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A Tootsie Pop, a Coin Flip and a Reinsurance Program - Understanding Probabilities

February 20, 2018| Von Rick Hartmann | P/C General Industry | English

Region: North America

The Tootsie Pop commercials that aired when some of us were kids made me wonder how many licks it might take before you could get to the chocolate center of a Tootsie Pop. Now, as a reinsurance professional, I still find myself asking about probabilities, but the language is more complicated and there is a lot more at stake with every business decision. Exceedance Probability, Probable Maximum Loss, and Tail Value at Risk...life seemed simpler back then.

One of the fascinating concepts about the insurance business is that when we price an insurance policy, we will not know the ultimate cost of that policy until years and sometimes decades later. We use various insurance pricing tools and rating models; we make assumptions about risk and exposure, and ultimately we make an underwriting judgment. Our decisions are a balance of science and judgment every day. Yet even when we think we achieve the right balance, the wind can still blow and the earth can still shake unexpectedly; therefore, we need to be prepared for a wide range of possible outcomes, each with a different probability of occurring.

It is abundantly apparent that investments in technology and decision analytics have helped to drive efficiency and support better decision making for the insurance industry. However, they have also led the industry to become more model-driven and model-reliant. The increasing reliance on models for insurers highlights the importance of understanding the underlying assumptions and the probabilities around the outputs that drive our business decisions.

The probabilities within our model inputs and outputs are not always what they may seem. For mutual insurers, the question becomes how are you balancing your business decisions against modeled outputs? Profitable performance can certainly be the direct result of planned execution and skill, but it can also be attributed to luck. The challenge lies in knowing the difference. In fact, Victor Haghani, co-founder of one of the best-known investment firms in history, demonstrated this point with a simple test to prove that it is difficult to pick a fund manager who can beat the index with actual ability - versus luck.

Mr. Haghani and several colleagues presented hundreds of finance professionals with a scenario: If they were to flip two coins, one that was weighted so it came up heads 60% of the time and the other was weighted normally, how many flips it would take to know, within a 95% confidence interval, which of the coins was weighted.

The median response was 40.
The correct answer is 143.1

Mr. Haghani's exercise revealed that the participants' expectation of the number of flips needed to achieve a credible sample size was many fewer than what was actually required. These finance professionals, similar to the owl in the old Tootsie Pop commercials, prematurely thought they had enough information to be certain. In fact, the time it would take to gain this level was much longer. Mr. Haghani’s test reveals we underestimate the amount of data needed to justify confident decision-making and we are incorrectly judging outcomes or performance with incomplete information.

Probabilities are challenging enough for finance professionals to understand, let alone the average person who thinks he or she can beat the odds. Casinos count on this and are certainly not going to remind roulette players that each spin is an independent event - even though we might believe the 11th spin “HAS” to land on black because the last 10 spins landed on red. Misunderstandings of probabilities are all around, a fact CNN recently illuminated when they ran this headline: "500-year floods could strike NYC every five years, climate study says."2 You can’t help but wonder how the general public incorporates a statement like this one into their decision process to purchase a home.

Probabilities are baked into the decision making that mutual insurers use in managing their underlying volatility, maintaining the capital to support unforeseen tail events and building an adequate and efficient reinsurance program. 

Here are a few examples of questions we are asking mutual company executives about their decision making process:

  • What is your level of confidence that you have the most efficient reinsurance structure in place?
  • What is the probability that your gross results will be better than your net results next year?
  • When setting your retention for your core lines of business, how did you decide on an acceptable Tail Value at Risk?
  • If you raised your limits above $2 million on a certain line of business, what is the probability that you would have more than one claim in that layer next year?

As a Global Reinsurer with an expansive team of actuaries, we have the ability to help you validate or shape what you are trying to accomplish in this volatile marketplace. Please contact your local account executive or Gen Re representative to discuss how we can provide an independent view on the assumptions you are using to support your business decisions.

  1. Jakab, Spencer. “Is Your Stockpicker Lucky or Good?,” Wall Street Journal, November 24, 2017.
  2. Howard, Jacqueline, "500 year floods could strike NYC every five years,” CNN.com, October 27,2017.


Gen Re's Mutual Practice is uniquely structured to specifically focus on helping Mutual companies improve gross underwriting results. Our Direct Model provides unfiltered insights and observations through our exclusive ability to have direct underwriter-to-underwriter dialogue.






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