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Hindsight IBNR to Case Ratio – Excel Template
This template is designed to complement the webinar on the same topic. This is available for free for a limited time. I hope you find this a valuable addition in your loss reserving toolset.
P&C Insurance Naming Conventions – Loss, Expense, and Reserves
Feel free to download this handy PDF to help make sense out of insurance terminology. Do you have a suggested edit or improvement? Let me know!
Supplement to Loss Development and Bornhuetter-Ferguson Methods Video
Estimates of Ultimate Loss as a Weighted Average of Two Common Methods
Like many actuaries, I often find myself selecting ultimate losses based on indications from standard actuarial techniques.
In some of my analyses, I now add a column that shows the implied weight given to 1) the initial expected ultimate loss assumption, and 2) the incurred (or paid) loss development method.
This “implied weight” column helps quickly identify where I am selecting along the stability/responsiveness continuum that exists between the respective methods. These weights are easily calculated using the age-to-ultimate factor.
There’s nothing earth-shattering about this but I do find it helpful in maintaining one’s bearings when making selections.
Feel free to download the Excel version of the above image here:
Triple Whammy Effect
In P&C insurance, bad news often begets more bad news, and good news often begets more good news. In this context, “bad news” means higher-than-expected loss emergence and “good news” is lower-than-expected loss emergence. Let’s explore the underlying reason for this, which I named the triple-whammy effect.
When reported loss emerges higher or lower than expected, there are three distinct effects. The first is a direct effect, and the second two are reverberations of the preceding effect.
Consider a case wherein reported losses emerge by a materially higher-than-expected amount:
Whammy # 1 – Ultimate loss estimates increase by an amount equal to the higher-than-expected reported loss emergence.
Whammy # 2 – Additional IBNR (aka unreported loss) is necessary to cover development on the higher-than-expected reported loss emergence.
Whammy # 3 – Additional IBNR is necessary to cover development as a result of revised assumptions about future loss development and its effects on the entire portfolio.
If you are familiar with the reported loss development method, it will be easier to understand each of these effects. The chart below illustrates a scenario wherein the effect of each of the three “whammies” can be observed.
In this example, we start with $5M of reported loss. Per the reported loss development method using a selected age-to-ultimate factor (ATU) of 1.5, IBNR of $2.5M is indicated, resulting in a total ultimate loss of $7.5M.
Suppose we discover an additional $1M of reported loss that was not previously included. The addition of this loss will require our estimate of ultimate loss to increase by $1M (whammy # 1).
We also need to include a provision for development on the $1M of additional reported loss in the amount of $500K (whammy # 2). Note that this amount is determined by the magnitude of the ATU factor.
Lastly, the additional $1M of reported loss results in a re-evaluation of our development pattern and the ATU factor is judgmentally increased from 1.5 to 1.6. This factor is applied to all of the underlying reported loss (the original $5M plus the additional $1M). Consequently, total IBNR increases by another $600K (whammy # 3).
In practice, actuaries do not rely exclusively on the reported loss development method, so this triple-whammy effect tends to be mitigated. However, this example accurately reflects the upward pressure created on reserve estimates when higher-than-expected reported loss emergence is observed. Of course, these principles apply similarly when there is lower-than-expected reported loss emergence.
Double Weighted Averages for Loss Development Factors
When selecting loss development factors, actuaries often rely heavily on loss weighted averages. These are generally superior to straight averages because they help prevent unusual data points from skewing averages.
In this post, I describe an enhancement that I call the Double Weighted Average. With the Double Weighted Average, the first weight is loss volume (as in the loss weighted average) and the second weight is a function of time, with the most recent data typically receiving the most weight.
Here is the simple scheme I often use to determine the time-based weights:
First, select a starting weight (designated in the example below by α).
Vary the value of the weight based on the recency of the loss data being evaluated.
Losses underlying the 1st prior development evaluation receive a relative weight of α1.
Losses underlying the 2nd prior development evaluation receive a relative weight of α2.
Etcetera.
When the selected starting weight equals 1.00 (α = 1.00), the time-based weights are applied uniformly across all periods. This special case reduces to a loss weighted average.
When the starting weight is between 0 and 1.00, the most recent periods receive more weight than the older periods. The smaller the value of α, the more weight is applied to the loss development for recent periods. When α is very close to 0, nearly 100% of the weight is applied to the most recent development period.
Note that the time-based weights are relative. The actual weights for a specific application depend on the number of data points in the calculation. This example uses 13 data points.
There is no “correct” starting weight. I generally look at double weighted averages using α values between 0.75 and 0.95. Actuaries commonly calculate a series of weighted averages (e.g., all-year, 5-year, 3-year) in recognition of the fact that older periods that may be less representative of current development patterns. The Double Weighted Average is a great way to contemplate ALL historical data while still reducing the influence of the older periods.
Feel free to download the sample Excel file below for a closer look at the formulas in this example.
Smoothing Age-to-Age Loss Development Factors
Actuaries – here’s an easy technique to help smooth lumpy loss development factors. You can use the relationship between adjacent age-to-age factors (ATAs) from a benchmark loss development pattern to “reallocate” the development for a company-specific pattern.
In the example below, the historical average ATAs exhibit some volatility in the age 36 to 72 month range.
No problem.
Using our benchmark pattern, we calculate the ATA factor for ages 36 to 72. This is simply the product of the respective ATAs for ages 36 to 48, 48 to 60, and 60 to 72, and equals 1.172.
Next, we calculate the logarithmic relativities corresponding to the 36 to 48, 48 to 60, and 60 to 72 periods. As illustrated in the exhibit, these are calculated as the ratio of the natural log of the ATA period to the natural log of the entire 36-month period (age 36 to 72).
Lastly, we apply the relativities as exponents to the initial selected (unsmoothed) ATA factor for the corresponding 36-month period (age 36 to 72).
So how did we do?
Pre-smoothing: The product of the initial selected ATA factors from ages 36 to 72 equals 1.143.
Post-smoothing: The product of the smoothed ATA factors from ages 36 to 72 still equals 1.143.
The shape of our ATA pattern between ages 36 and 72 now mirrors that of the benchmark pattern (which is nice and smooth in our example).
Success!
A cool feature of this technique is that the unsmoothed/smoothed age-to-ultimate factors for earlier ages (ages 36 and prior in this example) are equal.
If no benchmark pattern is available, a version of this technique can still be used but requires some judgment.
You can download an Excel version of this exhibit below.
Claims Disposal Ratio
Monitoring and interpreting claim closing rates are important to the success of any P&C insurer. In this post, I share a metric that is extremely informative, yet rarely seen in the wild. I call this metric the “claim disposal ratio”.
A claim disposal ratio measures the number of claims closed in a calendar period relative to the total inventory claims available to be closed.
The total inventory of claims available to be closed equals the open inventory at the beginning of the calendar period PLUS any claims reported during the same period.
Is this metric a part of your organization’s performance indicators? I am curious to hear feedback from anyone who uses this metric and what you call it.
You can download an Excel version of this exhibit below.
Exposure Adjustment for Policy Year Loss Development Factors
Exposure adjustments for loss development factors is a fairly straightforward procedure that is sometimes overlooked.
Two key occassions to consider exposure adjustments are:
- When developing incomplete policy years or accident years, and
- When interpolating LDFs for incomplete policy years.
Below is an Excel file containing sample calculations for exposure adjusting and interpolating policy year LDFs.
Estimating Tail Factors Using an Exponential Decay Model
An exponential decay model is one method P&C actuaries use to estimate tail factors for loss development patterns.
Although research has suggested that this model may not be optimal in all cases, it has several attractive features which support its continued use in the profession:
- An exponential decay model can easily calculate age-to-age factors that converge towards 1.00 at a decreasing rate.
- A tail factor can be calculated based on only two assumptions: a) the most mature credible age-to-age factor, and b) a selected average decay exponent.
- Decay exponents can be calculated from existing loss development patterns: a) between consecutive age-to-age factors, and b) the average decay implied in an existing tail factor selection.
The attached image describes the key formulas needed to estimate age-to-age factors and tail factors using an exponential decay model.
One of my favorite uses of this model is to calculate the implied decay exponents underlying loss development patterns (and tail factors). Over the years, I’ve gained a comfort level for what range of exponents is reasonable for various coverages. This is one more way to reasonability-check loss development factor and tail factor selections.
If you are interested in seeing a full example, feel free to download a free Excel spreadsheet containing sample calculations. In this example, I used an industry WC paid loss development pattern to illustrate the model. Surprisingly, my first attempt at selecting parameters resulted in an tail factor indication almost exactly equal to that selected by the original industry source.
If you’ve found this interesting, please let me know. Be sure to follow for more useful actuarial content!
Clarifying Questions to Ask about Incurred Loss Ratios
Insurance professionals: when you hear, “the incurred loss ratio is 60%”, how do you know if that’s a good thing or a bad thing?
The incurred loss ratio is a fundamental measure of profitability for insurers but in a vacuum, this measure is meaningless.
In the attached exhibit, I highlight the questions that must be asked to establish the context necessary to correctly interpret incurred loss ratios.
What other questions would you add?
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Case Reserves vs IBNR – A Summary
Why do P&C insurers need IBNR? After all, claims adjusters establish case reserves after a thorough, expert evaluation of each individual claim.
There are several reasons that case reserves are generally insufficient to cover the unpaid liability of a P&C insurer. And guess what – it’s not because claims administrators are not good at their job.
Below is a handy summary of the key differences between case reserves and IBNR along with the 4 primary sources of IBNR.
Types of Loss & Premium Reserves – A Quick Overview
We often hear about loss reserves for P&C insurers, especially case and IBNR. But there are other types of liabilities that insurers are required to recognize. The attached summary provides a 50 thousand foot view of the various types of P&C reserves.
I hope you find this summary handy. Be sure to follow me for more actuarial and risk management content!
Hindsight IBNR – Definitions
In the attached exhibit, I propose two distinct definitions of Hindsight IBNR and show how they are algebraically related.
Hindsight IBNR is a very useful concept, though in my experience, I have found it a bit too nuanced for non-actuarial audiences. I’m optimistic that can be overcome. I have been exploring new uses for this metric and plan on sharing more about it in future posts.
Any thoughts or anecdotes about your use of Hindsight IBNR (or Hindsight Reserves) would be valued.
Components of Loss Reserve Changes
What is in a loss reserve change?
Many actuarial reports focus on the change in loss reserve balances between respective reports. These amounts, while informative, do not give the reader enough information to accurately judge the performance of an insurer’s portfolio.
A loss reserve liability is the amount carried on the balance sheet – this amount represents an insurer’s recognized obligations to pay future loss and loss expense related to claims that have already been incurred. A change in this amount, whether positive or negative, does not allow the reader to draw definitive conclusions.
The attached exhibit shows the three items that can be used to reconcile an earlier loss reserve estimate with a later one. These items can be used to calculate more meaningful metrics, such as the change in incurred loss liabilities on the insurer’s income statement.
Ideally, a reconciliation similar to the one in the attached exhibit should be found in most actuarial reports for loss reserves. This presentation helps the reader connect the dots between loss reserves and other important financial metrics. It also shows the extent to which changes in prior actuarial estimates of ultimate loss influence current results.
How to Calculate Net Level Premium Reserves (For Life Insurance)
A well known concept in life insurance reserving is the net level premium reserve. Jeremy Levitt, CEO of the Graeme Group and I teamed up to create the attached summary that describes the formulas actuaries use to calculate net level premium reserves.
The net level premium method is a conservative approach used to calculate valuation reserves and is a staple of the life actuarial profession. In short, the net level premium reserve equals the present value of future benefits less the present value of future valuation premiums. You can find a PDF version of the attached summary on my website, below.
Did you know that Graeme Group (GG) is a powerful international network of top performing actuarial contractors? GG represents experts in the fields of life insurance, P&C, and healthcare. Its professionals are experts in crucial software programs such as Prophet, ResQ, Arius, ALFA, AXIS, R, SQL, Python, and others.
Grame Group is exclusively focused on actuarial needs, is owned and run by actuaries, and has powerful partners many of whom are the largest employers of actuaries in the world. I encourage you to check them out here: https://www.graemegroup.org/.
Loss Reserve Forecast for Self-Insured P&C Programs
For self-insured P&C programs, loss reserve estimates are generally provided at a single point in time. In this post, I describe the benefits of providing an additional loss reserve estimate evaluated at a future date, which I call a loss reserve forecast. Often, this amount can be calculated with relatively little additional effort, making it attractive from a cost/benefit perspective.
For most self-insured programs, actuaries provide an estimate of loss reserves at a the desired evaluation date. This estimate is used by company management to establish loss reserve liabilities that reflect future payment obligations. In many instances, actuaries also provide a forecast of ultimate losses for the prospective program period. This can be used by the self-insured to maintain adequate loss reserve liabilities between actuarial reports. In this post, I advocate for a third estimate, a loss reserve forecast.
A loss reserve forecast is just a loss reserve estimate at a future evaluation date, for example, one year subsequent to the loss reserve estimate provided in the actuarial analysis.
What are the benefits of a loss reserve forecast?
- Helps set expectations for future liability needs (e.g., are future loss reserve estimates expected to increase or decrease, all else equal?).
- Allows for more efficient management of cash flow and investment of assets.
- Enables management to contemplate the potential impact of the self-insured program over time.
- Surprise mitigation.
The benefits sound pretty good to me. So, what are the costs?
- Additional actuarial analysis needed; often only a single exhibit is necessary.
- Potential for management to put an over-reliance on an estimate with a large degree of inherent uncertainty.
The largest “cost” that I see is the potential for a client to interpret a loss reserve forecast too literally. As actuaries, we know that the further we look into the future, the more uncertainty is inherent in our estimates. This perspective is not always shared by other professionals, so it is important to highlight this aspect when discussing a loss reserve forecast.
Absent a loss reserve forecast, a client’s default expectation may be that a loss reserve estimate should roughly equal the amount from the preceding actuarial report. In practice, client’s may perceive an increase in loss reserves as “bad news”, when in fact, the estimates may be in line with actuarial expectations. A loss reserve forecast is an effective way to refine client’s expectations for future loss reserve estimates. Of course, in practice, volatility in loss experience and a host of other factors can significantly influence loss reserve estimates, and descriptions of these sources of uncertainty should accompany any loss reserve forecast.
What are your thoughts on loss reserve forecasts?
If you found this information helpful, let me know. Be sure to follow for more P&C actuarial content.
Characterizations of Loss Reserves: Indicated, Selected, and Carried
Loss reserves for P&C companies can be characterized in various ways. Three common types are indicated, selected, and carried. These labels loosely correspond to the loss reserving process:
First, indicated loss reserves are produced from various actuarial methods.
Next, actuaries assimilate the available information, including the indicated loss reserves, to produce selected loss reserves.
Finally, an insurer reflects the final selected loss reserves as a liability on the balance sheet, known as carried loss reserves.
Like most things in insurance, these terms are often used loosely, or even inaccurately. Feel free to download the attached one-page guide for future reference.
Incurred Loss – Disambiguation Guide
The term “incurred loss” is commonly used in P&C insurance with two distinct definitions. This ambiguity is the source of much needless confusion. This one-page guide clarifies the two popular definitions of incurred loss and suggests using more specific terms when possible: reported loss and ultimate loss.
If you find this helpful, please share a link or a copy of the PDF with your colleagues.
Ultimate Loss Development Patterns: 4 Archetypes
The success of a P&C insurer depends on its ability to accurately estimate ultimate loss. The uncertainty inherent in insurance claims virtually guarantees that estimates will never be perfectly accurate. That doesn’t stop us from trying!
This exhibit presents 4 common archetypes of ultimate loss development patterns for a hypothetical accident year that reaches maturity after 60 months.
In practice, one will seldom see any of these patterns repeat. In fact, a portfolio with persistently inadequate or redundant reserves, as represented in Chart 3 and Chart 4, may signal a bias in the reserving process.
My favorite take-away from this summary is the illustration in Chart 3. In this scenario, it is clear that loss reserves are consistently inadequate. When this reserving approach is applied deliberately, we call it “stair-stepping”. The term stair-stepping can also be applied to individual reserve components, like case reserves. Portfolios that show evidence of pervasive stair-stepping may generate questions about an optimistic bias in the reserving process. Chronically understating loss reserves means that insurers recognize earnings sooner than they would have otherwise. This has many implications that I have written about elsewhere.
Another interesting take-away is the similarity between scenario 3 (persistently inadequate reserves) and scenario 2 (no reserves / pay-as-you-go). In a way, a pay-as-you-go approach to “reserving” is the most dramatic form of stair-stepping: reserves are always $0 despite any evidence that it should be otherwise.
Do you find this interesting? Feel free to share with your colleagues.
Accident Year vs Calendar Year
P&C insurance professionals – do you know your AY from your CY?
Accident year and calendar year are fundamental to many aspects of insurance. This two-page guide distinguishes between the concepts via example, starting with a single claim.
Once you understand how a calendar year relates to paid loss for a single claim, it is easy to broaden the concept to include more complex scenarios.
We start with a single claim example in Table 1.
In Table 2, we generalize the calendar year concept to apply to an accident year.
In Table 3, we generalize the calendar year concept to apply to reported losses.
The final generalization allows us to see how calendar year (or any calendar period) relates to various ways of organizing claims: accident year, policy quarter, report month, etc.
Do you find this approach of describing concepts by example helpful? Let me know!
If you found this valuable, please consider sharing with your colleagues.
Negative IBNR
You know you’ve gone down the rabbit hole when you’re wondering about negative IBNR.
In P&C insurance, IBNR, or incurred but not reported, represents the estimate of unpaid claim liability that is not already contemplated in individual claim reserves.
Negative values of IBNR can occur when actuarial estimates of unpaid claim liability is less than the sum of case reserves on individual claims.
Most of the confusion around negative IBNR is due to a misunderstanding of the definition of IBNR. If the definition of IBNR is limited to late reported claims, negative values of IBNR is not a reasonable possibility. When IBNR is considered in its broadest sense (i.e., including any liability not reflected in case reserves), it is easy to see how negative IBNR values are possible. Learn more about types of IBNR here: Case vs IBNR.
Potential Effects of Loss Reserve Adequacy
Loss reserve adequacy for P&C insurers has implications far beyond actuarial considerations. Inaccurate reserves can make or break a company.
Loss reserves are typically the largest liability on an insurer’s balance sheet. They are also usually the largest risk factor identified in an insurer’s enterprise risk management plan.
In this chart, I’ve highlighted just a few possible implications of optimistic and pessimistic loss reserve positions. I hope you find this summary a helpful starting point to understanding how loss reserves relate to P&C insurers in a broad sense.
Disclaimer: The purpose of this post is to identify potential implications associated with optimistic or pessimistic reserve positions. I am not suggesting that insurers should carry loss reserves other than the actuarially expected amount (though there may be circumstances where this is warranted).
Anatomy of Ultimate Loss
The term ultimate loss is pervasive in P&C insurance. There is much that can be written about ultimate loss. The purpose of this one-page PDF is to compare the components of ultimate loss at macro and micro perspectives.
Do you find this helpful in your understanding of ultimate loss and its relationship to other loss types? Let me know!
Prior Year Development
Prior year development is a critical but nuanced concept in P&C insurance. Terminology related to prior year development, like “reserve strengthening” and “reserve release”, can be confusing at best or misleading at worst.
The purpose of the attached 2-page PDF is to help demystify the topic of prior year development. Below are the key takeaways:
- Prior year development is the change in estimates of ultimate loss between two evaluation dates for identical prior accident periods.
- The accident periods between respective evaluations must be identical, otherwise the comparison is not on an apples-to-apples basis.
- Positive prior year development is called adverse prior year development, or “reserve strengthening”.
- Negative prior year development is called favorable prior year development, or a “reserve release”.
- No prior year development (no change in ultimate loss between successive evaluations) is a common for mature accident periods.
- A change in ultimate loss (i.e., prior year develoment) does not necessarily correspond to a change in loss reserves.
Do you have questions about this topic? Let me know in the comments!
Schedule P Triangles – High Level Overview
Schedule P provides loss triangles in Parts 2, 3, and 4. This handy infographic summarizes the types of loss triangles available and how to derive additional ones.
I’m considering preparing an infographic that describes the nuances of the “prior” row in Schedule P. Let me know if this interests you.