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Insurer Probabilities of Operating Losses by Portfolio Size

$NHI$ and $B$ have probability 0.0000 of incurring operating losses, $PI$ has probability 0.0228, but $D$ and $E$ have much higher operating loss probabilities, 0.2635 (1.0000 - 0.7365) and 0.4207 (1.0000 - 0.5793), respectively.

Table 1 Row 6, shows insurers' probabilities of incurring operating losses greater than 5% ( $1.0000 - \Phi_N(0.9000)$), at PLREs above 0.9000. $NHI$ and $B$ incur such operating losses with probability 0.0000, $PI$'s probability is 0.00135, but $D$ and $E$ have probabilities, 0.1714 and 0.3821, respectively. Insurer D is 127 times more likely, and Insurer E is 283 times more likely, to incur such operating losses, than $PI$. Table 1 Row 7, shows insurers' probabilities of operating losses greater than 10%, at PLREs above 0.9500. $\Phi_{NHI}$(0.9500) = $\Phi_{B}$(0.9500) = $\Phi_{PI}(0.9500)$ = 0.0000, while $\Phi_{D}(0.9500)$ = 0.1030 and $\Phi_{E}(0.9500)$ = 0.3446. $D$ can expect such high operating losses more than one year in ten, and $E$ more than one year in three.


Table 1: Insurer Standard Errors, Financial Outcome Probabilities, Surplus Requirements, Maximum Sustainable Benefits, and Risk Adjusted Premiums by Portfolio Size
(1) (2) (3) (4) (5) (6) (7)
Row Operating Characteristic NHI B PI D E
(1) Size (N) (1,000s) 308,000 10,000 1,000 100 10
(2) Standard Error ( $\sigma_{e_{N}}$) 0.00285 0.01581 0.0500 0.1581 0.5000
(3) P[Profit$\geq$10%] 0.5000 0.5000 0.5000 0.5000 0.5000
(4) P[Profit$\geq$5%] 1.0000 0.9992 0.8413 0.6241 0.5398
(5) P[No loss] 1.0000 1.0000 0.9772 0.7365 0.5793
(6) P[Losses$\geq$5%] 0.0000 0.0000 0.0013 0.1714 0.3821
(7) P[Losses$\geq$10%] 0.0000 0.0000 0.0000 0.1030 0.3446
(8) SPLR 0.7586 0.7974 0.9000 1.2243 2.2500
(9) Surplus Needs $1M $0 $0 $200 $150 $56
(10) Agg Surplus $1 Trillions $0 $0 $0.616 $4.612 $172
(11) MSB 5% Profits 0.7972 0.7842 0.7500 0.6419 0.3000
(12) MSB 5% Profits $ 3,189 3,137 3,000 2,568 1,200
(13) MSB Avoid Losses 0.8443 0.8184 0.7500 0.5338 0.0000
(14) MSB Avoid Losses $ 3,377 3,274 3,000 2,135 0.00
(15) Prof Adj'd Risk Prm % EP 80.38 81.5 85.0 95.8 130.0
(16) Loss Adj'd Risk Prm % EP 75.67 78.0 85.0 106.6 175.0


next up previous contents
Next: Insurer Risk and Surplus Up: Quantitative Analysis of Insurer Previous: Insurer Probabilities of Profits   Contents
Thomas Cox PhD RN 2013-02-23