New meta-analysis study finds diminished size premium in stock returns

BVWireIssue #205-2
October 9, 2019

cost of capital
cost of capital, discount rate, private company valuation, risk analysis, cost of equity, size effect

The debate over the size premium in stock returns has raged for years, with no consensus over the magnitude or stability—or even the existence—of the size premium. There have been many studies on the size premium but with conflicting results. Now, the first “meta-analysis” of the size premium provides an estimate that is smaller than what many people believe, according to a new paper.

Meta-analysis is a quantitative research method designed to aggregate and synthesize past findings and explain differences in earlier studies. It is particularly useful when earlier studies have conflicting results. Authors of the new study collected 1,746 estimates of the effect of size on stock returns reported in 102 published studies and conducted a meta-analysis. The paper, “Firm Size and Stock Returns: A Quantitative Survey,” has been accepted for publication in the Journal of Economic Surveys.

Key point: The study finds that published academic research tended to overstate the size premium, so the authors adjusted for the publication bias using established statistical techniques. “The researchers found a strong bias of selective publication where journals initially published studies showing a statistically significant size premium in smaller stocks but the bias fell in later years as journals published studies with different findings,” says Dr. Michael A. Crain (Florida Atlantic University), who is both a valuation practitioner and academic. “The authors suggest as more people accepted the idea that the size premium diminished after it was first documented in the early 1980s that journals published research with other findings,” says Crain. The study found a drop of about 50% in the magnitude of the size premium in studies using data after 1981 compared to studies with earlier data.

The meta-analysis finds that the size premium in traded stocks was much larger prior to the publication of the first study on the topic (early 1980s). The researchers say, “[O]ur findings support the proposition that the magnitude of the size premium varies over time (Horowitz et al., 2000a; van Dijk, 2011) and more specifically that it has decreased after [the] 1980s.” Crain comments: “These findings should give BV practitioners pause in using return data from the distant past to estimate forward-looking size premiums.”

As to the practice of using data from traded stocks to pinpoint a precise size premium for a private firm, these data are “not an ideal proxy,” says Crain. He acknowledges that some data show price multiples of smaller private firms lower than multiples of larger private firms, which may be evidence that a size premium exists in private firms. “But illiquidity and inefficient markets for private firms may be confounding factors in the multiples,” he says.

The new paper’s authors are Anton Astakhov, Tomas Havranek, and Jiri Novak of the Institute of Economic Studies, Faculty of Social Sciences (Charles University, Prague).

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