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##

Insurer Probabilities of Operating Losses by Portfolio Size

and have probability 0.0000 of incurring operating losses, has probability 0.0228, but and 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% (
), at PLREs above 0.9000. and incur such operating losses with probability 0.0000, 's probability is 0.00135, but and 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 . Table 1 Row 7, shows insurers' probabilities of operating losses greater than 10%, at PLREs above 0.9500. (0.9500) = (0.9500) =
= 0.0000, while
= 0.1030 and
= 0.3446. can expect such high operating losses more than one year in ten, and 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 (
) |
0.00285 |
0.01581 |
**0.0500** |
0.1581 |
0.5000 |

(3) |
**P[Profit10%]** |
**0.5000** |
**0.5000** |
**0.5000** |
**0.5000** |
**0.5000** |

(4) |
P[Profit5%] |
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[Losses5%] |
0.0000 |
0.0000 |
**0.0013** |
0.1714 |
0.3821 |

(7) |
P[Losses10%] |
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:** Insurer Risk and Surplus
** Up:** Quantitative Analysis of Insurer
** Previous:** Insurer Probabilities of Profits
** Contents**
Thomas Cox PhD RN
2013-02-23