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Title: Evaluating factor strength with a large number of assets Authors:  Sermin Gungor - Bank of Canada (Canada) [presenting]
Richard Luger - Laval University (Canada)
Abstract: An asymptotic test is developed for evaluating ``factor strength" in linear factor pricing models using a large number of assets. Factor models explain the expected return differentials across assets as a linear function of their exposures (betas) to a small number of risk factors. In doing so, they rely on the assumption that factors under consideration are well identified (so-called strong factors). A failure of this identification condition implies that a factor is either ``weak" with small betas or ``irrelevant" with exactly zero betas. In either case, the estimation of the factor risk premium becomes unreliable with severe overrejection of a zero premium on the weak/irrelevant factor. The proposed methodology identifies weak and irrelevant factors while adjusting the probability of false rejections resulting from a large number of assets. i.e. multiple testing problems. An application using individual stock data for the U.S. stock market finds that the market factor is the only strong factor, but its strength varies over time with the market composition.