One of the key assumptions in health product premium rate development is the profit margin (i.e., contribution to surplus, risk charge, etc.). How should this be determined? How much is enough? How much is too much? There are multiple approaches used in today’s market. Some as simple as “let’s just assume x% of premium”. Others are more sophisticated approaches based upon an analysis of the risk characteristics of health product usually referencing confidence levels and return on surplus.

This article will discuss the more sophisticated approach which in most actuarial circles is the preferred approach. The process requires answers to several questions:

- What are the risk characteristics of this product line (i.e., its risk profile)?
- What is the desired risk protection in terms of percentiles or confidence levels?
- How much surplus should be allocated to support this product and its risk profile?
- What is a reasonable hurdle rate or return rate that the carrier/health plan should expect on the allocated surplus (i.e., cost of using that surplus)?

### Risk Characteristics

Each product line has a unique risk profile. The risk profile can be defined in terms of several items:

- High vs. low probability or frequency of claim
- High vs. low variability in size of claim
- Stable vs. unstable average health status of underlying population
- Presence and type of reinsurance coverage

Health plans usually cover a wide span of health care services ranging from high probability/low cost of claim to low probability/high cost of claim. Some coverages, such as dental, are limited to high probability/low cost of claim. Claim probability distributions can be used to project number and size of claims (See example in Table 1). This model shows a 13% probability of no claim during a calendar year. It also shows a 0.42% chance of having claims greater than $100,000 during a calendar year.

f(x) |
X |

13.05% | $0 |

4.14% | $47 |

5.76% | $150 |

4.60% | $248 |

4.09% | $350 |

3.65% | $449 |

7.54% | $619 |

5.77% | $870 |

4.60% | $1,121 |

3.81% | $1,371 |

3.23% | $1,622 |

2.79% | $1,872 |

2.49% | $2,122 |

2.16% | $2,373 |

1.94% | $2,622 |

1.74% | $2,873 |

3.00% | $3,242 |

2.45% | $3,742 |

2.06% | $4,243 |

1.74% | $4,742 |

1.49% | $5,245 |

1.29% | $5,744 |

1.14% | $6,243 |

1.01% | $6,747 |

0.89% | $7,245 |

3.44% | $8,665 |

3.81% | $12,166 |

1.87% | $17,229 |

1.09% | $22,318 |

0.70% | $27,339 |

0.49% | $32,371 |

0.37% | $37,397 |

0.28% | $42,396 |

0.22% | $47,370 |

0.89% | $68,643 |

0.31% | $136,283 |

0.07% | $241,878 |

0.02% | $342,948 |

0.01% | $442,101 |

0.01% | $642,433 |

0.00% | $1,336,053 |

This distribution can be used to model health plan claims using Monte Carlo simulation methods for an assumed enrolled population.

### Risk Profile and Required Surplus

The overall risk profile for a targeted or actual population can be approximated using Monte Carlo analysis. We have developed an overall claims projection for a population of 50,000 covered lives. The expected annual claims per individual from the previous claims probability distribution is $4,715. The expected annual claims for the 50,000 population is $235.7 million. Some key results from this simulation are shown in Table 2.

Percentile Level |
Expected Value of Claims in Excess of Percentile Level |
Percentile Claims Level in Excess of Mean |
Required Surplus |

50th | $3.10 million | $0.02 million | $3.13 million |

75th | $2.40 million | $2.58 million | $4.98 million |

80th | $2.19 million | $3.32 million | $5.51 million |

90th | $1.65 million | $5.20 million | $6.85 million |

95th | $1.15 million | $6.56 million | $7.71 million |

99th | $0.94 million | $8.56 million | $9.50 million |

The first column shows the expected value of claims in excess of specific percentile levels. The second column quantifies the percentile level of claims in excess of the mean. The third column is the sum of the two prior columns. The results in Table 2 are based upon no explicit margin built into the projection.

Assuming the company wants to establish their targeted surplus at the 80th percentile, they need to recognize the how much the 80th percentile expected claims exceed the mean or average claims (i.e., the $3.32 million shown in second column) in addition to the expected value of claims in excess of this level (i.e., the $2.19 million shown in the first column). The surplus requirement would be $5.51 million ($3.32 + $2.19 = $5.51) or about 2.34% of overall expected claims.

The above projections were based upon no explicit profit margin for the product. As an alternative we have developed projections with a 3% margin built into the claim estimates. In addition, we expressed this level of margin as a multiple of the standard deviation of the overall claims level so we could build in a comparable margin for claims in excess of the percentile attachment points^{1}.

The previous estimates of required surplus would be increased by the projected actuarial value of the margin on a consistent assumption.

Percentile |
Required Surplus (with no assumed margin)^{2} |
Value of Margin in excess of Percentile level |
Required Surplus (with margin in excess of Percentile level) |

50th | $3.13 million | $7.32 million | $10.45 million |

75th | $4.98 million | $7.50 million | $12.48 million |

80th | $5.51 million | $7.53 million | $13.04 million |

90th | $6.85 million | $7.69 million | $14.54 million |

95th | $7.71 million | $7.75 million | $15.46 million |

99th | $9.50 million | $7.86 million | $17.36 million |

At the 80% percentile level the required surplus increases from $5.51 to $13.04 million by considering and including the assumed pricing margin into the surplus calculations.

This derivation and use of required surplus with margin can be compared to Risk Based Capital. Insurance departments require companies to maintain at least 200% RBC to avoid tight surveillance. In many cases companies set objectives to maintain at least 375% – 450% of RBC as a strategic initiative. Applying these objectives to our 80th percentile with margin calculations this would suggest that assigned surplus for this 50,000 member block of business might be $48.90 – $58.68 million (3.75 x 13.04 = 48.90 and 4.50 x 13.04 = 58.68).

### Likely Hurdle Rate

Under the assumption that the company would require a 10% return on invested surplus (i.e., hurdle rate), this block of business would need to achieve a profit margin of $4.89-$5.87 million or 2.07%-2.45%. This is very close to the 3% margin initially assumed, although less.

Based upon this risk analysis, the initial 3% assumption is slightly greater than needed and could be reduced to 2%-2.5%. Ideally the projections would be revised using an updated profit margin target.

### Summary

The determination of how reasonable a profit margin is can be readily assessed using Monte Carlo simulation. This requires:

- A claims probability distribution for the product under consideration
- A measure of how significant the product is (i.e., projected members)
- The plan’s propensity to assume risk (i.e., percentile level)
- The plan’s surplus maintenance strategy (i.e., target surplus as a % of RBC)
- The plan’s hurdle rate (i.e., required return on invested surplus)

^{1}The margin for projected claims in excess of the percentile is based upon the same percentage of the standard deviation of those claims in excess of the percentile point that was determine for overall claims.

^{2}From Table 2

## About the Author

David Axene, FSA, FCA, CERA, MAAA, is the President and Founding Partner of Axene Health Partners, LLC and is based in AHP’s Temecula, CA office.