Statistical Properties of the Risk Transfer Formula in the Affordable Care Act

Open Access
Li, Michelle
Area of Honors:
Bachelor of Science
Document Type:
Thesis Supervisors:
  • Donald Richards, Thesis Supervisor
  • Murali Haran, Honors Advisor
  • health care
  • insurance
  • affordable care act
  • actuarial science
In March 2010, President Barack Obama signed into law the Affordable Care Act (ACA). This Act created a competitive Marketplace of insurance plans which are required to provide insurance coverage without regard to pre-existing medical conditions. Previously, it was common for insurers to use health information to set premium rates and deny coverage, if appropriate. Because of this major change, the Affordable Care Act introduced several measures to help insurers during a transitional period. This thesis investigates one such measure, namely the risk transfer formula. This formula transfers funds from insurance plans with healthy members to plans with less healthy ones. By means of these transfer amounts, the formula ameliorates the tendency for insurers to favor healthy members over less healthy ones. By treating these risk transfer amounts as random variables and investigating their means, variances, and covariances, we determine properties of the risk transfer amount for each plan relative to that plan’s market share. These results also allow us to quantify this relationship. The results in this thesis provide mathematical justification for a phenomenon, observed previously by the American Academy of Actuaries, that “Risk adjustment transfers as a percent of premium were more variable and likely to be higher for insurers with a smaller market share” [“Insight on the ACA,” 2016]. The results in this thesis determine conditions under which this phenomenon will hold, and also the rates of change of variability of risk transfer amounts as a function of the market shares of competing insurers.