Insurer Population Loss Ratio Estimates

Insurers' [Policyholders'] Population Loss Ratio Estimates (See Equation 3), ($PLRE_{N}$ [$PLRE_{i}$], are averages of their total Claims Costs to their total Earned Premiums:

$$\textrm{Population Loss Ratio Estimate} = \frac{\textrm{Claims Costs}}{\textrm{Earned Premiums}}$$ (3)

The standard deviation, $\sigma$, for an individual, randomly selected policyholder's Population Loss Ratio Estimate ($PLRE_{i}$) is much larger than the standard error, $\frac{\sigma}{\sqrt{N}}$, for a randomly selected insurer's Population Loss Ratio Estimate ($PLRE_{N}$). The expected values of sample standard deviations for a randomly selected policyholder's standard error, is identical in all portfolios. Insurers' PLRE standard errors decrease, and their accuracy increases, as portfolio sizes increase, and PLRE accuracy decreases as portfolio sizes decrease. Large insurers' PLREs more accurately estimate Population Loss Ratios than small insurers' PLREs, because their standard errors are smaller. I compare insurer performance using portfolio size adjusted standard errors (See Section 9 and Table 1).