Market Beta is not dead: An approach from Random Matrix Theory

In the 1980s, the first doubts about the validity of the Sharpe Single Index Model to explain the cross-sectional expected returns of financial assets appeared. Since then, the financial literature has proposed a wide variety of new factors, while many empirical studies have tried to determine their plausibility. In this paper, we present a new approach from the Random Matrix Theory to determine if the Arbitrage Pricing Theory models are better than the Sharpe Model to explain the cross-sectional expected returns. We will show that, except for periods of high volatility, just one factor is significant in the sample. We will also prove that this factor is the Market one. •We use RMT to provide new evidence on the significance of APT factors.•Our approach is purely statistical.•We found only one significant factor among all the periods: the Market one.•We show that Sharpe’s one-factor model performs better than APT models.