Individual Chapter 8: Forecasting and Modeling Flashcards
Purposes and Uses of Models
1. Purposes for Financial Models
- Pricing: Financial and sales models are typically used to determine premium rates necessary to achieve goals
- Reserve Calculations: gross premium reserves and deficiency reserves are results of forecasting models
- Monitoring of Results: to test validity of assumptions, warn of deviations from expected values, for resource planning or other reasons
- Solvency Testing: test for need for additional financial reserves (fross premium reserves) for future experience, also for some ERM purposes
- Appraisals: study the value of a block of business, typically used when transferring ownership of the block
2. Deterministics vs. Stochastics
- Deterministic model shows the interrelationships of variables, but each output is a single value (expected value) - Helpful in scenario testing, when looking at specific alternatives, and sensitivity testing
- Stochastic represents the variable’s whole distribution of possible results, instead of a single point estimate. Parametric representations are used when this distribution matches a known distribution (e.g. Normal Distribution), and then information on the characteristics of this distribution can be used - Stochastic models give distributions of results, not just expected value. This is important when impact of results is not linear (e.g. Stop-loss reinsurance or ruin theory)
- Monte Carlo Simulations may be used to develop stochastic results if underlying parametric distribution is unknown. These simulations are more feasible now with advances in computer processing power
Characteristics of a Good Model
1. Reliable Accuracy - should be good enough to predict future events and should be robust
2. Suitability for Use - should produce results for which it is designated, without unnecessary complications
- Granularity - level of precision
3. Appropriate Precision - how many decimal places should be used and displayed
4. Sensibility - underlying basis od model should reflect a logical approach to what is being modeled
5. Effectively Communicated - results are useless unless they can be communicated to users and clients
Step 1 - Choosing the Basic Structure of the Model
Building a Model
Step 1: Choosing the Basic Structure of the Model
1. Modeling Tools
- Spreadsheets
- Database Models - useful when large amounts of data need to be modified
- Sequential Programs - written in computer languages where programs are invoked
- Asset Share Type Models - most common model type
- Usually a spreadsheet where each sheet represents a given model cell/group and columns contain inputs while rows contain periods of time to predict results - Reserve Development Methods
- Claim lag (development), tabular reserve, active life reserve, etc. - Agent-Based Models
- Aka “micro-simulation models”
- Predict behavior of various agents (policyholders, insurers, regulators, etc) under various scenarios and strategies
- Reveal potentially unexpected and nonlinear relationships
- Able to test various theories about policyholder behavior
- Hard to select proper assumptions - Deterministic vs. Stochastic
- Stochastic requires more effort to build, interpret, so these are reserved for situations that need unique input and are less common.Otherwise, deterministic may be used - Cell Definition
- Each cell of a model represents a group needed to build an accurate picture of the business
- Number and type of cells needed depends on how each potential cell might behave. If they are similar, cells can be combined. If not, calls may need to be split. - Durational Characteristics
- Measuring and managing durational effects on claim costs is critical to success in the medical insurance market
- Policies for most coverages have modeled characteristics (claim costs, policy and claim reserves, persistency) that vary substantially over the policy life cycle
- These types of policies may have cells with the same policy characteristics but with different duration to model these differences
Step 2 - Choosing the Information to be Carried
Building a Model
Step 2: Choosing the Information to be Carried
1. Pricing Models
- Project “model offices” that are spreadsheet representations of an expected mix of policies. For each cell, asset share calculation is made to project all relevant financial values
- Detailed asset share model might carry a number of exposure values, such as number of policies at start of year, number of policies in force at end of year, and average number in force during the year
- If calculations are based on modal premiums, may be additional exposure items needed
- If asset share is calendar year based (rather than policy year), appropriate exposure factors are needed to calculate the impact of two policy years within the same calendar year
- Claim values needed may include paid claims, incurred claims (financial basis) and incurred claims (runoff basis)
- Reserve values needed may include premium reserves (unearned premium, premiums paid in advance, premiums due and unpaid), policy reserves, claim reserves and gross premium reserves
- Expense values vary based on company’s circumstances and by type of coverage
- For coverage subject to ACA, many new values to estimate - risk mitigation (3 R’s), Minimum Loss Ratio rebates, new taxes and fees and subsidy amounts
- Profit is calculated on either a statutory or GAAP basis (depending on purpose of the projection) and could be pre or post-tax
- Required capital is also important, due to the opportunity cost of using this capital
- Reserve Models
- For short term claim reserves (claims triangle) - usually based on paid claims and exposure
- For tabular claims - usually taken directly from a table or factors
- For policy reserves - involve exposures and claims and may involve premium
- For gross premium reserves - involve all of the major financial elements - Recoverability Test
- For GAAP purposes, are similar to gross premium reserve calculations
- Test whether current premium levels are sufficient to cover benefits, deferred acquisition costs and maintenance costs (all under updated assumptions) - Monitoring
- Comparison of actual results against expected results, used to manage the business - Solvency Testing and Risk Analysis
- Risk analysis is generlly modeled as financial risk and analyzes the likelihood of various unexpected and negative financial results
- Ruin Model (likelihood that existing capital and surplus will not be sufficienct to fund those results) is a common one and requires information about the distribution of results which occur over time - Financial Forecasting
- Many purposes - most common is asset share calculation, used for short term budgeting
- Corporate models include projection of needed capital, including risk based capital requirements - Appraisals
- Long term financial projections, used to set a value on a block of business. Usually the present value of projected future profits or distributable earnings
Step 3 - Choosing Assumptions and Building a Prototype Projection
Building the Model
- Asset Share Models
- Typically a two dimensional matrix: columns are data elements and rows are time periods
- Some elements are explicitly assumed and some are derived
- Number of years to project is an important consideration. For non-inflationary coverages, it is common to project many years into the future
- In appraisals, many users of appraisals will use first 5-10 years of projections and the napply their own rule of thumb. For this reason, some actuaries have shortened appraisals to this initial time period only, as they realize future years will be overriden
- Proejctions won’t always be highly accurate, but a bad projection is better than no projection
- Challenge in projecting is adequately communicating the level of uncertainty (and that the uncertainty increases with time) - Development Reserve Models
- Typically a retrospective analysis, so cells are addressed individually. There is no prototype cell, instead a collection of cells, each of which is subjected to a customized analysis
- Significant assumptions needed: numbers of months’ experience to use and averaging method, seasonality, method for experience in months that are not fully credible yet, denominator for trending purposes (claims per policy, per memer, per dollar of premium, etc), and trend rate - Other Models
- Tend to be specialized, designed and built in a way that depends on the coverage being modeled
Step 4 - Extending the Prototype
Step 4: Extending the Prototype
- Once prototype cell (proto-cell) is finished, the prototype must be extended. Proto-cell is chosen to represent a given subset of the business being modeled
- Proto-cell is composed of policies that are identical, either using average values or a specific, representative policy chosen to represent that cell
Step 5: Validating the Model
Step 5: Validating the Model
1. Model validation allows us to know how well the model represents the business
2. Four Key Model Validations:
- Compare starting year values directly to actual values for that year
- Measure year to year changes
- Reasonableness checks by people familiar with the business
- Stress testing
Step 6 - Documenting the Model
Step 6: Documenting the Model
1. This can be tedious, difficult and impending, but it is very important
2. ASOP #8 - Regulatory Filings for Health Plan Entities and ASOP #41 - Actuarial Communication shuold adequately describe the work and defend it
3. Aids in duplicating, checking, modifying, and discussing results
Step 7 - Designing Output and Communicating Results
Step 7: Designing Output and Communicating Results
1. Output should be put in the context of the question being asked
2. Should consider the following in communicating results: Code of professional conduct, state intent of report early and clearly, compare against some standard results, explore expectations of report’s users and report on the variance information in addition to the expected values
Choice of Assumptions
1. Lapse Assumptions
- Vary widely by product, duration and company, so there are not available intercompany studies
- Typically highest in year one and decrease thereafter
- Common to assume that they will level out after a certain number of years
- Can vary by age, occupation, and benefit plan
- Rate increases cause a higher lapse in the period following the increase (“shock lapse”)
- Healthy lives assumed to have higher lapse than unhealthy lives - (1) Unhealthy lives are less insurable (harder to find replacement coverage), (2) Unhealthy people tend to hang on to their coverage more than healthy people, regardless of rate increases
- Major medical coverage - many seek coverage for short term situations (before getting a job or going to school) and results in high first year lapse rates
- LTC coverage - lapse rates tend to be lower than other coverages because LTC benefits are focused far in the future
2. Mortality
- Commonly treated as a combined single decrement along with lapse rates and called “termination rates”
- Some models may account for mortality separately
- In healthcare, lapse rates may essentially overpower mortality rates, policy provisions don’t distinguish between the manner of termination and it may be difficult to determine the cause of termination. For these reasons, actuaries may not split apart the two forces
- LTC is an exception. Mortality rates much more significant, as policyholders are older, and lapsation is lower
3. Claim Costs
- This assumption often gets the most attention
- Credible experience from the company is better than theoretical experience
- If actual experience is used, the challenge is quantifying the differences between the experience period and the modeled projection period
- Medical claim cost assumptions - reflect benefit design, characteristics of claim payment process, characteristics of insured population, and regulatory impacts
- Databases can be purchased if company’s own experience is not available
- Disability coverage - typically use a tabular approach. Often modify an existing able based on incidence and termination rates
- LTC coverage - often uses tabular approach, but without a standardized table
- In forecast models, important consideration is how claim costs will change over time i.e. future claim trends
4. Expense Assumptions
- Some expenses such as commissions, underwriting costs, premium taxes, etc can be directly attributed to a block of business directly. Others are attributed based on an allocated formula
- Cost of capital has become an important expense over time as companies become more sophisticated in how they look at capital. Often model this Cost of Capital as the difference in earnings rate between what the capital actually earned and what it could have earned elsewhere
- Profits released model projects future profits according to the model’s assumptions and those profits no longer impact values within the projection because they are paid out
- Profits retained model might generate the same profit, but that profit then stays within the model and accumulates and generates additional investment income
- Expenses are usually on a per unit basis - per policy, percentage of premium, percentage of claim and per premium collection
(1) On percentage of premium expenses, must be clear whether it is on gross premium or net premium
(2) When building gross premium using expenses that are a percent of net premium: Gross Premium = (1+e) (Net Premium)
(3) When building gross premium using expenses that are a percent of that same gross premium: Gross Premium = (Net Premium) / (1-e)
- Expenses vary between first year and renewal years
5. Profit Assumptions
- All insurers include margin in their rates
- Restropective models - profit is a dependent variable and is the difference between revenue items and expense items
- Prospective models - two approaches: (1) Target profit is chosen and needed premium level is calculated or (2) Set premium levels based on other sources and solve for profit
- Various measures
(1) Percentage of annual premium
(2) Return on Investment (ROI)
(3) Return on Equity (ROE) - similar to ROI but with additional component - investment of capital
6. Model Office Assumptions
- Provide the proportion of business in the block being contributed by each model cell
Auto-Correlative Models
- How past experience for an individual or group can be used to predict future experience
- Underwriters give risk score to the individual to predict expected claims. Individual prediction doesn’t have high degree of statistical confidence unless combined with many other individuals
- Credibility theory mostly based on independence of Individual claims
- However, auto-correlative models recognize the dependence of these claims; someone with a chronic illness is more likely to continue to have an illness in a future year
- “Risk adjusters” are predictive models based on diagnoses or drug history and are becoming more popular
- Box-jenkins ARIMA Model; Econometric models that create linear combinations of leading indicators to predict claim trends
- Complexity science field - includes agent-based models and other ideas; Sophisticated algorithms go far beyond simple regressions
