April 9, 2020 by Adam Keung, CEO, New World Insurance
A few months ago, my daughter and her friends were playing a card game. It eventually dissolved into an intense debate regarding probability.
The group of friends consisted of engineers, bankers, computer professionals, and lawyers. They were debating the probability of at least one of six players drawing a diamond card out of a regular deck of 52 playing cards.
They became more interested in solving the question than in continuing the game. The group sought input from other friends, including math teachers and accountants. To their surprise, no one could articulate a simple answer to what seemed like a basic probability question.
My daughter was 25 years old at the time. She fell back to her habitual solution when she needed help: She asked her parents. That’s how I got involved.
Surprisingly, I did not get an answer from Google right away. I asked more people about the question; their answers inspired me to learn more. I wondered how this probability question could help me to discover important insights relating to my insurance practice.
Probability of a claim
I began by surveying people. I asked two questions. The first was: “If I am to write your auto insurance, what do you think is the probability that you will have a claim for the next year?”
Many people responded, “Zero.” I used my skill as a broker to ask them to think about their responses again in a different way: “When was the last time, say in the past 10 years, you had a car accident? It doesn’t matter whether it was small or large; whether you were at fault or not.” Many remembered having been involved in a car accident at least once within the past decade.
I continued by asking, “From my experience, and according to many insurance companies’ statistics, there are on average 10 claims for every 100 policies. Can we use this yardstick to measure the probability of you making a claim within the next year?”
Most people I asked agreed to the 10% probability yardstick. To simplify this mathematical exercise, we assumed only one claim for any given year. A good number of people further commented, “That is still a pretty low chance, isn’t it?”
My next question was: “Let’s say I will write your policy for 10 years. What do you think is the probability that you will have at least one claim in the next 10 years?”
I received a broad range of answers, ranging from zero to 100%. Most importantly, I found that a majority of the responses were 10%. This was supported by the rationale that since they only had one claim in the past 10 years, they are likely to have just a single claim in the next 10 years.
Those who did not have a claim in the past 10 years typically responded 0%. Naturally, based on their past history, they did not expect to be involved in a car accident in the future.
Here is what my high school teacher told me:
• The probability of having a claim in one year is 10%, so the probability of having no claim is 90%.
• The probability of being claim-free for 10 years is calculated as follows: Nine divided by 10, to the power of 10, which is equal to 0.348 or about 35%.
• The probability of having at least one claim for 10 years will be the exact opposite of being claim-free for 10 years. That’s 1.0 minus 0.348, equalling .652, or about 65%.
Here is the crux of the matter: 10% versus 65% is a huge difference. For those who believed the probability was 10% (representing half of my surveyed subjects), they believed the chances of having a claim was low to negligible. In fact, the math shows that their chance of making a claim is much higher.
Now think about talking to customers about their claims experience. Assuming a 10% probability of receiving a claim from one customer, the probability of having at least one claim from ten customers is also 65%.
This is important to bear in mind when explaining to clients that claims are more likely to happen than they think. It’s also important information for me when I’m training new brokers who need to understand how to handle the claims that fall on them. Finally, it’s important for insurance companies to think twice before jumping into writing certain classes of business: The probability is an aggregation when the numbers and years get higher.
In its December 2019 issue, Canadian Underwriter predicted the hard market cycle would continue for at least two years. Having experienced three major hard market cycles, I can say each one has its own defining causes and characteristics. One common feature of them is increased claims costs.
The probability model is by no means a complete way of reflecting the chances of loss in the complicated world of insurance matters. But maybe it will give you a way to navigate out of these hard market times.
Adam Keung is CEO of New World Insurance in Markham, Ont. He received his Ontario RIBO broker license in 1993.