Sharpe-ly Leveraged: A Model of Human Capital Formation Under Debt Service Constraint

Human capital, like any other form of wealth, lends itself to analysis through the tools of mathematical finance. No less than in other forms of enterprise, human capital formation involves risk. Returns on human capital and the risks inherent in its formation are affected by leverage. This is especially true in the United States, where a significant number of students finance higher education by borrowing. This article specifies a basic model of human capital formation that attempts to capture the essence of the risk-adjusted returns that students hope to realize when they pursue further education. This article adapts the Sharpe ratio of modern portfolio theory to measure the risk-adjusted benefit of education-enhanced earnings as the ratio of expected earnings to the volatility of those returns on human capital. It then adjusts both earnings and their dispersion to account for educational debt. On the debt service and earnings premium assumptions adopted by this article, debt-financed higher education will not enhance earnings on a risk-adjusted basis unless (1) the square root of the earnings premium (2) times the square of 1 minus the debt service ratio times the ratio of educational debt to annual earnings (3) exceeds 1.