in the household such as having children;

• The household’s income, spending,and savings habits;

• The type of assets the household owns and the liabilities the household owes; and

• The choices the household makes, both rational and behavioral.

Life Events• Getting married• Buying a house• Having a child• Retiring

Income Statement• Salary• Expenses

1. Nondiscretionary 2. Discretionary 3. Health costs

Balance Sheet• Assets

1. Home2. Financial assets

• Liabilities1. Mortgage2. Personal debt

Choices• Rational• Behavioral

1. Mental accounting2. Joint decision

making3. Financial literacy

Understanding Our Customer

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The goal is to understand how life events and the choices an individual make change over time such as when:1. He or she graduates from

college and gets a job;2. He or she marries;3. They buy a home and have

children;4. They become “empty

nesters”; and5. They retire.

Dependents Single & ‘Rich’ Growing Family Pre-Retiree Retiree New Generation

Liability Creation

Asset Transfer

Asset Creation Asset Creation

Asset Protection

Asset Preservation

Asset Depletion

Pol

icyh

olde

r Life

-Cyc

le S

tage

sLife Events

Adv

ice

Asset Cycle

• Paying off student loans

• Starting a career

• Paying off student loans

• Starting a career

• Getting married

• Buying a home

• Having  or adopting children

• Getting married

• Buying a home

• Having  or adopting children

• Paying tuition bills

• Caring for parents

• Planning for retirement

• Paying tuition bills

• Caring for parents

• Planning for retirement

• Withdrawal money for retirement

• Paying for health care

• Creating a legacy

• Withdrawal money for retirement

• Paying for health care

• Creating a legacy

Life events change the individual’s understanding of themselves and their relationship to others and to the environment.

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Micro-scale modelsAgent-based models simulate individuals, and their decisions and interactions, to re-create and predict the macro-level behavior.

Solves a broad class of problemsAgent-based modeling has been applied to many different areas. The common motivation for choosing this method is that “… only agent-based models can explicitly incorporate the complexity arising from individual behaviors and interactions that exist in the real-world”. 1

Increasing attentionThe first models were developed in the 1970s, since then a number of factors have led to their increased applicability:1. Increasingly complex world with more

interdependencies2. Data are being collected and organized into

databases at finer levels of granularity.3. Computational power is rapidly increasing1. Macal and North, Agent‐based modeling and simulation, Proceedings of the 2009 Winter Simulation Conference

What is agent-based modeling?

Agents of change, The Economist, July 22, 2010

The assumptions, including efficient financial markets and rationale expectations, are considered to be too simplistic.

A new approach called agent-based modeling is being explored to help address lessons learned from the financial crisis.

Mills, Alan. Complexity Science: An introduction (and invitation) for actuaries, Society of Actuaries (2012) Understands the complex nature of social systems. To grasp and manage the systems in which actuaries work, we must

augment our tools with the new methods of Complexity Science.

Mills, Alan. Simulating health behavior: A guide to solving complex health system problems with agent-based simulation modeling Society of Actuaries (2013) Agent-based modeling simulates agents’ (e.g., individuals and companies)

interactions with their environment and other agents The goal is to understand the emergent behavior of complex systems.

1

2

3

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Agent-based modeling is becoming a popular modeling technique to understand the emergent behavior of complex systems

Behavioral Simulation

Simulation of how individuals really make decisions and their emergent group behaviors based on modeling individual behaviors as ‘agents’. Choice made by individuals get reflected as ‘market‐level’ emergent behaviors that are calibrated with actual and survey data

Artificial IntelligenceCognitive thought throughmachines

Complex SystemsEmergent  system behavior from  individual actions

Computational PowerRapid cycle‐timefor intensive  calculations

Agent Based Modeling

Sophisticated, computationally intensive modeling technique that relies upon a decentralized set of behavioral rules and studies emergent behaviors

Classical EconomicsIndividual decision‐making driven by self‐interest and utility maximization

PsychologyScientific study of mental functions and behaviors ofindividuals and groups

Behavioral Economics

Study of individual decision‐making based on cognitive, heuristic, emotional and social factors

+

+

+

+

=

=

=

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Combining agent-based modeling with individual decision making

Example of life event impacts at the individual level

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Individual Events

44

1 2 3

4 5 6

Example of a “macro view” for a group of policyholders

Example of annuity withdrawal and surrender drivers

45

1 2 3

4 5 6

PwC

So why Behavioral Simulations?

46

Behavioral Simulations offers an alternative pathway towards answering very difficult questionsthat have been on the top of our professions’ mind for a long time.

NaturalSimulating at the individual level is intuitive:

• Path 1: Measure the embedded value of guarantees on a contract (complicated even for actuaries), and set behavioral deviances from a theoretical ‘rational frontier’.

• Path 2: Policyholders make decisions based on their health, employment and household needs.

An alternative pathwayWhere there is no directly relevant data (e.g. new product design, new socio-economic environment), there seems to be few recourses beyond our actuarial judgment.

Agent-based modeling provides one of the few (only?) analytical methods that can credibly complement our judgment in these situations.

HistoricalDeclining

interest rates

Future scenarioRising interest

rates

Blocked: no data

Macro level

Micro levelRecreate macro behaviors

Calibrate underlying drivers

Behavioral Simulations moves from macro-level phenomena to the micro-level drivers,

and then back to the macro-level.

Alternative pathway

1. Greater actuarial skill and knowledge as products become more complex with each generation reaching the market.

2. Increased consideration of risk management through risk mitigation and transfer strategies.

3. Increased tracking of contract owner decisions accumulating into emerging experience.

Questions?

Annuity Products are Requiring ...

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