Tuesday, August 21, 2012
Chen: The Mathematics of Law School Merit Scholarships
Jim Chen (Former Dean, Louisville), Scholarships at Risk: The Mathematics of Merit Stipulations in Law School Financial Aid:
Many law schools in the United States condition financial aid grants on the recipients’ maintenance of a certain grade point average. These merit stipulations require students to meet or exceed minimum academic standards in order to keep all or part of their financial aid. Law students should take merit stipulations into account when they decide whether to accept an offer of admission paired with a conditional grant of financial aid. By all accounts, they do not. Law schools should transparently disclose the likely effect of merit stipulations on their financial aid awards. By all accounts, law schools do no such thing. Absent external coercion, they are unlikely to change their current practices. In the absence of industry-wide standards counseling full disclosure of financial aid practices, this article will try to equip law school applicants with the mathematical tools to assess the real impact of merit stipulations on their financial well being.
This article first presents very simple models for discounting financial aid awards for the risk of failure to uphold a merit stipulation. It outlines a simple methodology for calculating the expected value of a financial aid award subject to a merit stipulation. The article also evaluates one extraordinary circumstance in which a law school has implicitly revealed its break-even point — the amount of aid that the school would award if it did not impose any merit stipulations.
Building upon those foundations, this article performs a comprehensive analysis of law school grades and merit stipulations as artifacts of the standard normal distribution. It performs three distinct tasks. This article defines standard scores and explains how law school grading is based on the relationship between the standard score of each student’s raw score and the mean and standard deviation of of the distribution as a whole. This article then describes the risk of failure to satisfy a merit stipulation in terms of the normal distribution’s cumulative distribution function. For those instances in which the risk of failure to satisfy a particular school’s merit stipulation is known, this article demonstrates how to use the inverse cumulative distribution function to estimate the mean and standard deviation of a school’s grade distribution. As a bonus, this final exercise provides an introduction to value-at-risk analysis, a leading tool for assessing risk in global capital markets.