Risk Adjusted Premiums

The real flaw in capitation is that smaller insurers need higher Risk Premiums than $PI$'s market based Risk Premium of 5%, while larger insurers can accept lower Risk Premiums. Portfolio Risk Adjusted Premiums (PRAPs) reflect insurers' different probabilities of adverse operating results. The ``Market Premium'' of $4,000 per policyholder, per year is adequate, and not excessive for the Population, and it works well for $PI$, because $PI$ has the only portfolio size that results in the operating characteristics described in Section 8. In an efficient insurance market, with large and small insurers, there exists only one portfolio size for which the market premium is adequate, but not excessive. $PI$ has the operating characteristics it has because 1,000,000 policyholders is the perfect size for a reasonably efficient insurer. The market premium ($4,000) is inadequate for smaller insurers, and excessive for larger insurers. Recall that $PI$'s Market Premium has a Risk Premium of 5%:

$$\textrm{Market Premium} = \textrm{Expected Claims Costs}$$ (5)

$$+ \quad \textrm{5\% Market Average Profit Margin}$$

$$+ \quad \textrm{5\% Market Average Risk Premium}$$

while insurers smaller (larger) than $PI$ need higher (lower) Portfolio Risk Adjusted Premiums to compensate for their higher probabilities of excessive Claims Costs:

$$\textrm{Portfolio Risk Adjusted Premium} = \textrm{Expected Claims Costs}$$ (6)

$$+ \quad \textrm{5\% Market Average Profit Margin}$$

$$+ \quad \textrm{Portfolio Size Adjusted Risk Premium}$$

This analysis will show that when $PI$ transfers its Claims Costs to other insurers, smaller insurers need payments that exceed 85% of $PI$'s Earned Premiums, guaranteeing Operating Losses for $PI$. Larger insurers can accept less than 85% of $PI$'s Earned Premiums, guaranteeing $PI$ certain profits. This happens because larger insurers are more efficient than $PI$ and all smaller insurers.

Insurer's Portfolio Risk Adjusted Premiums ($PRAP_{N}$) adjust for the fact that small insurers have higher probabilities of PLRE's above 1, 2, 3, 4 standard errors above the PLR than $PI$ and larger insurers. To earn profits of 5%, or simply to avoid losses, with the same probability as $PI$, they need additional payments, or additional Surplus, to cushion them from these Claims Costs. If $PI$ transfer its Claims Costs portfolio to larger insurers the transaction can benefit both parties (See Section 13, but if $PI$ transfers its portfolio to $D$ and $E$, at least one party is harmed. Risk assuming health care providers like $D$ and $E$, are, almost always, going to need higher Portfolio Size Adjusted Risk Premiums than $PI$ can provide without incurring Operating Losses or becoming insolvent.