Yet another actuarial blog

Pricing a parametric short-sightedness insurance – 2021 SOA Student Research Case Study Challenge Finalist

2021-06-05T00:00:00+00:00

COVID-19 broke out in practically every corner of the planet in 2020, making it a year of public health. Whether ordinary citizens or government elites, people have become increasingly concerned about their own physical conditions, public healthcare systems, and related health risks that may be induced by the broader epidemic or individual unhealthy lifestyles.

The theme of the 2021 SOA Student Research Case Study Challenge addressed this pressing phenomenon by assigning students to develop a parametric insurance product that protects individuals or communities from global health risk. With the new policy, people will be shielded against any financial loss caused by emerging health concerns such as obesity, high cholesterol, and diabetes. Under the revolutionary parametric plan, companies can save maintenance costs in today’s highly efficient environment thanks to the straightforward underwriting process and single reimbursement based on a specified triggering event or index.

Team HKU Actuarial Solutions from the University of Hong Kong is one of the finalists (Top 6 teams out of 64 teams globally) of the SOA Challenge. We have proposed a parametric insurance product NewVision to protect against short-sightedness (also known as myopia) that is going to worsen as technology becomes more integrated with our life. With NewVision, high myopes can be safeguarded from possible vision-related illnesses, such as glaucoma and cataract, that are caused by short-sightedness.

Brainstorming the product

We have followed a brainstorming checklist we had come up with in our last project, Marriversary - divorce endowment insurance. This four-section list ensures that our ideas are realistic and feasible.

First and foremost, we constructed a product description by defining the underlying risk to be insured by the product. We also laid out possible cash flows of the product.

Then, we reviewed the insurability of the brainstormed ideas, which is known as actuarial considerations. Considerations include whether the risk event is objectively measurable and diversifiable, any possible scenario of adverse selection or moral hazard, etc.

In order to prevent the aforementioned moral hazard and adverse selection, we did not choose standard health metrics that can be easily controlled by individuals, such as BMI and cholesterol, as the underlying global health risk. Hence, our focus is to explore a health metric that is unlikely to be manipulated by policyholders.

Access to data is also critical to ensure the brainstormed idea is feasible to price. However, we are provided with a limited amount of data since we are unable to obtain a comprehensive database besides academic journals available, which negatively affects underwriting as well. Therefore, we limit the coverage of this policy to newborns so that population data can be used to price the product.

The third section is business considerations. Marketing is essential to achieve targeted profit. We looked into customer’s demands and other similar products in the existing market to design marketing plans to make our product reach potential customers. NewVision, in particular, is the first-ever parametric insurance product that covers vision care, so we do not face any competitors. We also targeted parents and parents-to-be by creating NewVision as an insurance product that protects a child’s vision.

Last but not least, we also consider possible product variations. During this stage, we asked ourselves what could be changed, and whether alternatives would be better to justify that the original idea is best among similar products. In this project, we considered similar risks like long-sightedness, astigmatism, but we found short-sightedness to be the best due to its prevalence and rising demand for protection in the market.

Iterative development

One of the most interesting things about pricing is that the above process is iterative: change of a feature will affect other parts of the project. That is why we have to keep the above four sections in mind throughout the whole project.

One of the challenges involves setting the trigger level for benefit payment. After building a pricing model with premiums and financial figures, we encountered a problem: it is too expensive to protect against all short-sightedness cases. Thus, we increased the severity of short-sightedness required before a payout occurs. However, if the triggering point is too high, there is too little research data available, causing a huge amount of pricing risk.

After balancing both factors, we finally decide to use the cutoff of high myopia defined by the World Health Organization. The decision is also supported by our sensitivity and stochastic analysis. Results in our model will have acceptable confidence intervals and the severity of key risks are listed out.

The result

After many cycles of development and problem solving, we finally came up with a product which led us to the SOA finals.

Our team HKU Actuarial Solutions was honoured to have an absorbing, fruitful, inspiring and leisure presentation and discussion with the panel of judges. With the increasing trend of myopia reaching epidemic proportions in our world, the value of this product goes beyond insurance and in fact it is more like a revolutionary parametric eyecare protection for your children and the younger generation.

We, the HKU Actuarial Solution Team, will keep on developing our skills in the actuarial field. And one day, we hope we can continue to innovate insurance and bring greater good to society.

What’s more

For more details, take a look at the original files for NewVision:

Remember to connect with us on LinkedIn:

Jackson Leung,
Elaine Cheng,
Tiffany Wong,
Elizabeth Zhu, and
Kelvin Cheung.

How many exams should you pass before you graduate? Let’s do a NPV anaylsis.

2021-02-25T00:00:00+00:00

One of the most common questions I heard is whether passing more actuarial exams before graduation is a good thing. Since we all want to be actuaries, let’s look at this question in an actuarial way. We will perform an NPV (Net Present Value) analysis.

Gains and loss of passing exams

To begin, let’s identify what are the gains of passing exams before and after graduation.
For passing exams before graduation, the gains are:

Getting exam salary raise added to starting salary
Progress faster in exams, reaching fellowship exams with much higher salary raise earlier

For passing exams after working in a company, the gains are:

Full reimbursement of exam fee and study materials
Study leaves

To find out which benefits are greater, we will proceed to the analysis.

NPV of a single exam

Our first model will only consider “salary raise vs reimbursement” for each exam individually. From the SOA website, we find out how much each exam cost and how often they are offered. Also, SOA tends to release results 2 months after an exam. I will assume no further expense but you can add additional study expense in the spreadsheet. The effective pass rate for each exam can also be found on Actuarial Lookup.

Then, I grab exam salary raise from Reddit. I used numbers for John Hancock (aka Manulife) as an example, but I encourage you to plug in your own numbers as they can vary from company to company.

To calculate the NPV, we need to first consider the cash flow of the two options. If we take the exams now, we need to pay the exam fee ourselves, but we will have a higher start salary when we graduate if we passed. If we defer taking the exams, our employer will reimburse our exam fees and study materials, but we will receive our salary raise later. The following timeline summarizes the cash flows.

C: Exam cost
S: Basic salary
R: Exam raise
P: Probability of pass

To calculate the marginal NPV, we only need to discount the difference in cash flow between both options back to the present. The following table summarizes the results for preliminary exams. (I assume there is 2 year until graduation and interest rate is at 3%)

Exam	USD Salary Increase		Fee USD	Offer frequency (Months)	Months til result release	Effective pass rate	Payback Period (Months)	Value of taking 1 siting ahead
Exam	Annual	Monthly	Fee USD	Offer frequency (Months)	Months til result release	Effective pass rate	Payback Period (Months)	NPV	Profitability Index
P	3,000	250	250	2	4	49%	1.00	209	84%
FM	3,000	250	250	2	4	54%	1.00	255	102%
IFM	3,000	250	300	4	6	55%	1.20	475	158%
LTAM	4,000	333	365	6	8	55%	1.10	839	230%
STAM	3,500	292	300	4	6	55%	1.03	595	198%
SRM	3,000	250	260	4	6	71%	1.04	732	282%
PA	3,000	250	1,250	6	8	59%	5.00	-285	-23%
FAP	5,000	417	2,100	6	8	100%	5.04	622	30%

From the result, we can see that almost all exams and FAP have a positive NPV, so it is profitable to take them now. Exam PA may seem unprofitable at first, but if you are confident enough to pass it with a probability greater than 77%, it will become profitable. The more confident you are in passing the exam, the higher the NPV.

NPV of passing all preliminary exam before graduation

Since the first model only considers each exam individually, it does not take into account that the fact we pass exams one by one. Therefore, let’s build a timeline to model this effect.

In the model, we will compare 2 options:

Option 1: Passed all 7 preliminary exams and FAP before graduation
Option 2: Passed only exam P, FM, IFM before graduation

For simplicity, I will assume passing all exams on the first attempt (to avoid building a decrement table or stochastic model). I build a timeline that attempts to take all exams as fast as reasonable. Detail can be found in the excel model at the bottom of the page.

The first graph shows the yearly cash flow resulted from all exam raise. If we pass more exams before graduation, we need to pay the exam fee ourselves, causing a negative cash flow during the first 2 years. However, our starting salary is much higher and we can move on to FSA exams sooner. If we defer exams until graduation, our salary is playing catch up, but we don’t need to pay for the exams.

Marginal cash flow can be calculated as the difference between the two cash flows. The graph below shows marginal value gain or loss during each year if option 1 is chosen instead of option 2.

From the model, if we can pass every exam on the first attempt, we gain an NPV of USD 45,180 at the time we graduate, which is quite a lot. Note that this is the best-case scenario, you can play around with the model to simulate different cases. (Or maybe comment or message me, I would build a stochastic model if a lot of you are interested.)

Taking exams is profitable

To summarize, from an actuarial perspective, taking exams as soon as possible is profitable if you intend to stay in the actuarial field after graduation. However, my model only considers the financial aspect of passing actuarial exams. There are also other qualitative things to be considered when it comes to exams.

In general, I recommend getting them done as fast as you can. You gonna have to pass them anyway, why not do it now. If you what to know how to pass them quickly, check out my other blog post.

You can download the spreadsheet model here. I encourage you to use it to simulate different scenarios and put in more accurate assumptions that you have. The model works for all currencies, just input the exam fees in your local currency.

Just a small caveat, I am writing this based on what I observe in Hong Kong, so your experience may vary from country to country.

Thanks for reading. I appreciate any feedback. Connect with me on LinkedIn and tell me what I should write about next.

How I passed all 7 SOA actuarial preliminary exams in two and a half years

2020-12-24T00:00:00+00:00

I’m excited to share some studying strategies that I’ve used to pass 7 actuarial exams on the first attempt in two and a half years. Passing 7 exams may seem difficult at first, but it is feasible with the right method and determination.

The strategies I shared works very well for me, but it doesn’t mean it will work for everybody. I hope this can help you to formulate your unique strategy and pass exams.

OK, let’s get to it!

1. Make a timetable and stick to it

Planning is very important because it encourages discipline and provides a sense of security. When I follow my plan, I know that I am not falling behind and have adequate time to study. I won’t panic and rush through books, nor will I ran out of time to practice.

It is also very important to plan earlier. I usually start planning at least 4 months before an exam. 4 months seems a lot, but it doesn’t mean I am studying every second during that time. I only need to read less than 10 pages each day on average, which can be fully integrated into my lifestyle without sacrificing anything significant. (OK, maybe less time for social media.) I was able to take a full university course load or a full-time internship and work on other projects during the same time.

So, the first thing I do when planning is to create an Excel study schedule. I then count the number of days I have until the exam and allocate them for reading each chapter of each book with respect to the number of pages in that chapter. When I finish each chapter, I record the date in my Excel file to I verify that I am on schedule. I target to finish reading 30 days before the exam and use the rest of the time for practice. Similarly, 30 days doesn’t mean I shut myself away and study. It takes less than an hour per day on average. (I will explain more below in section 3.)

At first sight, reading 3-4 books per exam is quite daunting. However, spreading them to 3 months and it becomes very doable. Just keep calm and follow the plan. 3 exams per year are very practical without a deal with the devil.

2. Don’t buy study manuals, make your own notes

I see a difference between studying actuarial concepts and studying for an exam. The former focus on understanding, while the latter focus on passing. I personally prefer the first.

When I study, I focus on understanding the concepts instead of memorizing, because by understanding the concept, all those complicated theories become much more intuitive. I can easily derive and adapt my knowledge to any situation. It quickly becomes second nature without much effort. On the other hand, if I just memorize a concept, I can’t adapt if the question changes a bit. Moreover, it always leads to frustration when forgetting something.

That is the main reason why I never learn from study manuals, they don’t fully explain the ideas behind the concepts. (And they are too expensive.) I did not spend a single dollar in purchasing study materials as I was able to find all textbooks either in my university library or online.

When reading textbooks, I have a very simple strategy: read through each chapter twice and only twice. During the first time, I highlight key points and try to have a general idea of what the chapter is about. During the second time, I make sure I understand each and every concept and summarize them in my notes using my own words. There are two benefits to this. One, I ensure I digest all concepts and able to present them on my own. If I can present a concept, I can answer exam questions about it. Two, I never need to open the textbooks again because I have everything I need in my notes. If I forget anything, I only need to search for it in my note. No more wasting time searching through 400+ pages of textbooks.

When I am done reading a textbook twice, the book goes away. There is no such thing as saving a difficult topic for later. This is no going back. This is how I make sure my every second when holding a book does not go to waste. When I do practice questions, I only need to refresh my memory with my notes. And I can understand every symbol in my notes, obviously, because I wrote them.

3. SOA sample questions are more than enough

Before asking how many practice questions do we need, let’s try to figure out why do we need them. For me, practice questions have 2 purposes: accustom me to the question types, and verify I learn all the required concepts.

Why SOA sample question is enough? First, those sample questions are prepared by SOA themselves. It is the closest to the real exam questions. I even feel that the difficulty level is the same as the real exam. Second, those questions can cover almost every concept required in an exam. Since I focus on understanding the material, I don’t need to train for every possible variation of the questions. I just need to make sure I didn’t miss a chapter or misread something.

What if I already complete the questions once? I will do it again. By doing so, I build familiarity and confidence. With more confidence, I am less likely to second guess my answer and I will go with my instincts. Completing the sample questions 2-3 times is adequate for me to feel safe and confident. Anything more is unnecessary. To be honest, the exam questions are also very repetitive. You definitely have learned a way to solve it. When facing difficult questions, I will just fall back to first principles and try multiple approaches until it works. And, it works.

4. There are no shortcuts

Success doesn’t come easy. Passing actuarial exams requires a huge amount of commitment. SOA exams are not only a test of intelligence, but also a test of determination.

Moreover, from my perspective, if you pass an exam only by study the questions but not understanding the concepts, you incur a debt. You trade off the ability to understand more difficult concepts later on and will likely struggle in later exams. That’s why I find building a strong foundation is the most important.

But there is one thing that I can guarantee: The feeling of success after passing the exams will be second to none.

That is all I have for now. I hope my journey through the prelim exams can inspire yours. Feel free to connect with me and message me on LinkedIn.

You can download my schedule templates here: