CAPM’s expected returns and delivered return on equity: an approach to the S&P500
This paper aims to reconcile two measures of return on shareholders’ capital: on one hand, the expected return arising from the use of the Capital Asset Pricing Model (CAPM), and on the other, the realized Return on Equity (ROE) as an accounting measure of capital efficiency. Both metrics ultimately refer to the same underlying variable—the cost of equity Ke—yet they are seldom analyzed jointly in the literature. Using quarterly fundamental data for all S&P500 constituents from 1996 to 2025, we construct aggregate earnings yields and book ROE series and compare them against realized index-level total returns. Our hypothesis is that, over sufficiently long horizons, both indicators should converge, since expected returns should equal realized returns when expectations are fulfilled on average. We find that the long-run annualized S&P500 total return (10.1%) lies between the average aggregate earnings yield (4.3%) and the average book ROE (13.3%), with the wedge fully explained by the Price-to-Book ratio and the earnings growth rate through the Gordon Growth Model identity E(R) = (ROE − g)/(P/B) + g. The convergence tightens as the observation horizon lengthens, consistent with the theoretical prediction.