In developing our approach to modeling risk, we have drawn insights from modern portfolio theory and investment management, where useful and applicable. We note the limitations to this approach, however, as social impact measurement is more complex and less developed as a discipline than capital asset pricing. See a detailed description of how we integrate financial risk into impact models here.

Our formula for calculating the expected performance of a grant, inspired by y = a + Bx (from the Capital Asset Pricing Model), is y = aB, where y is our predicted North Star ROI, a is the expected impact on earnings, and B is the mid-point of the confidence interval on reach and scale.

The concepts of alpha (a) and beta (B) are integrated into our North Star ROI model calculations as follows:

1. Alpha: is expressed as both an absolute and as a percentage increase in annual income compared to a counterfactual comparison, for all individuals reached by the investment (the aggregate present value of lifetime earnings)
2. Beta: is expressed as one or more key probabilities that determine a range of outcomes (i.e., confidence intervals) that are grant-specific.
   1. For example, completion rates, hiring rates, cost projections, scaling projections, and income projections are all outcomes that can be modeled with probability ranges that affect the Beta of an individual grant.

Using this modeling approach, grantees that are taking innovative, yet risky, approaches to generating social impact often generate higher ROI values than grantees with programs that are proven, yet less innovative, with no scaling plans. Our research has shown that most leading philanthropies use risk as a discount factor in their models, leading them to risk-averse behaviors.

While our North Star model plays a key role in how we assess grants, the model is not the only determining factor. Organizational leadership, previous track records, ability to form partnerships, and impact evidence quality, among other components, factor into our grant selection process as well.