Actual-to-Expected Apocrypha

A few months ago, Life Risk News published my commentary article regarding life expectancy (LE) apocrypha. Given the positive feedback I received, I decided to write a follow-up, focusing on industry suppositions about actual to expected analysis (A-to-E), no stranger to controversy over the years.  

Although many philosophies and theories about LEs have been proffered by life expectancy providers, virtually every type of participant in the life settlement market has contributed to the apocrypha surrounding actual to expected analysis.  

Let’s first define actual to expected analysis. According to the actuarial profession, it is the process of calculating and analyzing A/E ratios over a selected time period, (i.e., actual deaths in a group of lives being evaluated, over a specified period divided by the expected deaths, the number of deaths statistically expected over the same period). 

With that in mind, consider the following assertions that have been expressed by industry participants, but in my view, are not valid: 

A-to-E is a perfect measure of LE provider accuracy 

It isn’t, at least, if presented as a single number with few or no insights into the methodology behind it. In fact, a single number A-to-E tells us very little (just as using a single number LE instead of the underlying curve can be misleading). An extreme example would be a block of policies where the A-to-E on half of the policies is 150, and the other half is 50; this makes the overall A-to-E 100. Is that perfection? No, it is nowhere near perfect; in fact, it’s not even mediocre.  

Further, the nature of the A-to-E calculation introduces bias over time. A-to-E trends to 100, even if insureds do not die when expected. For example, an insured who was given a very short LE, say 12 months, lives 75 months and then dies. In month 76, the A-to-E on this policy is 100. That’s not helpful. 

A-to-E is worthless in assessing LE provider accuracy 

Based on the above-noted weaknesses, A-to-E seems worthless. Not true! The key to unlocking the value of A-to-E is in breaking it down: by age, by gender, by smoking status, by impairment, by mortality multiplier, by year of underwriting, etc. If we turn that single number into many numbers, true insights can be obtained. 

An A-to-E of 100 is a perfect score 

We as an industry did ourselves no favors by proclaiming 100 to be the ideal for A-to-E. The ideal is a consistent A-to-E, when broken down by age, gender, smoking status, etc. Consistency from those specific measurements can be relied upon, and adjustments made to improve accuracy. For example, if an LE provider’s A-to-E is 80% across gender, face amount, year underwritten, impairment, multiplier, etc., it is easy to adjust their LEs to eliminate their bias by multiplying each mortality rate by 80%. On the other hand, if there are large differences when these calculations are broken out, it’s almost impossible to rely on the LEs or correct for inconsistent bias. 

In two recent industry meetings on both sides of the Atlantic, similar questions were asked: If all you LE providers have A-to-Es around 100, why are your individual LEs so different? At the very minimum, it is a result of the fact that the A-to-E statistic, which is an average, bears little resemblance to the individual policies that make it up. There may be different methods and assumptions employed as well. 

Although exploring different A-to-E methodologies is beyond the scope of this commentary, allow me to touch on a particularly important assumption – incurred but not reported deaths ( IBNR, for short).  

IBNR is a perfect example of good logic gone bad in our business. It’s reasonable to expect that when someone dies, that information is not reported for some time. Actuaries have recognized this for decades and that is the genesis of the IBNR assumption. Depending on the time lapse between the period we are studying and the calculation date, most actuaries agree that a 3-5% IBNR is reasonable. 

Given the importance of the statistic, A-to-E studies should include results with and without IBNR so users of the study can adjust the assumptions should they desire. Unfortunately, many studies do not disclose IBNR, even when it drives the results. I have heard of IBNR assumptions as high as 60%, although the worst I have actually seen was 38%. All in the name of getting a 100 A-to-E. 

How do we make this A-to-E statistic meaningful? By standardizing its calculation, disclosing the underlying methodology and presenting meaningful breakdowns.  

A-to-E can be calculated from LEs that do not include a mortality table 

Not true. Think about it; if there is no mortality table, how does one calculate expected deaths for a given period? For example, let’s assume an LE of 72 months and we want to calculate the A-to-E after 12 months has elapsed. We can easily count the actual deaths. But not the expected deaths. 

Some LE providers have used this to their advantage. They never provided a mortality or survival curve with their LEs but insisted that all A-to-E calculations utilize the actual LEs sent to customers. Notice the wording – not the actual survival curves sent to customers, the actual LEs. When it came time to calculate A-to-E, they simply chose a mortality table with low early duration deaths to back solve their LEs into and they could artificially create an A-to-E close to 100.  

A lesson learned is customers should require their LE provider to give them the expected survival curves underlying their LEs. Also, they should question any A-to-E results that are not based on the actual survival curves in place at the time the LEs were issued (although there might be a good reason to present a modified analysis along with the historical analysis as seen below). 

There are no rules regarding A-to-E calculations 

The American Academy of Actuaries set forth rules for calculating A-to-E in what they call Actuarial Standard of Practice (ASOP) Number 48, published in December 2013, to be applied to work done after April 2014. Recognizing that certain misleading practices in calculating A-to-E had crept into the public forum, ASOP 48 was promulgated by the governing actuarial body. Although its official title was Life Settlement Mortality, it contained guidelines for A-to-E calculations too.  

ASOP 48 noted two specific bases for use in A-to-E calculations: historical basis and modified basis. Historical basis was the use of a survival curve developed from the base mortality table, mortality improvement factors, mortality multipliers, and other pertinent information for each LE that was used on the original underwriting date. Modified basis was the substitution of any pertinent information other than what was used on the date of original underwriting (for example, a different mortality table or mortality multiplier). Many LE providers calculate A-to-E using their current mortality tables and methods. 

Importantly, ASOP 48 clearly states that if a modified basis is presented that the historical basis also be presented if the actuary believes doing so is appropriate. To be fair, this allows some wiggle room, which is unfortunate. However, the actuary is required to disclose why those results are not provided, if the historical basis is not presented alongside the modified basis. I cannot think of a good reason why the historical basis results should not be disclosed. I can think of many bad reasons. 

The Historical Basis A-to-E is preferable to a modified basis that utilizes current methodology 

Some folks suggest that the only meaningful A-to-E statistic is the historical basis, i.e., the mortality table and mortality multiplier that was used to create the LE initially. Certainly, this is important information, and it speaks to the accuracy of an LE provider’s work over a long period of time. 

However, a modified basis A-to-E, under the right circumstances, is also very useful. Use of the LE provider’s current mortality table and underwriting debits is particularly valuable in that it indicates whether the modifications the LE provider made to their tables and debiting over time resulted in a more accurate product going forward. 

Substituting a VBT will not affect LE accuracy 

Advocates of the VBT should not be surprised to find that it overstates deaths vis-à-vis a life settlements mortality table. Therefore, substituting the VBT in a life settlement underwriting will result in an understated LE. The corresponding A-to-E using this approach can be significantly lower – 20 points in our recent calculations.  

A-to-E cannot be helpful in determining underwriting changes 

Like many other assertions in this paper, under certain circumstances, it could be true, even though under others, it is clearly false. It is true that the single number A-to-E is virtually useless in determining changes. However, as we saw above, more granular breakdowns can provide actionable information. For example, a by impairment or age band breakdown can point to areas of concern.  

This brings us to the final topic. Your due diligence should include a discussion with the LE provider on how, how often, and under what circumstances are changes implemented in their LE methodology. Data should be the decider of the timing. Regression models can be utilized to determine changes in the debits and credits, but A-to-E (of the portion of lives in our database that have no or very minor impairments) could be used to determine if base mortality table changes are warranted. 

A-to-E is imperfect and imperfect analyses of A-to-E will lead to erroneous conclusions. When used properly, A-to-E can be a useful tool in assessing LE provider performance and prescribing modifications to consider when using LE providers’ products.  

Vince Granieri is CEO at Predictive Resources