Supply and demand in p/c insurance

Always good when someone shores up the ranks of blogging actuaries, so welcome to Todd Bault! I guess he’s been posting awhile, but I seemed to have missed his earlier work.

Todd is well-known in the actuarial community for being one of the leading insurance industry analysts, and he’s posting as part of the lineup at Sector & Sovereign Research’s blog.

Todd’s advancing a controversial idea – that insurance capital is not the ‘supply’ in the industry’s supply/demand equations. Controversial because most people will tell you that the price of insurance varies inversely with the amount of capital in the industry.

When insurers have lots of capital, the thinking goes, they are eager to write lots of business. Hence the price of insurance goes down. When capital is scarce – think of the losses from the World Trade Center paired with a loss of capital from the bursting of the dot-com bubble – prices rise.

But Todd doesn’t subscribe to that theory, and his recent posts – here, here and here – suggest that exposure is actually what drives the insurance industry’s supply curve.

To summarize his thinking: Loss trends would drive accident year loss ratios ever higher, except for rate change (and catastrophes, which he accounts for). So if you back out loss trends, any year-to-year movement in loss ratios will reflect rate changes. Then he notes that premium growth = exposure growth * rate change.

Having estimated rate change and exposure change, he graphs one against the other:

To prove this is difficult. At the macro level, data is thin, so his analysis is driven by the kind of squinting you do when you look out the window of a plane at 30,000 feet – you can’t make out much in detail. But since you are operating at a high level, imperfect information will generally be good enough.

So his key assumption – that change in CPI serves as a good proxy for loss trend – will seem outrageous to most actuaries. Essentially he implies that claim frequency doesn’t change over time (though it has). But given his data limitations, it’s reasonable.

And he has what looks like a nice supply curve mapping data from 1980 to 2010:

As you can see, this graph has the “right” relationship: a downward-sloping line reflecting the negative correlation one would expect for supply & demand.  It’s not a 95% R-squared, but I wouldn’t expect it to be.  It just has the expected relationship, without any other unnecessary assumptions.

It would even slope downward if it were modeled the way most economists do – measuring price vs supply with price on the y-axis (instead of change in price vs. change in supply with price on the x-axis).

But I think the negative correlation is an inevitable result of the formula used to calculate exposure growth

premium growth = price change * exposure growth

The formula, I think, requires price and exposure to be negatively correlated. For example, if premium didn’t grow, premium growth would be a constant of 1.00. If price change was positive, exposure change would necessarily be negative, and vice versa.

Of course, premium growth isn’t zero. It follows GDP over the long term. Nominal annual GDP growth from 1980 to 2010 is about 5%, so absent any data, we’d expect an exhibit like the one above to be a negatively sloped line with a y intercept around 5%, which it is.

I don’t think this means the underlying analysis is wrong, just that the negative correlation isn’t as meaningful as portrayed.


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