Tim Worstall is a British economic commentator with a free-market bent who writes for Forbes and the Adam Smith Institute. His usual beat is the economic fallacies of some other, less insightful British econ commentators and his denunciations to them are often highly amusing, if a little salty.
In a recent post on the economics of insurance, I think he screwed the pooch. He tries to explain why writing insurance which are unprofitable on insurance basis might still be a good business:
The answer to the insurance question though is simple: premiums are not the only revenue stream in an insurance company. We pay our premiums in and the insurance company only has to pay them out at some point in the future. They thus get to play with that vast pile of cash for some amount of time. What they actually do with it is invest it. What they invest in will depend a little on what type of insurance they're writing, what the likely time scale is before any potential payout. Someone writing car insurance will probably have a more liquid investment (ie, shorter term) portfolio than someone writing earthquake reinsurance (ie, insurance to insurance companies about earthquakes). The reinsurance companies have some of the longest term investment portfolios around, often longer even than pension providers.
This argument seems to make intuitive sense. We all pay insurance premiums on a regular basis, but don't usually get a payout. So the insurance companies must be accumulating money and earn interest on that until we have a payout and these investment returns must help with their profitability, even when the premiums alone aren't. But this is wrong.
To understand why, consider this stylized example:
An insurance company writes a policy that has a $1,000 payout with a monthly risk of 1/1000. The neutral (i.e., generating neither profit or loss) premium for such a policy is $1/month ($1,000 × (1/1000 months)).
In a typical month such a premium will result in no payout, so money accumulates in the insurance company's kitty. Every 1,000 months or so there is an insurable event and the policy pays. So doesn't the money in the kitty generate an investment return for the insurance company?
No, because on average there is $0 in the kitty. It is true that if the policy takes more than 1,000 months to pay out, there will be some money in it. But even at one payout on average every 1,000 months, half the time there will be a payout before 1,000 months are up and, after that payout, the amount in the kitty is negative. On average the kitty will contain $0.
This may be easier to see in the slightly more realistic example that the company writes one million insurance policies like this. Every month the company will collect $1 million ($1/month-policy × 1,000,000 policies). But every month the company will also pay out $1 million ($1,000/payoff × 1 payoff/1000 policy-months × 1,000,0000 policies). Inflow equals outflow, so there is no net accumulation.
One might respond that it would be irresponsible to run an insurance company like this because it means that if due to chance some months there are more than expected payoffs, the cash flow becomes negative and for the company to stand behind its policies it would need to supplement the fund from other sources.
So let's say the insurance company, as a responsible company would, puts in a year's expected payouts of $12 million ($1,000,000 payouts/month × 12 months/year) into the kitty as a cushion against bad months. In that case, the company would indeed on average have $12 million in the kitty and earn investment returns on those funds. But that has nothing to do with insurance! The company could just have stayed out of the insurance business completely and invested its original $12 million directly and, on average, earned the same investment returns.
Alternatively, the company might increase its premiums to $2/month, for example. In that case, $1 million would accumulate in the kitty every month and the company can earn investment returns on that money. But that just means that the company wrote profitable policies, contrary to the premise of the puzzle Worstall tried to explain in the beginning.
So why do insurance companies write unprofitable policies? In many cases, insurance companies just can't perfectly identify prospective clients with above average risk and just end up writing the policies anyway in the hopes that on average high-risk and low-risk clients will cancel out. In many other cases, such as US health insurance policies, the insurance companies are required by law not to discriminate between high-risk and low-risk clients and must extract rents from the low-risk clients to subsidize the high-risk clients. Finally, the insurance companies may just misestimate the average risk; it happens.
But in no case do investment returns turn unprofitable policies into profitable ones.
