Do we always underprice tail risk?

What in the world might underpricing mean when referring to a true tail risk? Adequacy of pricing assumes that someone actually can know the correct price.

But imagine something that has a true likelihood of 5% in any one period.  Now imagine 100 periods of randomly generated results.

Then for each of three 100 period trials look at 20 year periods. The tables below show the frequency table for the 80 observation periods.

20 Year Observed Frequency Out of 80
0 45
5% 24
10% 12
15% 0
20% 0
20 Year Observed Frequency Out of 80
0 9
5% 28
10% 24
15% 8
20% 7
20 Year Observed Frequency Our of 80
0 50
5% 11
10% 20
15% 0
20% 0

if the “tail risks” are 1/20 events and you do not have any information other than observations of experience, then this is the sort of result you will get. The observed frequency will jump around.

If that is the situation, how would anyone get the price “correct”?

But suppose that you then set a price for this tail risk. Let’s just say you picked 15% because that is what your competitor is doing.

And you have a very patient set of investors. They will judge you by 5 year results. So then we plot the 5 year results.

And you see that my profits are quite a wild ride.

Now in the insurance sector, what seems to happen is that when there are runs of good results people tend to cut rates to pick up market share. And when the profits run to losses, people tend to raise rates to make up for losses.

So again we are stymied from knowing what is the correct rate since the market goes up and down with a lag to experience.

Is the result a tendency to underprice?  You be the judge.

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3 Comments on “Do we always underprice tail risk?”

  1. Jean-Pierre Berliet Says:

    This is enlightening! I can see the predicament in which a smart insurer is: If you do not write the business and earn the implicitly overstated profit, you cannot compete and keep your job..If you lose your gamble, you are just a victims of events, like everyone else, and life goes on. Pity investors in insurance companies and ask yourself whether this issue may have something to do with the permanently poor valuation levels (i/e. high cost of capital) that plague most public companies in the industry?


  2. Two drivers:

    Specifically in insurance – we used to see rate cycles many years ago. But now with a huge capital base, the industry must lose in the scores of billions, before it burns through investment earnings, much less contracts capital to the point of price increases. Worse, new capital can flow in readily. By November 2001, there were prospectuses for new insurers seeking to take advantage of the “new hard rates” in the wake of 9/11.

    More generally, consider the human psychology. A one-in-ten event is a budgeted item. We know we’ll need a new car or new roof…
    A one-in-thousand item is outside our career expectations.
    So general corporations, insurers, banks, all play in the one-in-hundred range.
    It’s not so much that we mis-price risk, as that we (1) ignore it, or else (2) dismiss a threat as one-in-thousand, blissfully unaware of the unrecognized correlations that make it far more likely that we perceive.

  3. Sam Kiranga Says:

    Nice stuff. Got an actuarial commentary myself. http://my.opera.com/TheSetta/blog/


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