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Approximate factor structures defined by  Chamberlain and Rotschild (1983 ) allow to test whether a given quantitative firm characteristic (the nominal stock price in this paper) is a determinant of the idiosyncratic volatility of stock returns. Our study of 8,000 U.S stocks over the period 1980-2014 shows that small price stocks exhibit a higher idiosyncratic volatility than large price stocks. This relationship is persistent over time and robust to variations in the number of common factors of the approximate factor structure. Moreover, this small price effect does not hide a small-firm effect because it is still valid when we analyze the tercile of large firms. Our result confirms that small price stocks have lottery-type characteristics and, therefore, it is not in line with the efficient market hypothesis.

Idiosyncratic volatility and nominal stock prices: evidence from approximate factor structures