Yesterday with the NYU Stern class that I am co-teaching with Arun Sunderarajan we focused on the fundamentals of different businesses. The class is about product market fit but looking for that doesn’t mean you can ignore the economics of the market in which you operate. If you want an example of what I mean, read my post from a while back about vertical integration in on-demand services.

Later today I am meeting with an executive from the insurance industry. Given that we have invested a lot in financial services innovation we have been looking around at insurance. So far we have not made an investment although we have met several startups working on interesting approaches. I have invested in the past in insurance and one of the things I was struck by is how few people seem to really understand the fundamentals of insurance. So as a reminder to myself I though I would write a few blog posts about that starting today.

The first fundamental equation of insurance is that the following inequality must hold:

Expected total payouts ≤ Expected total premiums

Over time this must be true for the system as a whole (unless government is subsidizing) and it must be true for any particular insurance company (otherwise it will go out of business).

Now you may say, “Duh, that’s obvious” but there is a lot more here than meets the eye. The right hand side of the inequality is (relatively) straight forward. After all, premium payments are (seemingly) highly predictable. Everyone who is insured pays their monthly or annual or one-time premium (for the insured the premium is the cost of having the insurance).

But the left hand side is a lot trickier. Because what matters in aggregating up payouts are not just individual probabilities but also their correlation. Imagine you are insuring home mortgages against default. What matters is not just the probability of any one home owner defaulting on their mortgage but the likelihood that many of them do so at once. And if you are assuming too low a correlation, well then the premiums you have collected won’t be enough to cover the payouts. That’s exactly what happened during the collapse of the mortgage bubble and I highly recommend watching “The Big Short.”

Another way that this inequality can break down fundamentally is by being wrong about the frequency and severity of extreme outcomes. That can happen with so-called fat tailed distributions where the risk of outlier events is larger than assumed. Take earthquake risk as an example. There can be reasonable disagreement even among experts on the topic as to how likely a very large quake around the San Andreas Fault is. Since these events are so rare and possibly not at all observed one might significantly underestimate their actual probability. That could easily lead to a scenario in which all premiums don’t come close to covering all claims. 

Next post we will look at what the relationship should be between expected payouts and premiums for an individual insured. Here too things are a lot more complicated than one might at first think and this lies at the heart of insurance.