Actuarial Sciences 2: Erik Haereid, M.Sc., on Actuarial Sciences in Practice (2)

Author(s): Scott Douglas Jacobsen

Publication (Outlet/Website): In-Sight: Independent Interview-Based Journal

Publication Date (yyyy/mm/dd): 2022/07/22

Abstract

Erik Haereid, born in 1963, grew up in Oslo, Norway. He studied mathematics, statistics and actuarial science at the University of Oslo in the 1980s and 90s, and is educated as an actuary. He has worked over thirty years as an actuary, in several insurance companies, as actuarial consultant, middle manager and broker. In addition, he has worked as an academic director (insurance) in a business school (BI). Now, he runs his own actuarial consulting company with two other actuaries. He is a former member of Mensa, and is a member of some high IQ societies (e.g., Olympiq, Glia, Generiq, VeNuS and WGD). He discusses: actuarial sciences in professional life; applicability in everyday life of a non-expert; using expertise to analyze the risks of something; mathematics and statistics; the maximum level of qualifications a Norwegian actuary can get; an actuary; and the major lessons.

Keywords: Actuarial Sciences, actuary, Erik Haereid, mathematics, statistics.

Actuarial Sciences 2: Erik Haereid, M.Sc., on Actuarial Sciences in Practice (2)

*Please see the references, footnotes, and citations, after the interview, respectively.*

Scott Douglas Jacobsen: How does one apply actuarial sciences in professional life for you?

Erik Haereid[1],[2]*: As a bachelor in statistics, when I worked on my Cand. Scient. degree (which is almost the same as an M.Sc.), I had a part-time job in an actuary department in a Norwegian insurance company (from about 1987 to 1990). There I learned the basics about private individual life insurance products and life tables. At that time there were not usual with personal computers, and we used table books for each life insurance product. “N1964” (or was it 1963? I can’t remember) was one of some books with life tables and related formulas, describing how to calculate all possible premiums and reserves based on that single insurance product. Annuities and disability-products were based on different tables and had their own table books, and so were all group insurance products. These table books were the life insurance actuaries’ bible and tool.

A lot of the work in this actuary department was to control the mainframe systems, ensuring that all calculations that made the premiums and reserves were correct. When there were changes to a product or computer system, the actuaries had to be involved to include the formulas and calculations adapted to that new system. To everybody else, what happened inside the calculations were a black hole. We actuaries had to understand and translate the math into code and calculated numbers. We communicated a lot with the mainframe computer system programmers, and we used our calculators and after some time our personal computers and spreadsheets to ensure that the formulas and calculations where right; testing the mainframe computer’s calculations was an important job for the actuaries. When there were flaws, computer bugs and so on, we had to step in and find what’s wrong (and this happened often).

In general, you can say that an important part of actuarial science is about optimizing premiums; make it as small as possible to meet the customers need, and as big as necessary to meet the insurance company’s need (solvency). This balance is challenged all the time. I will talk much more about this later.

In my first jobs, the actuarial science part was to know and understand how the premiums and reserves, all the calculations, was build and why. All life tables were based on the same principles; the math was stable, and we didn’t change premiums based on more experiences (like one did in let’s say automobile insurance). We didn’t alter the mathematical foundation of the life tables. The death rates were reliable; they were quite easy to predict. The relative high levels of the interest rates were also rather established. The solvency of the insurance companies was subject to no worry. At that time.

It’s scientifically more demanding working with risks that are under great volatility and variation, and/or are subject to few experiences. Non-life insurances are in that manner more demanding than life insurances; traditionally. I have never worked with non-life insurances, and have of that reason never been exposed to great changes in risks, with the demands to continuously modify different mathematical methods. But, as I will talk about later, throughout the 1990’s and 2000’s the challenges occurred even in the life insurance discipline.

After my first job, I finished my final exam and started in a new job as actuary in another insurance company (1991 to 1995). The products and tasks were to begin with quite similar to those in the previous job, but I became more involved in product design and development of new formulas. The traditional life insurance business (including pensions and annuities) was under change, and converged towards more bank-oriented products; separate module-like products. Traditionally, the insurance risk elements in life insurance, pensions and annuities were parts of a mandatory package; the premium included savings (either as a lump sum/single premium, a general annuity or a pension premium), some sort of death benefit, spouse and children benefits if the insured died (riders and modules linked to pensions) and a disability coverage. The insured couldn’t choose elements and riders freely. You could of course buy a pure annuity, but then you had not many choices as to the death benefit part of the policy. This was under change, not at least because the old products at that time demanded a quite skilled salesman/agent, who usually used a lot of time selling and explaining to the customers, making the product’s administration cost part much higher. If one could sell insurance through the bank channels, like any other bank saving product, one could reduce the cost and make the insurance products more available, and the life insurance companies could grow.

I was part of a group (in my second job) in the beginning of the 1990’s, where we developed such a pension product, which aim was to make it simpler, more understandable and to sell it through the bank channels; a Unit-Linked kind of a product (ULIP). As to actuarial science, the challenges was not of other mathematical art than adapting a for the government sufficient risk element to the savings; either as part of the pension itself, or by making some of the additional coverage compulsory. When the executives and authorities agreed upon what kind of risk structure we could provide, the actuaries’ job was to create the necessary mathematics, resulting in right/sufficient premiums and reserves. And after that implementing this into the mainframe service system and the computer sales system that the salesmen (e.g., employees in the banks) used (this was the dawn of personal computers, and the agents started to use software programs instead of pen, paper and calculators to communicate with their clients).

At this time, the yield raised sky-high. The old structure operated with consistent guaranteed interest rates on pensions, annuities and other life insurance products, which from 1964 and until then, at the beginning of 1990, was 4 percent. This resulted in an increasing surplus, which was shared between the insurance company, its owners and the customers. Instead of handing out money to the customers, one could reduce their premiums. As to promotion and sales, this was cleverer than give “something” back after the insurance companies’ accounts were closed some months after year end. But as to ensuring the solvency in the long term, this was catastrophic, because it wasn’t built on actuarial science or basic financial methods. It was based on some naïve unscientifically drive born out from the illusion of eternal and exponential growth.

Maybe one should have used actuaries more consistently as consultants. It was damaging to promise customers up to 10 percent interest rates on their savings, for up to 10 years, only because the prognoses were sky-high. Nevertheless, as a young actuary with no other influence than pure mathematical, I saw it as a fine challenge contributing to an interest rate stair; 10 percent guaranteed interest rate for the first ten years, 7 percent for the next few years, and finally 4 percent for the rest (often for the rest of the insured lives).

Such products were of course stopped some years later, when one realized that these kinds of promises would kill the insurance companies. The insight was established, as usual, by explicit experience. When the interest rate dropped, one started debating guaranteed interest rates per se. Since one has to use some kind of interest rate in the calculation of pension premiums and reserves, and since it’s not a custom in the insurance business using expected values of stochastic variables concerning the interest rate (i.e., establishing an interest rate risk pool, similar to the other risk pools), one decided and decides to use guaranteed interest rates with almost no probability exceeding the actual return within the particular timespan, and limit this timespan to a certain termination age; e.g., 77 or 82 years (fixed term).

Since interest rates are volatile by nature, one would have a sensibility towards the development in the financial market; the expected future basic interest rate should theoretically change from year to year, or at least let’s say each 5 years, to gain a better estimate of the expected future interest rate than using a constant and almost arbitrary interest rate, like 4 or 2 percent over some long period of time (Btw, this is what happens when assessing DBO’s (Defined Benefit Obligation) in companies’ balance sheets; as to pension liabilities; the discount rate used in the calculations is determined based on the market at (year-end) measuring date; this has its big disadvantages too, which I will talk about later.). From an actuary’s point of view, you would then operate with several paid-up policies; e.g., one for each year you have been insured. Every paid-up policy would then result in a calculated single premium and continuing reserve based on that year’s basic interest rate, and from this a future benefit (e.g., pension or annuity). The total reserve on a given time would then be the sum of all those previous paid-up policies’ calculated reserves at that time, all with different basic interest rates. But still, you have the eternal issue concerning defined benefit saving products; you promise some kind of future benefit, and then also some kind of interest rate. For the actuary, these products define life insurance saving products. The quick fix products, the defined contribution pensions, lack the stochastic variables and the risk elements. This is bank, and exclude actuarial sciences.

One difference between a traditionally used guaranteed, basic interest rate and a theoretical best estimate (i.e., the optimal estimate of the expected value) of a stochastic interest rate, is that the guaranteed interest rate is contracted as a minimum, while the expected stochastic one would be given you independent of what the actual return became (like a fixed interest rate). If one would start to treat the basic interest rate as a stochastic variable, and promise the customers the expected future interest rates, you would, because of the increasing uncertainty and problematic statistical foundation in the long term, have to operate with quite low, and certain, interest rates many years from now. Even though you could say almost for sure that 5 percent interest rate was a very good estimated expected value for the next 10 years, you couldn’t say anything certain about the expected value of the interest rate in the period let’s say 40 to 50 years from now, and that is a main challenge by using interest rates like this. But it shouldn’t exclude scientific approaches to it.

A decent statistical model could deal with a decreasing interest rate stair, starting with a high expected value (e.g., 6 percent) the first few years, and then reduce the interest rate systematically until the last possible year from now, which for some annuities and pensions are about 100 years (e.g., a 20 years old got a longevity pension).

To sum up: One way to optimize and preserve the traditional defined benefit saving products is to create annual paid-up policies as mentioned, and use actuarial science to create some sort of a probability function based on a stochastic interest rate stair, which changes parameters from year to year, dependent of the financial market.

The concept of the traditionally arrangement, where the customers and the insurance companies have to deal with some kind of future interest rate in the contract and in the settlement of the liabilities, is in the area of group pension schemes known as Defined Benefit Pensions/Plans (DBP). The alternative is called Defined Contribution Pensions/Plans (DCP), and is similar to ordinary bank accounts; you get what the market gives you, afterwards. You are not promised anything in advance; the insurance companies’ obligations are nothing more than what is on the customers’ accounts at every moment. To make it an insurance product, you have to include, make mandatory, some sort of death/health/disability economical risks. If the beneficiaries just get the savings when events occur, you don’t have any economic risks to it, and it’s not insurance. DCP’s are typically pure savings with no guaranteed interest rates, but with additional life insurance elements like something more or less than the savings paid by death (e.g., a fixed-term deferred annuity, riders like spouse and children’s pension, and disability coverage).

Another actuarial challenge is the fact that people live much longer than before. The (life) insurance companies normally dealt with this the same way as with the interest rate issue; they tried (and try) to reduce the risks the easy way, by avoiding promoting longevity annuities and pensions (i.e., they promote fixed term annuities), and they reduce the risk by minimizing the difference between the savings and the benefits. It’s understandable, because there are statistical and mathematical uncertainties linked to both future interest rates and long lives. It’s not the short-term risks we do not know much about, but the long-term ones. But as an actuary, promoting actuarial science, it’s not optimal. You could say there is a minor clash between actuaries’ and the authorities’, executives’ and owners’ need and wishes.

Folketrygden (The Norwegian national social insurance scheme) has gone through quite severe changes since 1990, in accordance to meet the problems mentioned. In addition to the risk-factors, you have the flexibility that people demand. In the old days, twenty-thirty years ago and before, the pension products, both concerning private and public, was quite sterile and non-flexible. E.g., the retirement age was (normally) 67. Period. You could not work while you got pension, without losing money. This has changed; now you can get your pension from 62, and whenever you want until 75 or so, and you don’t lose pension if you work besides. In Denmark, where I worked for some while, you could choose between getting your pension benefit as an annuity or a lump sum. The demands for flexibility also have some influence on the actuarial work.

Jacobsen: How do actuarial sciences have applicability in everyday life of a non-expert?

Haereid: Interesting question, that I haven’t thought much about. You can as a layman learn some basic combinatorics, probability theories and statistics, using it to enhance your winning chances in games and competitions, e.g., increase the probability for profit, and use it to gain more out of your investments in the financial market.

Everyone can be aware of different daily risks, and make some simple calculations to avoid certain situations or seek other. E.g., you can avoid driving your car at certain places and moments, by collecting information about when and where the most dangerous car accidents appear. But “drive carefully” is something everyone intuitively knows will reduce the risk of car accidents. You could also use actuarial science into health-relevant situations, like related to what you eat and how you exercise; treat your body in a way that reduce risks for diseases.

In general, thinking like an actuary could become exhausting, because one would tend to overthink risks; make fast risk calculations about any- and everything through your day. Then you would reduce every risk factor, but also end up with fewer experiences and less fun. The gain is to reduce risks where the consequences are really bad in case of an event, and to increase your profit and earnings.

I want to give an obscure example of use of combinatorics:

Let’s say you are confined in a room with a combination lock; a panel with the digits 0 to 9. There are no one to help you out. You know that you have a livable environment for two days, and after that you will die if you don’t get out. You have also noticed that the code has 4 different digits in a fixed sequence, and that you, in average, except when you rest, will manage to push one possible combination each two seconds. You can then calculate if it’s probable that you will manage to open the door within the time limit, or if you should try some other way out.

There are 5040 possible outcomes (let’s simplify it and suppose there are no equal digits in the code), and just one of them is right. Then you, statistically, will get the answer midway; after 2*5040/2 seconds = 84 minutes (plus pauses), and if you are really unlucky you will get out after 168 minutes. That’s sufficient. But if the code consists of 6 digits instead of 4, you would get out within one week without pauses (3,5 days and nights in average), and there would be a possibility that you would die before you got out.

Another example: If you are middle-aged, especially a male because of the higher mortality than females, and you live healthy and have good genes as to family diseases, you should purchase a fixed term annuity (i.e., with no death benefit before the termination date); because of the mortality bequest. Since you think you will live longer than the average, you will, if you are right, pay less to gain more, e.g., compared to if you saved the same amount in a bank.

Finally, I will mention a Swedish physician and statistician, Hans Rosling, who had a tremendous ability to explain statistics in a simple way for the people, and make everyone a bit wiser and more informed. Maybe he could be an inspiration for us who work with mathematics and statistics.

Jacobsen: Following from the previous question, if you have an ordinary event in life, how can an actuary use expertise to analyze the risks of something? What is the relevance of this in one’s life?

Haereid: I haven’t thought a lot about this either, maybe because I want to work as an actuary and not becoming one 24/7. As long as the ordinary events in life are stochastic, or random if you like, and you have a minimum of information, i.e., empirical data about those events to occur (when, where, how and so on), you can most often use math to say something about the future outcome. It’s about using probability functions and knowledge together with collected information, to draw some kind of risk analysis. The difference between the layman and the actuary is the amount of knowledge; the actuary will have access to better estimation procedures, and therefore give a better prediction of possible events.

There are a lot of probability distributions (e.g., normal, chi-square, student’s t, binomial, Poisson…) that fit into daily life events’ patterns. In lack of a probability distribution that fits, you can draw your own by plotting the collected data into a graph. E.g., the probability for car crash divided by age (in lack of knowledge of an existing one): If you search for statistics on this, you will probably find that there are quite many young men that crash their cars often. The curve will fall until a certain age (men in the 30-50-year area drive more carefully), and then turn around and rise; old men crash their car more often than middle-aged men. If you have a lot of data, you can draw a quite nice curve, that probably would look something like an inverse normal distribution, or as a distorted parabola, if you like. Then you have made your own probability distribution in lack of an existing one, that fits into these events. And then you can say something about the probability for car crashes categorized by age.

One of the mantras in statistical analysis is correlation and the amount of empirical data. You can gather tons of data, but it doesn’t help if it’s uncorrelated. Without enough data, it’s difficult to establish if there are correlation or not. But, when you have enough collected historical information about any unknown future event, and you have detected a correlation, you can say something about this event in the future. If you gather data that don’t show any correlation (you can’t say anything about when, where, how, who and so on, that results in crash), you can’t draw any statistical analysis which say something about such events to happen. It happens by chance. One nice thing with this is that you don’t necessarily need to know the cause of events, if you can establish a correlation. If two seemingly independent variables, like peoples’ vacation habits and the habitats of mallards, show strong statistical correlation, it could be used (to something) without knowing the reason why this is so.

In general, if you know something about probability theories, you can use this to determine an actual or estimated probability distribution to every event that you don’t know the outcome of (when, where, if, how much… will happen), and to use this probability function to direct your own behavior. If you know that the probability of occurrence of an event hitting you is 10% if you choose the one direction, and 8% if you choose the second, you would choose the 10% direction if you want that event to happen (e.g., earning money, getting friends, increasing happiness…) and the 8% direction if you want to avoid that event. To this kind of events the layman would think it was a 50/50 chance, but with some math and data you could say something more precise about it, and (in the long run) take advantage of this. E.g., into gambling or being active in the stock market.

Jacobsen: What mathematics and statistics are used in an actuary’s professional life?

Haereid: I will focus on my own branch; life insurance and probabilities for death and survival. Keywords are the Gompertz-Makeham distribution, the Thieles differential equation and the Markov chain, which all are essential in life insurance.

The life tables are based on the Gompertz-Makeham distribution, which plots mortality divided into age. It describes how mortality basically increases exponentially with age, which is based on Gompertz research from the 19th century. Since human also dies of other than “natural” reasons, e.g., pandemic diseases, natural catastrophes and so on, one added an age-independent part to the distribution (Makeham), also this in the same century.

The Dane Thorvald Thiele made one of his contributions to life insurance when he, also in the 1800’s, introduced the Thieles differential equation. This made its influence in life insurance through the 19th and 20th century. It describes the premium reserves as a differential equation, as the expected discounted value of future events (benefits minus premiums paid), and is basic in life insurance.

In insurance we have something called the equivalence principle. This states that the expected present values of payments should be equal to those of benefits. Usually, premium formulas contain a death probability (and sometimes disability and other health-related probabilities), evolved from a life table (as mentioned), and an interest rate, which usually is a parameter and not a probability. These two quantities are involved in the equivalence principle. One calculates the expected present values of the upcoming premiums and benefits respectively, weighted with the probability of occurrence of the events involved, at any time in the insured period. Reserves are calculated at any time based on the same principle.

Because we operate with only one stochastic variable, one life, the formula is simple. But there is possible to expand this into several random variables, e.g., using a Markov chain (stochastic process).

Jacobsen: Theoretically, what are the maximum level of qualifications a Norwegian actuary can get now? The upper limit in education, experience, credentials, memberships, etc., to know the entire discipline.

Haereid: Since, as said, there have been different paths the last fifty years to achieve an actuarial competence in Norway, it’s not a unique set of qualifications. Some actuaries add a doctor degree to their education, and become university lecturers (assistant professors, professors). As to experience, I would say being an “actuary in charge” in an insurance company, is the peak. There are no major credentials beyond “actuary”. There are some additional credentials to those who take courses through their professional lives, as an adult education, e.g., in financial mathematics and related disciplines. There are primarily one actuarial society in Norway (Den Norske Aktuarforening), where most of the Norwegian actuaries are members. An experienced actuary in Norway is typical a senior consultant, either in an independent actuary consultant company, in an insurance company or in governmental department. Some actuaries have been (and are) executives in insurance companies and units.

Jacobsen: How many years have you been an actuary?

Haereid: From 1991; 31 years. I worked as an actuary novice from 1987, beside studying and finishing my final exams.

Jacobsen: From this extensive experience, what have been the major lessons from the discipline for you?

Haereid: There is traditionally a canyon, a cleft, between actuaries and the rest of the insurance realm. We speak different languages. We have to learn each other’s dialects.

Besides that, I will mention:

– The insurance business, including the social welfare pensions and insurances, often choose unscientific solutions to the extent they are able to fulfill their obligations. Keep it as simple as possible, is a common mantra. Understandably. And archetypical. The tendency during the last forty years is not only more transparent and flexible insurance products, which is good, but also products with less risks; the (life) insurance business moves away from its essence (providing products containing risks and probability). One reason is to be independent of a small group of professionals (actuaries), another to make it easier predicting the future. Other reasons are to prevent insolvency, fulfilling the obligations, making the administration simpler and cheaper, creating products that are easy to explain and understand (both to the customers and the employees that are not actuaries or sufficient skilled) …

– The insurance companies could profit on cooperating and communicating more with the universities, get access to updated research and theoretical knowledge, that would improve the business. I don’t say there isn’t any communication, but this is an area for improvement, and especially associated with the many issues we see and will see. There are probably (for sure) some (actuarial) scientific theories that is never applied, because the communication is poor, the level of knowledge in the insurance companies is too low, and the aversion to more complicated products and structures is too big.

– One of the positive sides is that transparence, computer evolution and more flexible products have made an old fashion rigid and conservative business into something modern and more accessible.

I have to say something about the increasing openness and transparence from the 1980’s. Before that process started, there was close to no information available. If the customers wondered what the premium contained of risk and savings elements, the answer was “n/a”. If they wondered what the premium reserve consisted of, e.g., what this year’s actual return was, the answer was the same. There was no law that forced the insurance companies to create such detailed information. This changed dramatically from the 1980’s, not at least because of the development in computers and software. The technology made it possible to become more transparent, and this increasing transparency also created new products. I remember vaguely when we created and sent the first detailed account statement to our customers. This was really a cutting-edge happening.

– The longevity contracts in life insurance, pensions and annuities, which terminates when the insured dies, entails some big challenges. The mathematical risk models are not that good when it comes to predictions 40-100 years from now; it’s not easy to calculate valid probabilities as to interest rates and death within that time span. We just don’t know enough about what happens then, and this impels the insurance companies and social pension entities to evolve either products that terminates within a certain age (fixed term), or to create contracts that make the customers bear the burden. This should be a pleasing area for actuaries, since it demands more scientific creativity.

– Why use low guaranteed interest rates, and volatile discount rates, when calculating premiums, reserves and companies’ pension liabilities? Why not using probability theories and actuarial science to create more intricate and better solutions to the very important “interest rate” issue?

– Paid-up policies have always been abandoned in Norway; there are huge funds that only get a return equal to the guaranteed interest rate, which usually is far less than the actual return. Over a period of some decades, this amounts to large sums. The owners are not sufficient aware of this thievery. The customers lose a lot of money; the same amount which the insurance companies earn. I can’t understand that this is legitimate.

– General solvency issues in the insurance business. Volatile financial markets, roller coaster interest rates, too wide guarantees and long lives have led to unstable funding situations. This has led to a necessary reinforcement of the solvency rules in the insurance business.

– Actuaries could contribute more to the overall insurance business. We are not used enough to form the future insurance politics and products, neither to direct the insurance business. Actuaries could into a larger degree contribute to the developments of social welfare programs and life insurance. A recent example of this is a group of different experts and politicians that in 2020 was selected with the aim of writing a paper of how to make our Norwegian social security pension system more sustainable in the future. Their suggestions were released some days ago. My point is that there was not one actuary selected to be in this diverse group of people. Why is that? Competition between professions?

– Actuaries have traditionally been occupied with the liability side of the balance sheets. This has changed the last couple of decades. My impression is that actuaries are used increasingly more into the asset side.

– In group pension insurance, there has been a stream of changeovers from the traditional and far betterer Defined Benefit Pension schemes (DBP) to the United-linked (this is primarily associated with single persons) similar kind of products, labeled Defined Contribution Pension schemes (DCP). This is a benchmark regarding the «deactuaryization» of life insurance products, especially those with long duration. The main goal is not to reduce the pension cost for the group (companies and employees’ pension scheme), but to remove the uncertainty with the liability side of the balance sheets. This is done by transferring the responsibility for the investment return from the employer to the employees. The impact on the account is clear: From a volatile and uncertain net amount in the balance sheet, to a net amount = 0. And from an unstable pension cost to a stable and predictable one. For the employer this is Shangri-La. For the employee this is uncertainty as to pension planning.

– This is associated with the previous point, and is about calculation of companies’ pension liabilities and accounting. It is a huge disadvantage that one is obligated to use the discount rate estimated based on the market at the year-end-date. This parameter is without comparison the most important and influential quantity in the calculations, and have huge impact on the volatility of the liabilities in the balance sheets. If one could estimate a more stable discount rate, based on financial and actuarial mathematics and statistics, we could prevent an unwanted coercion from DB to DC pensions.

– Traditionally, the communication processes between the actuarial environment and the executives and other involved in the insurance business, have been bumpy. It’s a challenge communicating difficult products and their frames. My experience is that this issue leads to an insurance culture that avoids the actuarial involvement. And this leads to simpler products, with less demanding risk elements, and less actuarial science related to them. It’s like limiting buildings to three floors because skyscrapers are complicated.

– The Norwegian national social insurance scheme (Folketrygden) has gone through several changes the last many (30-40) years (e.g., because of long lives and increased flexibility). This is too broad to say more about here, but it’s important to mention.

Footnotes

[1] Member, World Genius Directory. Actuary.

[2] Individual Publication Date: July 22, 2022: http://www.in-sightpublishing.com/actuarial-sciences-2; Full Issue Publication Date: September 1, 2022: https://in-sightjournal.com/insight-issues/.

*High range testing (HRT) should be taken with honest skepticism grounded in the limited empirical development of the field at present, even in spite of honest and sincere efforts. If a higher general intelligence score, then the greater the variability in, and margin of error in, the general intelligence scores because of the greater rarity in the population.

Citations

American Medical Association (AMA): Jacobsen S. Actuarial Sciences 2: Erik Haereid, M.Sc., on Actuarial Sciences in Practice (2) [Online]. July 2022; 30(E). Available from: http://www.in-sightpublishing.com/actuarial-sciences-2.

American Psychological Association (APA, 6th Edition, 2010): Jacobsen, S.D. (2022, July 22). Actuarial Sciences 2: Erik Haereid, M.Sc., on Actuarial Sciences in Practice (2) . Retrieved from http://www.in-sightpublishing.com/actuarial-sciences-2.

Brazilian Natio0ffffffnal Standards (ABNT): JACOBSEN, S. Actuarial Sciences 2: Erik Haereid, M.Sc., on Actuarial Sciences in Practice (2). In-Sight: Independent Interview-Based Journal. 30.E, July. 2022. <http://www.in-sightpublishing.com/actuarial-sciences-2>.

Chicago/Turabian, Author-Date (16th Edition): Jacobsen, Scott. 2022. “Actuarial Sciences 2: Erik Haereid, M.Sc., on Actuarial Sciences in Practice (2).” In-Sight: Independent Interview-Based Journal. 30.E. http://www.in-sightpublishing.com/actuarial-sciences-2.

Chicago/Turabian, Humanities (16th Edition): Jacobsen, Scott “Actuarial Sciences 2: Erik Haereid, M.Sc., on Actuarial Sciences in Practice (2).” In-Sight: Independent Interview-Based Journal. 30.E (July 2022). http://www.in-sightpublishing.com/actuarial-sciences-2.

Harvard: Jacobsen, S. 2022, ‘Actuarial Sciences 2: Erik Haereid, M.Sc., on Actuarial Sciences in Practice (2)’, In-Sight: Independent Interview-Based Journal, vol. 30.E. Available from: <http://www.in-sightpublishing.com/actuarial-sciences-2>.

Harvard, Australian: Jacobsen, S. 2022, ‘Actuarial Sciences 2: Erik Haereid, M.Sc., on Actuarial Sciences in Practice (2) ’, In-Sight: Independent Interview-Based Journal, vol. 30.E., http://www.in-sightpublishing.com/actuarial-sciences-2.

Modern Language Association (MLA, 7th Edition, 2009): Scott D. Jacobsen. “Actuarial Sciences 2: Erik Haereid, M.Sc., on Actuarial Sciences in Practice (2).” In-Sight: Independent Interview-Based Journal 30.E (2022): July. 2022. Web. <http://www.in-sightpublishing.com/actuarial-sciences-2>.

Vancouver/ICMJE: Jacobsen S. Actuarial Sciences 2: Erik Haereid, M.Sc., on Actuarial Sciences in Practice (2) [Internet]. (2022, July 30(E). Available from: http://www.in-sightpublishing.com/actuarial-sciences-2.

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