As well, when “innovative” cost control mechanisms are used, such as capitation, episode based care, or DRGs payments schemes, these mechanisms transfer “insurable” risks to health care providers. While some prefer to characterize such risks as performance and/or inefficiency risks, they are quite clearly exchanges of liabilities for uncertain costs in lieu of fixed payments – the classical definition of an insurance risk transfer.

Fortunately, we can characterize the impact of insurer size on operating characteristics fairly easily. While complex models of insurer risk, beginning with models for individuals and building toward aggregate risks are the usual route preferred by actuaries, these models are unduly complex, offer little insight accessible to the general public and policymakers, and become obstacles to understanding risk and insurance rather than highways. We can, using the insight that the Central Limit Theorem provides information about the impact of insurer size on loss ratio variation, compare the operating characteristics of insurers.

I call this form of analysis “Professional Caregiver Insurance Risk.” Interested readers can look at any introductory statistics book for explanations of the mean, variance, standard deviation, and standard error the critical concepts that underlie this manner of comparing the effect of size on insurer operating results.

We start with a paradigm insurer (PI) that allocates premiums as follows: Expected loss ratio $0.75, Profit contingency $0.05, Risk premium $0.05, and Non-loss related operating expenses $0.15. PI writes 1,000,000 policies at random, and the standard error for a portfolio size of 1,000,000 for PI’s estimate (i.e. PI’s actual
loss ratio) of the population loss ratio is $0.05.

PI earns profits of at least 5% at or below loss ratios of $0.80, occurring with probability 0.8413. PI avoids operating losses (LR < $0.85) with probability 0.9772. PI can withstand extreme losses, the essence of insurance, if it sets aside liquid assets, called "Surplus," sufficient to cushion it from a single year loss ratio of $0.90, which protects PI from insolvency with probability 0.9987 (Protection against a loss ratio occurring with probability 0.0013). PI will become insolvent if its loss ratio exceeds 0.90. PI's surplus requirement is 5% (0.90 – 0.85) of its gross premium revenues.

Insurers writing more policies have higher probabilities of profitability, avoidance of operating losses, and solvency. Smaller insurers (including insurance risk assuming health care providers), have far lower probabilities of profitability, avoidance of operating losses, and avoidance of insolvency.

A true national insurer (NI), with 307,000,000 policies would have a size adjusted standard error of 0.0029 compared with PI's 0.05. For identical premium charges, NI would have a probability of profits of at least 5% 0f 1.0000. NI's probability of avoiding net operating losses would be 1.0000. NI would not, because it has such a small standard error, require any surplus to protect itself from a loss ratio occurring with probability 0.0013. NI could provide benefits of $0.7971 per dollar of premium collected.

A small insurer SI [readers are encouraged to make the leap to risk assuming health care provider] insuring 100,000 policyholders has dramatically different probabilities of these same operating characteristics. SI's probability of profits of at least 5% is just 0.6241 because SI's standard error is 0.1581 rather than PI's 0.05. SI avoids operating losses with probability 0.7365 and SI should protect against a loss ratio occurring with probability 0.0013 by maintaining surplus adequate to cover a single year loss ratio of 1.2261.

Small insurers manage risk so inefficiently that they cannot provide benefits anywhere near those achievable by NI. PI, for example, can provide maximum sustainable benefits of $0.75 per dollar of premium and meet the performance goals above. SI, on the other hand, can only provide benefits of $0.6419 per premium dollar. The difference between NI's benefit levels ($0.7971) and SI's benefit levels are solely due to inefficient risk management operations, based solely on portfolio size.

We must lay aside the myth that all insurers face the same operating characteristics if we are not going to continue a specious debate. The erroneous assumption that private insurance markets are more efficient than a national health insurance program can be refuted by a reasonably bright high school student and our public policy debate ought to be at least this informed.

A draft version of this analysis is available at:

http://drtcbear.servebbs.net:81/~PCIR/Oct2009.pdf