LTCI Rate Adjudication and Neutrality

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LTCI Rate Adjudication & Neutrality

A Guide for the Consumer Side

 

© 2019, 2020 Samuel T. Cuscovitch and David Y. Schlossman

Since 2005, the authors have conducted substantial research on a wide range of personal finance (PF) issues. The authors published PF architectural specifications (“Systems and Methods for Strategic Financial Independence”, June 2006) and currently manage an integrated, multi-domain financial planning model.

Attempting to include an LTC/LTCI component model within that PF framework led the authors to conduct the research within. Other research by the authors include extensive coverage in the Health domain, also contributed to this effort. The authors would characterize the present state of LTCI legacy products as unreliable, unstable and potentially toxic to policyholders. Nonetheless, we have chosen to include an LTCI component within the PF architecture to enable clients to better understand options available to them.

View/Download “LTCI Rate Adjudication & Neutrality” PDF


Table of Contents

Introduction

LTCI Framing & Terminology

The 7 Models Described

High School Math To Evaluate CBM Rate Models

Method’s Steps

Fundamental Causes of future rate Instability

Summary and Conclusion

In retrospect, would you still have signed on?

Path Forward

Entity Relationship Diagrams, Formal Systems Treatment

Exhibits, Views

End Notes

Figures

Figure 1: Seven CBM Models Evaluated

Figure 2: Master Exhibit Template

Figure 3: Discount, Life Cycle, Corrective Scaling

Figure 4: Analysis Of an LTCI contract, Key Metrics

 Introduction

From 1990 – 2010, the cohort of then aged 50 – 70 middle-income/asset seniors was the target of insurance carriers of a product known as Long Term Care Insurance (LTCI). Couples were especially targeted to protect one another and offered teaser discounts if both signed on. LTCI was heavily marketed as a hedge against what carriers asserted was a high probability occurrence to cover very expensive LTC services if a client were to become deficient in two or more activities of daily living (ADLs) or experience cognitive impairment. It was first intended, marketed and sold as a level premium contract. The premium included a prefunding component that when invested by the insurer would cover a policyholder’s financial risks for the contract’s life. If an LTC event were ever triggered, it would most likely occur many years after purchase.

Many purchasers were urged by their advisors (legal, financial, estate planners) to acquire such protection to “round out” their retirement plan. In the early ‘90s, States got in the act with programs to encourage LTCI. A policy type known as the “Partnership Plan” provided Medicaid Asset Protection. This plan specified certain minimum coverage. For the younger class, one required feature was a 5% compound annual benefit inflator. This feature increased the premiums considerably over plan types that offered either simple interest benefit inflation or none at all. Several payment options were available, most buyers selected annual premiums

Unfortunately, LTCI of this generation has emerged as a distressed and diseased legacy product. From 2000 – 2010, these products became increasingly more expensive and began to lose buyer’s favor. Carriers saw only a 10% market penetration well below the expected 30%. Without the pot of gold materializing, with credibility and customer trust becoming tarnished, 90% of the carriers abandoned the industry by 2010. About a dozen remain, several acquired the book of those abandoned, and others came back as silent partner reinsurers.

From a broad examination of industry documents, industry actions now appear clear: to scale premiums rapidly; lose customers; and encourage, if not force, policyholder to reduce coverage. This places the LTCI cohort (now aged 65 – 90) in a precarious and vulnerable financial state, especially having already paid substantial premiums into their contracts for two to three decades. The sudden, pervasive and continued carrier rate hikes, approved by regulatory authorities, affect in excess of 7.2 million policyholders nationally. The industry reports that the face coverage value of outstanding policies is $2.1 trillion and growing at a compound rate of 4.5%*(i). Given that LTC is a family matter, the impact is far more reaching than these number suggests. The industry’s actions suggest a push to lower their long-term liabilities. Hence, the now aged-up policyholders face the threat of these actions with the outcome that they, or their families, may not have the means to afford nursing home, assisted living, or home care per original terms and conditions.

Whatever the well-intentioned plan was, it has now turned to dust.

Few consumers have any insight or guidance into the direction of premium hikes per their specific book(ii). Disclosure of their carrier’s plan or intent to increase premiums has been stark if not absent, a subject matter of a current class-action lawsuit(iii). Future directions of closed book policy premium pricing are largely unknown to any individuals outside of the industry and regulatory bodies controlling costs. Policyholders are forced to make distressed decisions whether they can or should continue paying further. They can receive a fraction of their contractual benefits through a feature called Contingent Benefit Upon Lapse (or feature similarly named). Yet, if this feature is exercised, there remains heightened uncertainties regarding any decision’s aftermath that affect an otherwise well constructed retirement plan. To make matters worse, their lapse options have a 30-day expiry date upon notice of a premium hike on a matter so critical*(iv).

This paper examines and discusses product pricing instability problems in textual, mathematical, and visual format. It further identifies the industry’s misguided and apparently never vetted Claims Based Modeling (CBM) for long duration contracts*(v). It further identifies an alternate method within CBM that remedies future LTCI rate instability and places the burden on carriers and regulators to shore up a serious accounting flaw.

LTCI Framing & Terminology

The current state of Long Term Care Insurance (LTCI) industry legacy products, often referred to as LTC 1.0/1.5 in industry circles, is in turmoil. It is this paper’s contention that much of the blame can be attributed to the industry’s use of Claims Based Modeling (CBM). This modeling method is commonly used to evaluate and grant LTCI rate premiums on a legacy, book of business now closed to new policyholders (PH). The concept of loss-ratio is a driving factor behind rate actions taken by LTCI carriers. A loss ratio is the sum of total claims or benefits paid to customer divided by the sum of total premiums paid. A lifetime loss ratio refers to the entire life of a book where claims & premiums are adjusted for a discount factor (df), alternatively referred to as the Investment Return, to yield Present Values (PV). PV recognizes that a dollar’s worth in the past is greater than a dollar’s worth in the future. This is crucial as the time span for an LTCI book is measured in decades, as many as 8, no fewer than 6. A discount factor vector, 𝐷, can be expressed by (1.0 + 𝑑𝑓)−𝑘 where k>0 is the number of years forward in time while k<0 is the number of years rearward from a referential period, normally defined as a year. Understanding the discount concept is fundamental to understanding CBM’s dynamics*(vi).

Example: df = 0.045. It is 2019. For 2017, D[-2] = (1.0 + 0.045)2 = 1.092025; For 2021, D[2] = (1.0 + 0.045)-2 = 0.91573

See a plot of 𝐷 over a period Figure 3: DISCOUNT, LIFE CYCLE, CORRECTIVE SCALING.

As is demonstrated in the paper, the use of CBM has not worked well. Its use results in a power function progression of rate increases manifesting itself in premium unpredictability for policyholders, endangering those who live on fixed income. For this reason, LTCI can be toxic in a retirement plan where the plan relies on it to perform as a hedge against LTC risk. LTCI was intended to be and presented to prospective buyers as a level premium product though not guaranteed as such. It turns out that the use of CBM has tilted the contractual edge towards the carrier, is unfair to policyholders, and discriminatory to those who have aged-up.

This paper concentrates on CBM though there is an alternate, scientific approach known as “First Principles”, referred to by the “American Academy of Actuaries”*(vii). CBM is being dissected in this paper for it is the most often used model in rate adjudications for legacy LTCI products. Within CBM, seven different projection approaches are considered. The term MLR refers to Minimum Lifetime Loss Ratio, a level above which carriers are entitled to file for rate increases. ALR refers to the Actual Lifetime Loss Ratio based on the book’s expected performance based on the As Is model.

Figure 1: Seven CBM Models Evaluated

Description – All CBM

Purpose

1.  MLR 60% loss ratio

Used by regulatory bodies in assessing rate
increase requests where

statutory MLR loss ratio is 60%

2. MLR 80% loss ratio

Used by regulatory bodies in assessing rate increase
requests where

statutory MLR loss ratio is 80%; many states have
adopted 85%

3. 100% loss ratio

Illustrative mostly, defined as Lifetime PV Premiums
= Lifetime PV

Claims

4. Step Up

Illustrative. To show what the one-time rate
request should be to

achieve statutory MLR

5. Uniform

Illustrative. Theoretical to show what a
gradual rate increase should

have been from a base year (e.g. 2000) to achieve
the statutory MLR

6. As Is

Known. Show actual historical rates and future
rate increases that have

already been granted but not a good predictor
unless rates are frozen.

7. Rate neutral

Equitable. Achieve statutory MLR by creating
synthetic premiums to reflect what rates should have been by use of 1 or more model variants.

 The 7 Models Described

Standard Loss Ratio Models 1, 2, 3

Model variations 1, 2, 3 are considered standard and vary based on the MLR target. State insurance regulators or their legislative branch determine the MLR target hence the term statutory MLR. In Exhibit 1, all 3 curves are shown with typical progression to illustrate rate sensitivity to the MLR.

What is the importance of MLR to a policyholder? It is the threshold that would allow carriers to file for rate increases. If a carrier’s actual loss ratio ALR is lower (<) than the statutory MLR, then a rate increase is unjustified. The LTCI industry can be characterized as operating above (>) the MLR. A sampling of ALR from major carriers reveals a range from 78% to 173%, with 78% being an outlier. Most are >100%, two as high as 173%. Other factors weigh whether regulators grant a rate increase in full or in part but loss ratios determine the long-term direction.

A policyholder might consider their own loss ratio. What is a policyholder’s expectation of LTCI payout (claims) for the life of the contract divided by the expected premiums paid? Is this really calculable by policyholders? Obviously, such a consumer-oriented, commercial model would as a pre-requisite consider the expectation of LTCI industry futures as it relates to premium behavior, the subject of this paper.

Theoretically, if a consumer’s expected lifetime loss ratio >1.0, a policyholder’s LTCI contract has a net PV>0, a financial asset. But from the carrier point-of-view, this condition is a long-term loss or liability, something that the carrier wishes to shed. If you were to accept a carrier’s claim that their ALR>1.0 then you as a policyholder are presently holding a favorable contract. Don’t expect this condition to persist as the carrier will attempt one or more filings that: (a) increase premiums, (b) offer unattractive offers to reduce coverage known euphemistically as benefit buy-downs, or (c) outright encourage you to lapse with a small fraction of original benefits. Whatever the tactic, it is their intent to chase any future liability off their books.

The relationship of ALR to MLR is a determinant for a policyholder to gauge their contract’s destiny. Since the industry runs with higher ALRs than the MLR, it is common to see frequent filings, some carriers even seem to do as an annual ritual. This confuses PHs not knowing what the future holds and questioning whether their contract is worth the paper it is printed on. It causes excess decision making with each filing. Yet many PHs continue to pay premiums to avoid losing their so-called investment. You can find cases where a couple purchased LTCI 20 years ago, paid in for 15 years at level premium, in some cases having paid in excess of $100,000, and without advanced disclosure get hit with a series of jarring rate increases. It is not unusual to see current premiums more than double, triple, or quadruple original premiums. PHs may be offered the option to accept a CBUL option, but realize the value is nothing remotely close to coverage they are giving up. The issue receives state and national press attention as well as the attention of industry organizations like National Association of Insurance Commissioners (NAIC) who seek a permanent solution to the problem*(viii). PHs should know the wider the spread between MLR and ALR, the greater the expectation of greater or more frequent rate increases.

Carriers do not file for compound annual increases. Instead, they achieve the same result through a through a series of rapid calendar rate increases, sometimes overlapping increases in one year from two separate rating filings where allowed by a state. To policyholders, this is the equivalent of Chinese water torture since it masks industry’s long-term intent. Had you known that your LTCI contract would experience late stage prolonged and repeated rate hikes, might that have changed your decision to purchase LTCI in the first place or chosen to lapse the policy closer to the beginning of its life horizon rather than towards the end? It is strange that these legacy products typically had no premium increase for 10 – 15 years, then wham! Why?

Step Up

Variation 4, the Step Up, dispenses with the annual rate filing ritual. It a one-time increase to bring the book immediately to statutory MLR. The future is now. If the Step Up correction was disclosed by the carrier, policyholders might bolt in mass or take to the streets. For this reason, the Step Up is a theoretical exercise. One might say a Step Up is political suicide for a regime that even whispers it. Even with the never happening Step Up, the carrier could in theory return in the future and assert their claims projection model was wrong yet again (as they claim each rate filing) and ask for an additional rate increase. At this point, will all its uncertainties you may wonder whether LTCI meets the basic criteria of a regulated insurance product.

You might ask, “why are rate increases necessary if the product design was intended to be level premium from inception”? Note that LTCI carriers’ out for this question is what contractual fine print discloses, the now well-recited phrase “carriers may raise rates”. In the sales process, policyholders heard a different message “though carriers could raise rates, this particular carrier has never raised rates”. The industry now claims the product was underpriced from the beginning. If true, then it took the carriers no less than 20 years to rise to the occasion to address that known problem with their earliest filed rate increases. You can find industry sources that state, “carriers were reluctant to raise rates in the beginning for the stigma that it would cause”.

Uniform

Now enters the Uniform model. Another illustrative, artificial model, the uniform model corrects the past through incremental increases that should have taken place early on. It is the post mortem cure to early rates that some claim were low-balled to entice PHs into the game and keep them in. Note that this model still relies on CBM but instead of causing late stage dramatic premium increases as we witness now, clarifies what should have been done early in the book’s life cycle. Had you known about incremental increases then and given that you were told “…this particular carrier never raised rates”, you might have left this game early and prepared your LTC plan using non-insurance options with sufficient lead time. There’s a cost associated with not knowing the true condition of LTCI for the past 15 – 20 years. There’s also a cost not knowing now what might be in your immediate future, but that’s why you are reading this paper.

Exhibit 2 shows the disparity of the Uniform or Implied Pricing and the historical As Is pricing. As Is — defined as the actual rate history and a future rate projection based solely on the most recent rate grant. The As Is model is not a good representation of future premiums if the carrier has not reached MLR even with the most recent increase that might seem large. This means in most cases, As Is – is merely illustrative except you may not have known that until now. Exhibit 2 illustrates the extent to which a PH is a victim of carrier under- pricing. If the spread is wide, the duration long and suddenly the carrier asks for an especially large rate increase, you have the right to question what new information has emerged that has caused the carrier to file late. In a later graph, we will see the expense price of a delayed rate request.

Rate Neutral

The Rate Neutral model is the final model. The CBMs have an inherent characteristic that makes future rates increase according to a power function. There are two primary reasons: (1.) unless the regulatory body dismisses a carrier’s claim to recover past under-pricing, it is the current PHs, a group that has been diminished in size due to other lapsed policies in the same book, that is called up to make up for past losses. Current PHs might construe this as discriminatory since the previously departed PHs were beneficiaries of under-pricing and may have gone on claim to receive benefits. It is the remaining in-force aged-up members who are here to make up these losses, (2.) it is the nature of the discount factor that the past is heavily weighted and the future far less so as the book moves beyond mid-life, as is true with legacy LTCI. What is especially pernicious is when the policyholder has already been exposed to rate increases and the loss ratio still does not satisfy the MLR, the contract still remains in an under-priced state. The dynamic continues, the product continues to age, the policyholder count decreases, time to correct diminishes, a death spiral emerges and the remaining in-force are left holding the proverbial bag. Meanwhile, the industry believes the problem solution can be found by developing more attractive benefit buy-down or lapse options for the consumer.

The Rate Neutral (a.k.a. Step Down) model filters out accounting gimmicks that work in the carrier’s favor by not making the remaining in-force responsible for past losses due to under-pricing. One (1st) variant does this by inflating past premiums synthetically to account for what the fair premium should have been all along thus denying the carrier a recovery mechanism for lost premiums. Even actuaries believe there is merit or fairness to this but are concerned about issues of carrier solvency*(ix).

The Rate Neutral model has these benefits and objectives: (1.) provides future rate stability; (2.) eliminates discriminatory pricing for age-up policyholders; (3.) restores the concept of a level premium product as was intended & suggested at the time of sale, and (4.) provides a contractual level playing field between carriers and policyholders. The Rate Neutral model is the endpoint for rate stabilization or true ups for past overpricing resulting from excessive rate grants*(x).

In some cases, the Step Down increases premiums from the As Is. Why is that? That would be the effect of a carrier’s claims expense projection model suggesting that the As Is premiums severely lag in relation to what is already apparent in the Claims-based model. Note that this paper merely accepts carriers’ claims projections at face value to avoid getting into any unnecessary actuarial discussion at this time.

Other Step Down variants are far more aggressive than the one used in this paper. For example, if a carrier were granted a premium that were 3x the original, a consumer position could lay claim that this 3x premium is the fair premium that should have been charged from inception. Indeed, sounds logical. A quantitative analysis reveals this 2nd variant if applied would synthetically raise past premiums to such a high degree that in some cases this Step Down approach (a variant that only corrects forward) would fall well below the original premium. Some would say it would over-correct to the downside tilting unfairly to the consumer side. Doing so would violate the principle of a uniform lifetime premium as described in objective 3 above and lose the sense of neutrality. However, it would certainly stem the tide of unbounded rate requests. A third variant could be a compromise between two variants described above – e.g. x% variant 1 + (100 – x)% of variant 2.

Exhibit 3 illustrates the difference between As Is, Step Up, and Step Down. The difference between Step Up and Step Down is due mainly to under-pricing and recovery of past losses, not due to often cited reasons of actuarial errors in estimating lapse rates, investment returns, claims projections, etc. Even with the series of rate increases granted by some carriers over the past several years, they continually remind clients that their actuarial models are chronically deficient. Can they really be that bad? Or, are they playing catch-up for chronic under-pricing which is equally bad, if not more so? Strict accounting is necessary to parse the difference.

Overlay

Exhibit 4 is an overlay of all 7 curves. It is intended for one who has mastered all curves and wants a summary view. This Exhibit makes LTCI carrier comparisons easier.

Though nearly all carriers operate with an ALR>MLR and thus share a common theme that of creating a financial risk exposure to policyholders, there can be significant variations among the carriers. Four cases are presented to illustrate how cases can be different. Variations within a carrier are possible based on how a book has performed and how it is viewed to perform in the future. From a policyholder’s perspective industry trending is important but they may be more concerned about their specific book. 

High School Math To Evaluate CBM Rate Models

You might think that predicting rate increases is a complex subject only available to highly skilled actuaries. Nothing can be further from the truth. Like most problem solving, data is key and tells the story. Where to look for data? Carrier’s recent Final Filing at one’s state insurance regulatory web-site or industry web-site called SERFF where filings are public for review & comment. The Final Filing can be extraordinarily thick heavily comprised of revised rate tables that take up much of the space and are of no interest (Ø). However, the essential contents can be found in as little as 3 pages:

  • a 1 page Master Exhibit that looks like a spreadsheet;
  • the discount rate, most often found on this exhibit or listed elsewhere; often, the rate is 5%
  • previous rate history, often found in landscaped template if there have been several, otherwise a brief description in an actuarial

The idea is to create an Essential Data Table or data grid that would look like this. Later, Entity Relationship Diagrams (ERD) provide formal tabular definitions. This ERD is known as an “LTC Carrier Rate Filing”.

Year Gross Premiums Gross Claims Rate History Discount Factor
2015 250000000 392000000 1.51 0.045
2016 237000000 393000000 1.51 0.045
2017 287000000 556000000 1.73 0.045
2018 253000000 490000000 2.12 0.045
2019 303000000 499000000 2.75 0.045
2020 382000000 511000000 3.3 0.045
2021 431000000 527000000 3.3 0.045
Example of a 2018 Filing : For illustration purposes only

The table above is an excerpt of the full book’s life cycle that begins in ~1990 and ends ~2060. Years 2019 and above are carrier’s predictions. The past is set in stone. History and predictions of gross premiums, incurred claims and the discount factor are needed to determine lifetime loss ratio. This is an easy spreadsheet exercise. Acquiring the data and properly formatting it for analysis is the challenge.

The easiest column to explain is the Discount factor. With a variable discount, there exists the need for an additional column in the spreadsheet and only slightly complicates the setup and analysis. Note, if you reject carrier’s future projection of their discount rate and insert your own, you can frame a what if problem.

Regarding Rate History, the value shown in the column is relative to the original premium charged using a aggregate basis of 1.0. A value of 2.12 shown for the year of 2018 means that the premium charged in 2018 is 212% the original. The carrier in this case has been granted a future rate increase in 2020 & beyond so that the policyholder will be charged 330% their original premium, nearly double what was charged in 2017, which was already granted 173% from the original.

Where to find Gross Premiums and Incurred Claims? This is a Master Exhibit data grid, the fundamental CBM that includes the record of Past Premiums, Claims and future projections for each. The Master Exhibit is the “roll up” of actuarial work that creates the numbers in the grid. It is the Projected Premiums that we intend to find (predict) using the 7 rate models. In this paper, the projected claims are accepted as true. This paper’s conclusions about future premiums, and the inherent instability caused by CBM, does not hinge on an expert’s debate about some mysterious claims projection model.

How to find the Master Exhibit in a public filing? They look similar to the template below though format & headings vary. Commonly, separate National and State exhibits reflect their respective experience & projections. State regulators might be concerned with both though the state exhibit might weigh more in whatever ruling is ultimately made on a rate request in that state. The national exhibit may carry weight because the state experience may not meet statistical credibility tests(xi). As books age and have a reduced in-force size, statistical credibility becomes challenged. Books which previously had separate filings are often consolidated with others to pool experience to satisfy credibility tests. It may be that the national exhibit carries the day. Use the columns that are post-increase. Note whether the discount factor has been applied (not the usual case). In the template below, entries marked Ø are of no interest. “Prior to” columns are illustrative and so is loss ratio by year. The discount factor is often omitted in cases where there is a single discount factor covering all years. Other extraneous columns may appear.

Figure 2: Master Exhibit Template

Exhibit (I, A, 1.) – Nationwide Experience Projection

Earned Premium Incurred Claims
Year W/o Proposed Rate Increase Actual Past & Projected Future w/ Proposed Rate Increase Actual Past & Projected Future Loss Ratio Discount Factor
…past years Ø Past results Past results Ø Past assumptions
2015 Ø 2015 Actual 2015 Actual Ø 2015 Actual
2016 Ø 2016 Actual 2016 Actual Ø 2016 Actual
2017Q1-3 Ø 2017Q1-3 Actual 2017Q1-3 Actual Ø 2017 Actual
2017Q4 Ø 2017 4Q Projection 2017 4Q Projection Ø 2017 4Q Projection
2018 Ø 2018 Projection 2018 Projection Ø 2017 4Q Projection
2019 Ø 2019 Projection 2017 4Q Projection Ø 2017 4Q Projection
…future years Ø Projections Projections Ø Projections
Summary                                       Validate your calculations using info below. Most critical is the target ALR after the proposed rate increase.
Past Ø Up to 2017Q1-3 Up to 2017Q1-3 Ø N/A
Future Ø 2017 4Q Projection 2017 4Q Projection Ø N/A
Lifetime Ø Total Premium Total Claims Target ALR N/A

The above is an excerpt of a filing, with rows before 2015 and after 2019 stripped off. The bold columns are the data to place in the appropriate columns in the Essential Data Table.

Cut & paste into EXCEL stripping out columns of no importance. There could be as many as 60 – 80 rows (years) spanning the entire book’s time frame. With proper setup, the analysis becomes one of trivial math for those possessing moderate math aptitude.

For example, let’s look at Standard claims-based model, 80% loss ratio target. What is the minimum information necessary to derive a uniform compounded annual rate increase that will achieve the 80% target? Note that this exercise is performed only when ALR>MLR (e.g. 80%) since if below, a rate increase is not justified. Here is notation to help in the methods steps appearing on the next page:

(Mathematicians: Refer to the link to paper for detailed methodology that includes mathematical notation for easy readability).

Method’s Steps

Step 1: Define PVNR = (PVLC/MLR) – PVPP, the required present value of all future premiums, which is intended to replace the future premiums as defined in the spreadsheet.

Step 2: Find the scale or Step Up factor, ϝ = PVNR / PVPF; since the future premiums as filed are understated, future premiums need to be boosted to attain this factor; note that simply scaling all future PVP[y] by this factor does not solve the problem of finding the compounded annual increase.

Step 3: Develop FPW[y], future premium weighting; for each PVP[y], y>k divide by the sum PVPF to get the weighting vector FPW.

Step 4: Perform iterative refinement as follows, concentrating only on future premiums. In EXCEL with proper setup, Goal Seek performs this function.

a) Start the algorithm with some arbitrary upper & lower bound to the annual compounded increase we are seeking τ, a trial solution;

b) Let τ = 0.5 * (upper + lower bound);

c) Determine a trial ϝ* based on τ computed as
𝑦=𝑁    (1.0 + τ)y − k ∗ D[y] ∗ FPW[y]
    y=k+1

d) If | ϝ* – ϝ |< ε (a solution error tolerance e.g. 0.0001), the solution has been found, go to Step 5. If ϝ*>ϝ, then τ is too large thus set the upper bound to τ, else τ becomes the lower bound as τ is too small. Repeat by looping back to 4.b.

Step 5. Final solution is τ.

No actuarial abilities required. A Math honors High School sophomore would be capable of solving this problem once the problem is framed, data is available and placed in a grid. This can be as little as a 3 column EXCEL spreadsheet.

In many of the rate filings the past several years, τ is very often >0.05 and can be much higher. A compound annual increase of this magnitude is shocking. The reason can be discovered by fully understanding the mechanics of CBM. Some might say, “a 5% premium inflation is not so bad as the PH is getting older and health inflation is about this value”. No. These factors have already been accounted for in the initial policy pricing as the pre-funding component was designed to address age and LTC cost trending. While it is true that LTCI might have been underpriced due to actuaries’ underestimation of LTC costs, a great part of the increase is due to carriers’ attempt to recover past under-pricing.

Simply understanding the previous discussion allows one to understand the reasons behind future rate instability. Often, regulators will cite the under-estimation of LTC costs as the single biggest factor behind rate increases. Rarely, if ever, is there notation of past under-pricing. When this factor is not listed in an executive summary, policyholders are being mislead as to the true nature of their contracts. Past under-pricing effects can best be measured by the difference between Step Up and Step Down.

By contrast with the previous method, the Uniform and Step Down methods must reassess the premium past. To perform each, premiums that were raised in the past from original pricing must be discounted by rate increases. This is the importance of having Rate History as a tabular column, hence its inclusion in the Essential Data Table. Each of the algorithms must consider past premiums by their initial base premium (arbitrarily defined as 1.0).

The Uniform method uses the exact method as previously described with this past premium adjustment applied. The method is similar as before but with a look-back in time.

The Step Down method does not use the power function (i.e. (1.0 + τ)^(i – k)) as it adheres to the objectives previously stated (level premium, non-discriminatory, no chargeback for under-pricing). Though the method uses iterative refinement, the equitable variant seeks to find a flat rate that is good for the entire book’s life (past, present, future) to meet the statutory MLR target. Like other models, it does not contest carrier’s actuarial future claims expectations.

A carrier or regulator might argue that higher premiums would force policyholders to additionally lapse therefore these projections are unrealistic. If premiums were 10x original, who would not lapse? The response is that it is true that none of the models consider forced lapses due to hiked premiums. If forced lapses were an intent, that should be disclosed and even then might be construed by some as bad faith pertaining to a long duration contract. Turns out they are disclosed. From one carrier’s recent rate filing, “In addition to the lapse rates shown, we assume a 2.9% lapse rate due to the rate increase. The additional lapse rate is used to adjust future premiums and claims down by 2.9% starting at the effective implementation date of the rate increase”*(xii). Yikes! Does this mean that carriers are really intending to force lapses as a way to shift liability from themselves to PHs? Surprised that they say this publicly in a rate filing. LTCI contracts were intended to shield consumers from LTC financial risk not cause consumers to un-shield due to deleterious effects of deferred and untimely rate actions or expose them to late stage financial risk.

For the moment, consider another metric that is easily obtainable that could “solve” the MLR problem without raising premiums. That would be the required percentage of future claims reduction to bring the book to its MLR target. The calculation is within reach of a Freshman High School math student.

Step 1. All of the following are usually stated in the Master Exhibit on the summary line

– Let pvCTL denote Present Value Claims to Last Rate Increase;
– Let pvCLIFE denote Present Value Claims Lifetime;
– Let pvPLIFE denote Present Value Premiums Lifetime;

Step 2. Let tFC denote Target Future Claims = (MLR * pvPLIFE) – pvCTL

Step 3. Solve for Reduce Future Claims % = 1.0 – (tFC / (pvCLIFE – pvCTL))

If methods that use power function, iterative refinement, or EXCEL Goal Seek are too much to digest, the fallback would be to use simple algebra to determine what is required on the claims side. Using the result of Step 3 and (pvCLIFE – pvCTL), you can easily determine what future claims liability the carrier is attempting to dump. Now that is telling! Another industry offered “solution” involves rate dampening and reduced coverage, somehow presented as a good faith one-way negotiation between you and carrier. These so-called solutions tell a seemingly different story, but it really is the same story. All this is intended to do is to transfer the LTCI liability from their balance sheet onto yours. Spoken as architects of a personal strategic financial planning model, you need to be aware of this external threat should your financial (LTC) plan be based on an LTCI legacy product.

Fundamental Causes of Future Rate Instability

Rates would not be unstable if ALR<=MLR. Secondly, this section does not apply to the rate neutral model or the As Is model. For the others, there are 3 factors that contribute to high, late life cycle premiums:

  • The degree to which future rates need to grow is related to ALR/MLR. For example, if ALR is 1.8 and MLR is 0.6 somehow suggests a multiple of 3.0. On the other hand, if ALR were 1.2 or a 2.0 multiple, that would suggest smaller premium growth needs.
  • The extent to which past premiums have led to the current ALR. If past premium growth has say doubled and the ALR is still well above MLR, the projected premium needed to correct for MLR will rise as a multiple of your higher average premium level.
  • Most important — where the book is in its lifecycle!

A graphical illustration helps. This graph is typical for the entire LTCI industry although differences exist among carriers & books. D[i] is the discount rate with 2019 as the referential year (i.e. D[2019] = 1.0).

Figure 3: Discount, Life Cycle, Corrective Scaling

LTC Discount, Life Cycle, Corrective Scaling

Consider this sample book with the inception year of 1999 with a 50 year life. What is illustrated in the Life Cycle curve is the percentage terms using Premium weights. LTCI premiums are front-loaded to deal with claims that lag. From the graph you see it takes a dozen years (2011) to mid- or 50% life*(xiii). Most legacy cases have a mid-life 2009 – 2011. The Corrective Scaling curve is computed as (1.0 / (1.0 – lifecycle %)). This represents a factor required to correct for past premium deficiencies. Beyond mid-life, the scaling ramps up rapidly as an LTCI (premium) book is running out of real estate due to discounting effects. The uncorrected errors of the past weigh heavy whereas the future is lightly weighted. This is an inherent deficiency of CBM’s usage in LTCI. Failure to correct premium deficiency early leads to a death spiral.

An approximate back-of-the-envelope calculation requires minimal information plus the graph above. Say your carrier files for a rate increase in 2018 with an ALR (1.2)/MLR (0.6) having under-priced their book for the past 20 years. Step Up suggests a 6-fold (2 x 3, refer to 2018 Corrective Scaling in graph) raise in premiums. To perform a precise analysis requires the data and formal approaches previously described.

Summary And Conclusions

This paper has summarized methods that the LTCI Consumer Advocates can use to evaluate LTCI legacy products. The models presented can help in projecting the financial destiny of an individual or couple’s LTCI rather than to leave them to solely rely on what carriers or public officials might claim or predict about LTCI. While some might argue with the nature or accuracy of projections, projections are nonetheless an important feature in any holistic financial planning. Carriers and regulators rely on projections, so too should the consumer but with a version customized that clarifies their view and future stake in LTCI ownership. If carriers’ projections heretofore have been wrong, as they have consistently claimed as part of rate justification, why would you trust what they say or determine as a remedy?

Legacy LTCI appears to be a failed product not living up to its intended purpose as a risk hedge for Long Term Care expenses. This is largely due to unproven and untested methods used by the carriers for LTCI, particularly Claims-based modeling (CBM). While this approach may be appropriate for other insurance lines, it has proven unsuitable for LTCI.

In a previously well-thought out retirement plan, a legacy LTCI product should now be viewed with suspicion due to its unpredictability relating to recent history of scaled-up premiums with no apparent end or industry remedy in sight on these questions.

Though not the subject in this paper, there may also be issues related to carriers’ long-term claims paying ability and solvency. Industry publications, especially those from NAIC, can be found that shed more light.

Inherent in traditional CBM models are recognizable elements that create rate instability. There are several factors, a key one is the result of LTCI carriers failure to file rate increases early in a product’s life cycle. Late stage recovery efforts, through a hidden but rarely disclosed chargeback scheme to a diminished in-force results in highly scaled-up premiums now being witnessed. Does it seem reasonable that premiums should be treble what they were just a few years ago when they were flat for the prior 10 – 20 years? Nor does it seem reasonable that regulatory bodies require carriers to issue written rate increase notifications to policyholders only 30 days in advance, then put pressure to make a critical decision (whether to pay the increase, exercise a benefit buy-down option, or lapse for contingent benefits) within such a short time window.

Finally, policyholders, or their agents, should insist upon a more neutral and equitable method of adjudicating rates. A Step Down method was discussed that: (1.) would not make policyholders responsible for carriers’ past losses due to under-pricing, (2.) would address of issue of discriminatory pricing, (3.) would meet MLR targets immediately, (4.) would clarify a book’s true ALR/MLR status immediately to all stakeholders, and (5.) would be a one-time change, avoiding the extraordinary maintenance in handling a legacy product.

In Retrospect, would you have signed on?

At the time of sale, policyholders heard “though carriers could raise rates, this particular carrier has never raised rates”. A savvy purchaser might have asked, “under what conditions could the carrier raise rates”? Had the agent been knowledgeable, trained to answer, or prescient, he or she might have answered, “if lapse rates are too low, if interest rates do not oblige, if our claims expense projection models are wrong, if we need to chargeback due to under-pricing, if our mortality tables are dated, if our morbidity tables…,etc.”.

Bad luck to PHs, all the if(s) came true. You might have been better off in Vegas. 

Path Forward

Before departing, the authors would be remiss not to offer remarks on strategic modeling as that is our forte and reason for being here. Some points that seem obvious or curious:

  • If the product pricing was known to be interest rate sensitive, then why not do what is customary in any modeling or financial engineering exercise? And that is, would it not have made sense to stress test the product by running a wide range of interest rate scenarios*(xiv)? What is the LTCI industry’s reaction and response to the emerging world-wide interest rate environment, including such a remark made by former Federal Reserve Chairman Alan Greenspan, “It will not be long before the spread of negative interest rates reaches the S.”?
  • The industry has made the frequent claim that that lapse rates were understated and therefore has frequently been used in the actuarial justification for rate increases. Calculation of lapse rates is not rocket science. For example, if a lapse rate of 10% was expected for 1st year lapse and you have 1000 in-force to start, 950 by 1st year, the actual is a 5% lapse rate with a deviation of -5%. After a decade of experience, lapse rate modeling should fall into the bin of deterministic modeling. Further, if product pricing was known to be lapse rate sensitive, why not stress test to determine pricing adequacy to account for possible sensitivity?
  • The chronic under-projection of claims expenses is bewildering. It is normal practice to frequently retune or recalibrate with a highly sensitive ear knowing what the impact could be on an LTCI business model and do this right out of the gate. How is it that under-projection is used by a carrier numerous times as a rate increase justifier? Has there ever been an instance where a prior claims expense projection has later been determined to have over-stated future expenses? One skilled in projection modeling would, as normal practice, consider a model commercially usable only when it exhibited stability or robustness within an acceptable error tolerance with neutral bias to either (i.e. the over & the under) side.

The contents of American Academy of Actuaries “Exposure Draft of the Practice Note on Long-Term Care Insurance” of January 2019 alludes to deficiencies and remedies. But, why so late?

As practitioners of strategic personal financial planning, it would be necessary to get at the source of confusion. Whether or not a client of financial planning has LTCI or not (or intends to acquire new LTCI product set, known as LTC 2.0), one aspect that is particularly important is to reasonably project LTC experience using proposed “First Principles”. Once LTC projection modeling is isolated and addressed, then the next logical step would be to consider some of the above open issues regarding LTCI. It’s important that, if there are fundamental LTCI modeling errors, those errors should be identified, not allowed to propagate and cause harm.

The subject of claims expense modeling might well be the next avenue of pursuit. This topic is more complex than techniques described in this paper but far less complex when measured against other models that comprise an integrated, strategic financial planning model.

Entity Relationship Diagrams, Formal Systems Treatment

The following is a formal description of tabular definitions and relationships to construct a more comprehensive view of claims-based modeling (CBM). This is the approach used in reporting results in tabular or graphical format after applying the analytical methods described herein.

Claims Based Modeling Entity Relationship

The LTC-Carriers is a table containing all carriers identified by a unique Company Code. Such a table can be constructed from publicly available NAIC documents.

Typically, an LTCI carrier has one or more Policy Forms or Book-of-businesses identified by Company Code, Policy Form, and whether Individual or Group policy (some policy forms can be both individual and group). This table too can be constructed from NAIC publicly available documents. Combining books seems to be accepted as policy counts dwindle and done for reasons of administrative efficacy.

Many of the data elements listed in these tables have no relevance to the discussion in this paper, but might be used in an extended LTCI application on behalf of Consumer needs and interests.

For each carrier’s Policy Forms, there may be one or more rate filings spanning years. Each filing is known by a unique SERFF-ID, an industry naming standard.

Each SERFF filing has many row elements in an LTC Carrier Rate Filing depending on the Policy Form’s span of years from inception to finality. The LTC-CarrierRateFiling table is what was earlier referred to as the Essential Data Table.

The tabular construction of these 4 tables shows several one-to-many relationships. One carrier may have several Policy Forms (or Books). Each of those may have had or will have several Rate Filings. Each Rate Filing will have a separate Rate Filing table but within each will have multiple entries or “rows” to reflect each year.

These tables are so constructed to allow many other types of analyses that are beyond the scope of this paper.

Further, other table definitions not shown can integrate with this set to greatly expand information processing as it relates to LTCI.

This is the Entity Relationship diagram that defines the output table from analysis.

CBM Entity Relationship

The relationship to the prior Rate Filing table is indicated. The contents of the LTC Rate Projection table are then accessible to Reporting systems that created the graphs contained in this document.

Use of ERD, other methods described in this paper, and other methods yet to be developed allow the creation of a customized application that can shed further light on a PH’s contract, what their expectations should be, and what decisions or actions that they might take to advance their best interests.

An at a glance review of key metrics for an individual skilled in the art of LTCI metrics. An output presentation such as this one can be constructed from the ERD and analysis methods described in this paper.

The information content might be beneficial to an LTCI consumer or advisor.

Figure 4: Analysis Of an LTCI contract, Key Metrics

Claims – Based Model : Metrics Result
Last year of granted increase per filing 2020
Contract life (using premiums as the basis). Half-life year / percent for year above 2009 / 77%
Net increase since contract inception 230%
Therefore, premiums will be this multiple of your original premium 3.30
The lifetime loss ratio target for the following analysis is 0.80
Predicted lifetime loss ratio resulting from filing 1.06
Carrier projected claims in the class-based model is accepted true But not proven true
Future premiums need to be scaled by this factor to meet loss rate target, known as CBM Step Up 2.41
If Step Up were applied, your premiums have scaled up this factor since inception 7.95
In lieu of CBM Step Up, the compound annual rate increase needed to meet loss rate target 11.0%
Or, without any further premium increase, a reduction of claims paid by 54.9%
To achieve the target loss ratio, carrier liability would be reduced in billions $3.71
A rate neutral, non-discriminatory premium would be this multiple of your original premium, CBM Step Down 1.77
The contract remains in an uncorrected state, exposing you to further premium increases or claims loss
Premium to year of last rate increase, the average premium multiple over the life 1.26
Life scale factor, defined as 1.0 / (1.0 – life cycle%), a key factor in rate correction 4.33
Loss ratio / target loss ratio scale factor, a key factor in rate correction 1.33
All 3 factor above combined to arrive at an Analytic Step Up 7.23
Analytic Step Up and CBM Step Up difference, CBM often greater since it accounts for reduced policy count 0.73

The example shown above is an example for one rate filing. By collecting a representative sample of such forms, one can extrapolate certain interesting industry metrics. For example, the line item “carrier liability would be reduced in billions” can be scaled up by aggregating samples and noting each carrier’s market share and the % of book that filings represents of each carrier’s total book.

Exhibits, Views

A series of exhibits follows. The term View means a Consumer perspective, one that has been developed from publicly available data sets, processed and presented in a way to reveal or disclose a storyline that the consumer has not heard but would benefit from hearing.

The first 4 exhibits (Exhibit 1, 2, 3, 4) derive from one actual case. While each case (i.e. carrier’s rate filing for a specific book) has a story to tell, this particular 4-set is representative of many cases.

The 3 exhibits that follow (three additional overlays or Exhibit 4s) are separate cases with their own story.

In reviewing the exhibits, note that Premiums are graphed relative to a basis of 1.0. For example, if the original premium was $2,500 annually, a curve that has grown to intersect at the 2.0 y-axis means a premium of $5,000. A 3.0 y-axis intersect is a trebling of original premiums and is not uncommon for legacy products.

Note that for any policy form (“book”), there are a wide variety of coverage options & riders. There is no attempt here to discuss the various coverage permutations. At the time of purchase, an agent might have spent considerable time customizing coverage for proper fit. The issue in lapse decision making is that, under duress of rising premiums, the customized fit is lost in the shuffle.

A premium basis of 1.0 is considered “in the aggregate”. In some filings, for example, a policy that has No Inflation benefit might be the main object of a rate increase while the more conventional option of having a compound annual benefit increase % may not be, vice versa. But if you were to look a historical series of rate increases for the same book, it is often the case that if one benefit option was the object in one increase, the other is the object in another. Analyzing the aggregate gives a broad look at overall industry or carrier trending, but lacks the detail necessary to analyze your specific policy.

As an example, in one jurisdiction, a carrier filing recently filed for a 0 – 331% increase. If you were the policyholder, you would naturally want to know whether you are on the 0% or the 331% end. You would need to have knowledge of your policy form and consult the rate filing for specifics. If you were to perform the analysis described in this paper, you would have to take great care in locating which Master Exhibit in a rate filing pertains to your policy form. Most aged-up policyholders are stopped right here, not knowing what the industry jargon obfuscating term “Policy Form” means, a vital piece of information you need to know. Your attention might be drawn elsewhere wondering, “how is it possible for such an enormous range to even exist”?

As a footnote, the analysis does not consider other payment plans that other policyholders might have chosen. If, for example, a policyholder elected a One-Time payment option (for the lifetime contract), or Ten-Pay (pay in 10 years for the lifetime contract), or Pay ½ annual premium upon reaching age 65, are these policyholders subject to rate increases – or is it just those who elected to pay annually? If those alternate payment plans (e.g. paid up) are excluded from rate increases, does this unfairly penalize those in the same book who decided to pay annually for their lifetime contract? LTCI is often compared to and categorized as Health Insurance, but a health insurance contract renews each year with different Terms & Conditions whereas with a lifetime contract, such as LTCI, the Terms & Conditions are static.

LTC Implied Future Rate

The lines representing future rates have been created using data in carrier filed rate requests & then applying claims-based modeling to achieve lifetime loss ratios. Note this is not an exercise requiring actuarial background nor does it require great quantitative sophistication. The curves are not created by the use of mathematical curve fitting techniques though one might think they are. You might ask which target loss ratio line seems to fit the curve the best.

LTC Historical vs. Implied Pricing

The above history suggests 75% of the product form(s) life cycle. A percentage past mid-life (50%) suggests less latitude to correct for the target loss ratio without dramatic action. Such implies greater policyholder risk to future rate increases or offers of unattractive benefit buydowns. The risk is particular great with aged LTCI contracts or when the gap between the Actual and Uniform is or has been large.

LTC Step Up vs. Step Down (Rate Neutral)

The Rate Neutral Premium (Step Down) method shifts burden of past underpricing onto carrier where it belongs and not on to present policyholders in a declining pool. The illustration is derived from the most recent rate filing. The method   uses carrier’s historical & projected claims as a given but attibutes underpricing loss to the carrier by scaling premiums to achieve the target loss ratio. In doing so, the method avoids: 1. the constant ramping up of future rate increases inherent in standard claims-based industry models by using the power function for smoothing effect, and 2. discriminatory pricing to aged-up policyholders.

  • When the Step Down line appears above the Actual line prior to rate increases, one might view this as a chargeback to the carrier from their underpricing in the form of an artificially scaled-up premium which reduces loss ratio to better meet target. Note: The graph does not show scaling due to the discount-in-arrears (inflation) factor.
  • In some cases, the Step Down line may appear below the Actual line in the recent past. This means the policyholder has been overcharged to the degree represented by the gap between the two lines.

When the Step Down appears below the line in the future, this is prospectively what the policyholder might be overcharged. Refer also to the Composite View for future comparisons against other loss rate scenarios.

4 Case Examples Follow, all Ugly by degree

Case 1: Many rate hikes already (ALR >1.0), still going strong!

LTCI Rate Projection, Composite View

The illustration above does not include the effect of additional lapse behavior nor does it include the effect of benefit buydowns (e.g. CBUL), actions solely attributed to higher premiums that one could consider forced. Such forced actions are likely to benefit carriers who seek to reduce loss ratios but come at policyholders’ expense, especially if the benefit buydowns are unattractive (in terms of loss of policyholder net present value). Thus, the analysis does not reduce claims projections so as to properly reflect the true risk exposure to policyholders

This case is the same as Exhibit 1, 2, and 3.

Case 2: ALR <0.9, but appears headed to MLR of 0.6

LTCI Rate Projection, Composite View

The illustration above does not include the effect of additional lapse behavior nor does it include the effect of benefit buydowns (e.g. CBUL), actions solely attributed to higher premiums that one could consider forced. Such forced actions are likely to benefit carriers who seek to reduce loss ratios but come at policyholders’ expense, especially if the benefit buydowns are unattractive (in terms of loss of policyholder net present value). Thus, the analysis does not reduce claims projections so as to properly reflect the true risk exposure to policyholders.

Case 3: A disaster waiting to happen!

LTCI Rate Projection, Composite View

The illustration above does not include the effect of additional lapse behavior nor does it include the effect of benefit buydowns (e.g. CBUL), actions solely attributed to higher premiums that one could consider forced. Such forced actions are likely to benefit carriers who seek to reduce loss ratios but come at policyholders’ expense, especially if the benefit buydowns are unattractive (in terms of loss of policyholder net present value). Thus, the analysis does not reduce claims projections so as to properly reflect the true risk exposure to policyholders.

Case 4: Good news! This carrier says they won’t head to 0.60, where then?

LTCI Rate Projection, Composite View

The illustration above does not include the effect of additional lapse behavior nor does it include the effect of benefit buydowns (e.g. CBUL), actions solely attributed to higher premiums that one could consider forced. Such forced actions are likely to benefit carriers who seek to reduce loss ratios but come at policyholders’ expense, especially if the benefit buydowns are unattractive (in terms of loss of policyholder net present value). Thus, the analysis does not reduce claims projections so as to properly reflect the true risk exposure to policyholders.

End Notes

i) The value of 4.5% shows up frequently. It is close to the value of face cap coverage benefit inflation; close to Federal Reserve reported US Consumer Health care long-term inflation; close to discount factor (aka Investment Rate) most often used in claims-based modeling.

ii) Policyholders are often surprised to learn that they are members of a book-of-business and then learn that their past and possibly future destiny depends upon the experience of their particular group to which they belong. Your neighbor across the street may have the same insurance carrier, the same fancy LTCI brochure (almost), and yet have a totally different experience with regard to premium behavior.

iii) JEROME SKOCHIN, SUSAN SKOCHIN, and LARRY HUBER, individually, and on behalf of all others similarly situated, Plaintiffs, v. GENWORTH FINANCIAL, INC. and GENWORTH LIFE INSURANCE COMPANY, Defendants. IN THE UNITED STATES DISTRICT COURT OR THE EASTERN

DISTRICT OF VIRGINIA, Case No. 3:19CV00049 – Excerpt “nationwide price increase action plan that required systematic annual rate increases on the scale of 60% in 2013, another 60% in or after 2014 and more 350% over the next 6-9 years”. Ambiguous — additive or multiplicative? If the latter, would be 9x by 2023!

iv) Failure to meet this expiry date can then result in the policy’s lapse with zero cost recovery.

v) LTCI is considered a long duration contract (LDC). In February 2014, the FASB (Financial Accounting Standards Board) initiated discussions targeted at improving the accounting for insurance contracts with special emphasis on long-term duration contracts.

vi) If the discount factor is non-uniform across a time span, a simple algorithmic method is needed in lieu of the simple formula.

vii) “American Academy of Actuaries” in a January 2019 “Exposure Draft of the Practice Note on Long-Term Care Insurance

viii) Long-Term Care Insurance (B/E) Task Force April 8, 2019, Minutes

ix) American Academy of Actuaries in an Oct 2018 Issue Brief, “Considerations for Treatment of Past Losses in Rate Increases Request”,

x) This paper does not take a position on recovery of excessive past premiums that a policyholder might believe due to them. We point to what is known as the Filed-Rate Doctrine — broadly applied as a federal and state common law doctrine to preclude lawsuits that challenge the payment of rates filed with a state or federal regulator and any wrongful conduct leading to or in connection with securing filed rates from the regulator. Whether or how this Doctrine applies here is outside our interests as financial planning architects of a forward looking approach to hedging LTC risk.

xi) There is an entire actuarial sub-science that addresses what is credible statistically. From elementary statistics, one learns that samples must of sufficient size to draw meaningful conclusions.

xii) SERFF-ID: MULF-130960272 final filing, “Actuarial Memo”

xiii) Some books are quite dated — past 80% life. Although of concern to affected policyholders, the in-force counts are often very low to be of national economic significance.

xiv) One interest rate generator designed by the authors is described in section Interest Rate Scenario in “Systems and Methods for Consumer Mortgage Debt Decision Support”, pp 5-6, https://www.financialmedic.com/Model/Portals/0/US20090063328A1.pdf