When is a Risk Premium Earned?
This is a difficult question. One that challenges our accounting systems.
Think of two insurance contracts. One lasts for one minute, the other for an hour. They are both sold for residents of Antartica. They cover the risk of being hit with a snowball. On the average, residents of Antarctica are hit with a snowball 3 times per day. The contracts pay out $10 every time the insured is hit with a snowball. Premiums are $5 for the one hour policy and $0.10 for the one minute policy. The policies are renewable.
On Antarctica it is the custom of insurers to publish quarterly financials, that is every quarter hour.
Right now, there are 4 people on Antarctica and two of them have policies. One bought the one minute policy and the other bought the one hour policy.
After the first quarter hour, there have been no claims. What are the profits from the two policies?
The answers are completely different depending upon whether you decide to look at earning risk premium over the maximum holding period for the policies or the minimum holding period.
Our accounting systems tend to take the minimum holding period approach. However, the maximum holding period approach might give a more useful answer.
The maximum holding period approach would be to think of the risk over the effectively infinite maximum holding period. To determine profits, look forward and consider the amount needed for future losses. You expect to have lumpy losses that average to a certain level. The maximum holding period approach would then tend to reflect the excess over the expected losses as the profits in a period as profits and allow a build up of reserves to take care of the lumpy losses.
The minimum holding period approach suggests that at the end of the minimum holding period, you are done and reflect any revenue not needed to pay losses as profits.
So if no snowballs were thrown that quarter hour, all premiums (less expenses, which are very high for insurers operating in Antarctica) as profits. If during any quarter hour there are snowballs, then there will be losses. Very lumpy results.
This is not just an insurance consideration, it applied to any risks, such as credit or any far out of the money derivatives where losses are not expected in every period.
The minimum holding period approach will tend to encourage risk taking. The maximum holding period approach would tend to make risk takers realize that they do expect losses sometimes.
Then if someone wants to recognize all of their profits from exposure to an infrequent risk during no loss periods, they would need to totally exit that position.
The following chart is referenced in the comment from Robert Arvanitis…
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