Note that there’s a few more aspects to risk analysis that can be relevant:
1) Risk distribution. A lot of outcomes are correlated in various ways, and models which don’t take this into account will sum the risks incorrectly. Ohio hurricane insurance tends to be safe most years, but all pays out at once when it hits. Laying off the risk earlier than a naive calculation would suggest is wise.
2) Threshold of Misery. At some point, bigger or more losses don’t hurt any more. Paying to reinsure some of the risk, if you’re going to be bankrupt anyway, is wasted (from the shareholder perspective; it’s certainly kind to customers and may be required by regulators). If a manager will be fired for a $60K loss, they may as well take a $200K risk (if they have to take any risk at all, that is).
Absolutely true—they are slightly less related to principle agent problems, but I can add stories illustrating these, because I have some good ones.
Re: Risk distribution, there’s a great game that someone suggested to understand what 100 year floods look like, since people complain they happen every year. Get a room full of, say, 40 people, and give them each 2 dice. Tell them snake-eyes is a flood, then have everyone roll, and to call out if there was a flood. Then roll and announce again. And again. Yes, many “years” will have no floods, but some will have 2 or even 3 - because the risk isn’t highly correlated across areas.
Re: Threshold of misery, I knew an underwriter who said they would write New York City nuclear terrorism insurance whenever they had the chance, at basically any price. His reasoning? He lives and works in NYC, so if a nuclear bomb goes off, he’s dead, and the fact that he lost money isn’t what matters. Otherwise he collects premiums.
Note that there’s a few more aspects to risk analysis that can be relevant:
1) Risk distribution. A lot of outcomes are correlated in various ways, and models which don’t take this into account will sum the risks incorrectly. Ohio hurricane insurance tends to be safe most years, but all pays out at once when it hits. Laying off the risk earlier than a naive calculation would suggest is wise.
2) Threshold of Misery. At some point, bigger or more losses don’t hurt any more. Paying to reinsure some of the risk, if you’re going to be bankrupt anyway, is wasted (from the shareholder perspective; it’s certainly kind to customers and may be required by regulators). If a manager will be fired for a $60K loss, they may as well take a $200K risk (if they have to take any risk at all, that is).
Absolutely true—they are slightly less related to principle agent problems, but I can add stories illustrating these, because I have some good ones.
Re: Risk distribution, there’s a great game that someone suggested to understand what 100 year floods look like, since people complain they happen every year. Get a room full of, say, 40 people, and give them each 2 dice. Tell them snake-eyes is a flood, then have everyone roll, and to call out if there was a flood. Then roll and announce again. And again. Yes, many “years” will have no floods, but some will have 2 or even 3 - because the risk isn’t highly correlated across areas.
Re: Threshold of misery, I knew an underwriter who said they would write New York City nuclear terrorism insurance whenever they had the chance, at basically any price. His reasoning? He lives and works in NYC, so if a nuclear bomb goes off, he’s dead, and the fact that he lost money isn’t what matters. Otherwise he collects premiums.