ASU 2018-12 spelled out a new methodology for calculating reserves for life insurance products. Kenji had worked many months to calculate the Liability for Future Policy Benefits (LFPB). He was exhausted. Yet, he was relieved. Cohorts were set up. The models were working as anticipated. Best estimate assumptions were in place. He had completed extensive single cell testing in Excel. The new roll forward reserve calculations allowed him to compute the reserves either retrospectively or prospectively. The roll forwards served as an excellent way to check the validity of the calculations. He was ready for a break. He handed over the initial reserves to the finance area. It was a time for a celebration with friends.

The celebration was short lived. The finance team called. They had placed the newly computed LFPB reserves into the overall financials. The results looked good, perhaps too good. Profits were very positive. The finance team was convinced a mistake had been made. No one in life insurance was supposed to have large profits now. Extra death claims due to COVID-19 had decimated results for the last year. Yet now, with the newly calculated reserves, profits appear to be good.

Kenji was tasked with figuring out what had gone wrong.

Some Basic Mechanics

ASU 2018-12 is also known as LDTI (Long Duration Targeted Improvements).  It is applicable for insurance companies that report under US GAAP.  LDTI made some major changes on how to compute reserves for traditional life products, such as term and whole life.  These reserves are known as LFPB.

The basic formula for the change in LFPB for the current reporting period is:

Actual Premiums * Net Premium Ratio (NPR)

+ Interest Accrual on LFPB

– Actual Benefits

+ True Up Impact                                      

Before LDTI, nearly no one had ever seen a simple formula for a change in a reserve.  It was a mystery.  But it was no longer a mystery.  The change in LFPB, often one of the most important items on an income statement, is relatively simple.  It works like as savings account.  A portion of actual premiums are added into the LFPB each period.  Actual benefits are paid out of the LFPB. Interest accrues to the LFPB.  It begins at zero at policy issue, and it ends at zero after all the benefits have been paid.

What do profits look like?

Normal Profit is:

Premiums

+ Investment Income

– Claims

– Change in Reserves

– Expenses

– Taxes

If we replace the “Change in Reserves” with the “Change in LFPB” we get:

Premiums * (1 – NPR)

+ (Investment Income – Interest Accrual on LFPB)

– True Up Impacts

– Expenses

– Taxes

Skip to the next section now if you are not really interested in all of the boring details.

The calculation is completed at the cohort level.  Cohorts are groups of policies defined by product type and issue year.

The NPR (Net Premium Ratio) is the amount applied to the Present Value of Gross Premiums to make Present Value of Net Premiums equal to the Present Value of Benefits as of the start date of the cohort.  Best estimate assumptions are utilized.

Cohorts will normally begin when policies are issued.  However, for many companies, cohorts will begin as of 1/1/2021, if they were issued before this date.  This is referred to as the modified retrospective approach. Many companies will not have enough data to do the calculations based on the original issue date.  There will be more on this topic later.

For each reporting period, normally a quarter, the NPR is recalculated.  It is always calculated over the life of the cohort.  After each quarter, for the present value calculation, one quarter’s worth of expected results is replaced with one quarter of actual results.  This has the impact of increasing or decreasing the NPR as needed.

If reality matches expectations, then the NPR never changes for a given cohort.  If things are better than expected, then the NPR goes down.  If things are worse, the NPR goes up.

Of course, there was one mystery element.  It was for the “true up impacts”.  This amount goes by many names.  This includes items like “Effect of changes in cash flow assumptions,” and “Effect of actual variances from expected experience.”  These are adjustments related to actual experience on mortality, morbidity and lapses not matching up to the assumptions used in the calculations.

If you do not have enough boring details yet, read ASU 2018-12 (FASB Org Link to ASU 2018-12).

When is it a good time for a pandemic?

The answer of course is never.  But if there is going to be a pandemic, it is best that it happens when ASU 2018-12 is being implemented.  Actual claims, even COVID-19 claims, are paid from the reserve.  The drop in the reserve offsets the actual claims being paid, producing no profit/loss impact.  Actual claims drop out of the equation from the previous section.

Wait a second!  This cannot be true.  OK, there is a profit/loss impact.  It is very muted, at least for now.   The reserving mechanism spreads excess claims (or smaller than expected claims) over the life of each cohort.  Since most companies will have their cohorts starting as of 1/1/2021, most COVID claims will be spread out into the future. 

No one wants a pandemic, but if there is a pandemic, LDTI could not have come at a better time.

But wait, there’s more!

So, LDTI has helped out with COVID claims.  Yet, the profit levels still seemed too high.  Kenji couldn’t help thinking about this.  Then it hit him.  The transition rules were producing steady streams of profit.

Under a true LFPB calculation, one needs the history of premiums and claims for all policies since the day they were sold.  Tracing back all of this information can be a daunting task, as some policies in force were sold 50 or more years ago.  So LDTI allows the modified retrospective method. 

Under the modified retrospective method, one chooses a transition date.  For most companies this will be 1/1/2021.  The LFPB reserves, on a best estimate basis, are floored at the prior reserve amounts.  The prior reserves had margins built in.  Under LDTI, these margins are released as a constant percentage of premiums.

The NPR for old cohorts will be low in order to release more profit.  For some old cohorts, it is even possible for the NPR to be negative.

Under the old methods the margins would have been released when policyholders surrender or die.  However, this can be a long way off.  The LFPB rules allow for much quicker release of margins.

Disclosures

LDTI requires public disclosures showing the details on the change in reserves.  What was once an actuarial thing would soon become something anyone could figure out. Well perhaps not just anyone.  Investor Analysts could certainly figure it out.

Investor Analysts would soon be able to make much better predictions about the change in reserves.  Afterall, the details were there.  Things seemed relatively straight forward.  Then again, Investor Analysts tend to ask a lot of questions.  Kenji knew that any amount in the “true-up impact” section of the “change in reserve” disclosure would require explanation.  If things were worse than expected, Investor Analysts would want assumptions changed to strengthen reserves.  If things were better than expected, they would want assumptions changed so that profits could be released.  After assumption changes were made, it would be easier to predict profits.

It looked as if Investor Analysts would allow no relief.  Then again, they had never allowed relief in the past.  This was their job.

So, this was good?

Kenji had figured out a few major items. Perhaps it was time to celebrate. Perhaps not. Yes, there was more profit now. That’s a good thing, isn’t it? The flip side is that there would be fewer profits in the future. This was especially true for policies sold after 1/1/2021, which would not have any margin in reserves. Sooner or later, this would need to be explained.

Kenji had taken the job in traditional life valuation simply because it was steady and predictable. He could see this would no longer be the case.

Kenji had never worried about assumption changes. Under the old rules, assumptions were set at the time the policies were sold, and then never changed. He used to simply walk over to the pricing area, get their assumptions, add some margins, and then forget about it thereafter. Afterall, changes to assumptions were not generally allowed in the past. Under LDTI, assumptions must be reviewed. If reality was not matching up to the current assumptions, he knew that the Investor Analysts would hound Senior Management, who in return would hound him.

Kenji had never worried about parts of the income statement, other than the “change in reserves”. This would no longer be the case. The change in reserves would be related to both actual claims and the size of actual premiums. The interest accrual on LFPB would be compared to net investment income.

So, Kenji was exhausted. Yet he was excited. His job would soon become less boring.

What the heck are reserves?  If one does anything with financial statements for life insurance companies, these seem to be a big deal.  Actuaries spend a lot of time computing these.  The insurance regulators, the IRS, and FASB make up a ton of rules about reserves.  Some accountants are frustrated with reserves, as they have an enormous impact on financial statements, but they are shrouded in mystery.

There are two reasons reserves exist:

• To determine how much money to hold now in order to pay benefits in the future.
• To control the timing of profits.

The second reason seems to be the more important reason.  Insurance commissioners, the IRS, and the FASB all want to control the timing of profits in some fashion through reserving practices.  Most companies produce at least three versions of reserves, which results in three income statements.  One of these statements is handed to state insurance commissioners.  A second is handed to the IRS.  The third and final version is used for financial reporting on Wall Street.

There are three sets of books, all perfectly legal. Like all actuarial work, it’s about the future, and the future is not certain.  Different parties have different viewpoints about how to recognize future events.

Regardless of which version is used, the amount of profits over the life a product does not vary, only the timing.  Three parties who want to control the timing of profits are:

• Insurance Commissioners –One of the goals of income statements produced for insurance commissioners is to delay profits.These statements are referred to as Statutory.   Insurance products are dependent upon many assumptions, and insurance commissioners would like to delay profits just in case they are needed later for unexpected results.
• IRS – The IRS of course wants tax money sooner, so their reserve rules work to accelerate profits.
• Financial Accounting Standards Board – The FASB is one of the parties which set reserve calculation rules for publicly listed companies.  These rules are part of US Generally Accepted Accounting Principles (US GAAP).  They appear to want steady state profits.

Surprisingly enough, all of the rules in use tend to delay profits, even those used by the IRS.  Do insurance companies want to manage profits through reserving?  This topic will be discussed at the end.

*** Warning:  This blog is at a high level. It focuses only on traditional life products.   The full set of rules to compute reserves is quite complex.  This blog only explores concepts at a very general level. ***

The Most Basic Definition of Reserves

Life insurance products are generally very long term, with premium and benefit periods stretching out over several years. For example, a person may purchase a 20-year term life product.  This product consists of 20 years of premium payments, with a death benefit which can be paid at any time during that period. With this the most typical, but not the only, method for determining reserves is:

Projected Benefits & Expenses – Projected Premiums, Fees & Investment Income*

On the surface, this all makes sense.  If benefits and expenses are bigger than premiums, fees and investment income, then one needs to set up something on financial statements.  Then to be safe, any insurance company should have assets larger than reserves.

Then again, let’s think about this.  Most insurance products are priced for profitability.  Premium, fees and investment income should be bigger than benefits and expenses when the product is sold.  Basically, reserves would be negative when the product is sold.  They would represent the future profits of the product.  If one would sell something, all the future profits would be recognized on day one.  Yet this is not how it works in practice.

So, what happens?  For most accounting rules, first, one is not allowed to use full premiums in the above equation.  Second, one may put margins on assumptions used to compute projected benefits.  These two items control the timing of profits. Each accounting regime has different rules on how to handle these.

Why does one want to control profits?

1. If one recognizes all of the profits up front, profits will be spent, or given to someone else.  Then if something goes wrong, there is no money to fix things.
2. Recognition of all future profits at the time of sale was one of the things that led to downfall of Enron.  No, Enron was not an insurance company, but the same basic principles would apply.  They would start a project and recognize all of the profits up front.  And if the profits were not realized, they would simply start up another project.  Enron had other problems as well.
3. Most life insurance products are around for several years.  Many would like to have profits distributed over the life of the products.

* Some people like to write this equation as the Present Value of Benefits and Expenses less the Present Value of Premiums.  The present value is determined using an interest discount rate.  The use of an interest discount rate is equivalent to using projected investment income.

Do Insurance Companies Manage Profits Through Reserves?

It may be possible to manage profits through assumption selection.  There is an incentive to managing profits. Short-term bonuses are often based on profits.  Having said this, such management is unlikely, and it will become even more unlikely in the future.

Actuaries are bound by a Professional Code of Conduct, and there is the Actuarial Board for Counseling and Discipline (ABCD) for enforcement.  Reserve calculations statements are reviewed by both regulator and external auditors.  In about 2 years, new US GAAP rules will require a number of new disclosures related to assumption selection.

While the process is not perfect, there are several safeguards to limit abuse.

Last Thoughts

One of the primary purposes of life insurance reserves is to manage the timing of profits.  There are many ways to manage such profits, with the insurance regulators, the IRS, and FASB all having different goals.  The next blog will provide spreadsheet demonstrations on how this works.

Reserving rules change all of the time.  Perhaps the best way to judge such rules is to determine how such rules will impact the timing of future profits.

Do you have ideas for actuarial blogs?  Send ideas to dmxure@gmail.com

Actuaries use assumptions for financial projections.  Assumptions include items such as mortality and policy lapse rates. Often these assumptions are based on a company’s own experience.  The experience represents a sample of a population.  The question is how much experience is needed for a good assumption.  Let’s consider an example.   The experience may indicate that the average lapse rate is 6%.  This particular experience set includes 25,000 policies.  The main question is whether or not the 25,000 policies is enough to make good decisions.

This can be a long topic.  I will focus on limited fluctuation credibility theory (LFCT).  Gee, that’s a long name.  It sounds precise.  Actually, it’s not.  Just like so many other things about the future, there is a great deal of subjectivity involved with measuring credibility. 

This blog will focus on the following.

• How does one determine the amount of experience (sample size) needed for full credibility?
• A spreadsheet which will help you with the calculations.
• The items one must consider when using and communicating credibility concepts.

I promise not to get too much into the mathematics.  As you will see, at the end of the day over precision simply isn’t going to help that much.  Much of the actuarial value comes from the qualitative analysis associated with the process.

Determining the Number of Observations Needed for Full Credibility

How can one be certain that the right assumption has been chosen?  Well you can’t.  Some senior leaders may demand certainty.  When they get it, the senior leaders have just heard a lie.  Or at least a very misinformed statement.  Neither situation is good.

It is probably best not to focus on being absolutely certain, and instead choose a comfort point for reasonable certainty.  This comfort point is called full credibility.

Selecting a level for full credibility focuses on two items.

• An allowable relative error, e.g., 10%.  This means that the rate found using experience is within 10% of the true underlying value.  So, if the rate from the sample is 6.0%, one would reasonably assume that rate for the population is between 5.4% and 6.6%.
• A level of confidence, e.g., 99%.  This means that one is 99% certain that the rate from experience is within the allowable relative error.

Once one knows the relative error and confidence level, there is a convenient set of formulas to determine the necessary amount of experience for full credibility.  So, here is the question:  which of these combinations gives the best level of credibility?

• (a) 95% confidence that one is within a 5% relative error of the true underlying value.
• (b) 90% confidence that one is within a 3% relative error of the true underlying value.
• (c) 90% confidence that one is within a 5% relative error of the true underlying value.

Most people probably can’t decide how to choose between (a) and (b).  This is where the subjectivity comes in. Option (b) actually requires twice as much experience as option (a).  So how did people originally choose between (a) and (b)?  It was likely because that sounded good, and that was exactly the amount of experience they had on hand at that time.  Then they stuck with it.

Number of Observations Needed for Full Credibility

Level of Confidence	Allowable Relative Error	Approximate Number of Deaths (Lapses)
90%	3%	3,000
95%	5%	1,500
90%	5%	1,000

These three combinations of confidence and relative error shown in the table are the most common ones seen in practice.  The relative levels are rarely explained or compared.  Someone typically uses a combination because they have seen it somewhere else.

A few notes are in order:

• The amount of experience needed to achieve full credibility is typically based on the number of deaths (lapses).  This is because varying the mortality rate does not affect the number of deaths to achieve credibility by much.  The table can be rewritten based on the number of observations, but it would need to be updated for each mortality rate.
• The number of deaths needed for full credibility will vary slightly by how one approximates the confidence interval, but this may not be that significant.  One can find several formulas.
• There are many unknowns.  Hence it probably does not make too much sense to get too worried about accuracy.  Many people lack rationale for (a) vs. (b).  Probability distributions are constantly changing. 
  • Mortality is improving (statins, better diets) …sometimes.
  • Mortality is declining (opioids, dying while texting) …. sometimes.
  • Policyholder behavior, such as lapses, changes continually based on information available to the policyholder, the economic environment, and a variety of other factors.
• Having said all of this, under the Principles Based Reserving rules for government reporting, the number of observations needed for full credibility for mortality does vary by age. https://www.naic.org/documents/prod_serv_2018_valuation_manual.pdf    

Amount of Experience for Full Credibility Spreadsheet

(Below is the link to download the spreadsheet)

https://dmxure.com/media/lfct.xlsx

The LFCT spreadsheet at this site is a tool for determining the amount of experience needed for full credibility.  There are three inputs: 

• The level of confidence
• The allowable relative error 
• The expected rate of mortality or lapse

This spreadsheet can be downloaded.  It is macro-free so it should be safe.  The spreadsheet relies on the “Solver” Excel Add-in.  The “Solver” add-in is free and in comes with all recent versions of Excel.  Like any spreadsheet, improvements can be made.  If you have ideas for improvements, please send me a note at dmxure@gmail.com.  I will even add your name as a credit for changes, but only if you want your name added.

How to Determine Partial Credibility

This isn’t too hard.  Partial credibility is defined as:

*The term deaths can be replaced with lapses or some other decrement.

So, if the number of deaths in your experience database is 374, and the amount needed for full credibility is 3,000, then the partial credibility is 35%.

How to Apply Credibility

To set an assumption using credibility, the experience data is combined with an established assumption.  The most common method is:

New Assumption = Experience Rate * Credibility + Established Assumption* (1 – Credibility)

There are a couple of items which make the application difficult.

1. How does one find an established assumption?
2. How does one group data?

Established tables for mortality can be found at https://mort.soa.org/.  The Society of Actuaries at the time of this writing had 3,006 tables in their repository.  The tables vary by country, type of product, underwriting, etc.  It may take some time to find a table that matches up with the characteristics of your product.  Communication about how an established table was chosen can be critical to evaluating the process.

Established tables for lapses are more difficult.  Lapse rates by company and product can vary greatly.  The distribution method, e.g., independent agents vs. career agents, can make a large impact.  Possible choices for established tables may be tables for similar products, tables available from consultant services, or simply the table that was last used.  The subjective quality of established tables may play a role on how to apply credibility.  This is where communication becomes critical.  Decision makers must understand the qualitative aspects of the established table to determine the appropriateness for assumptions setting.

Grouping of data is often necessary to apply credibility.  An insurance company may have over 50,000 mortality rates which vary by age, sex, policy duration, underwriting class, location, etc.  Establishing credibility for all of these rates may be impossible.  Grouping of rates can help.  This may best be seen in an example. 

Suppose that an actuary picks the 2008 VBT mortality table as the established table.  Then suppose that experience data comes in at 94% of the established table.  This percentage methodology essentially groups all of the mortality rates.  The experience data has 590 deaths. The insurance company, after long discussions, has set full credibility at 1,500 deaths.   The new assumption becomes 96.2% of the 2008 VBT.

This methodology groups all of the mortality rates into a single number as a percentage of an established table. When such a methodology is applied, the percentage is often graded to 100% beginning at an advanced age, say 85.  Experience is typically limited above this point.  It is also desirable to get a mortality rate of 100% at some age, e.g., 120.  Alternatively, some actuaries will group data into age bands when determining credibility.

Data for Deferred Annuity products are often grouped by phase for the purposes of determining credibility of lapse assumptions.  There are three main phases.

• Surrender Charge Period – A surrender charge may exist for a period of say 7 years.  During that period, lapses tend to be very low, as policyholders wish to avoid the surrender charges.
• Shock Lapse Period – Lapse rates can shoot up to 40% or higher in the year following the end of the surrender charge period.  Distribution agents are looking for their next commission, and hence have strong incentives to get people to change products.
• Ultimate Period – Beyond the shock lapse period, lapses tend to level off.   Having said this, few insurance companies have experience for policies at very late policy durations.

Examples and thoughts about established tables and grouping are too numerous to mention in a short blog.  More information may be forthcoming in future blogs.

Last Thoughts

This blog only scratches the surface of using credibility.  Due to the subjective nature of the process, credibility should always be thought of as a guideline as opposed to an absolute rule.  Understanding how the level of full credibility was chosen is important.  Even more important are the decisions on established assumptions and how to group the data.  Communication is critical to a well-designed process.

Wouldn’t be nice if all insurance companies gave more information about how they set assumptions?  Well that is coming.  At least it is coming for publicly traded companies with new accounting rules (ASU 2018-12).(https://www.fasb.org/jsp/FASB/Document_C/DocumentPage?cid=1176171066930&acceptedDisclaimer=true).  These rules will not become effective for about 2 years.  When they do, they will require greatly increased public disclosure about assumption setting.

More blogs to come.  Send thoughts or requests for specific topics to dmxure@gmail.com.

Thanks for joining me!

I used to live in Des Moines. Des Moines has been called ths insurance capital of the US*. I am an actuary. Hopefully you have figured out the meaning of DM XURE.

At one point I had a customized license plate, “DM XURE.” So I went to visit my mother. I said, “Mom, isn’t this great? XURE sounds just like actuary.”

Her response was, “So does that mean damn actuary?”

*https://www.freeenterprise.com/the-insurance-capital-of-the-u-s-look-to-des-moines/