Each factor is constructed as the equal-weighted average of value-weighted large and small cap strategies, where large and small are defined by NYSE median market capitalization.

Within the large and small cap universes each strategy buys (sells) stocks in the top (bottom) 30% of all stocks (large and small), using NYSE breaks, on the sorting characteristic.

These characteristics are log-book-to-market (HML*), cumulative returns over the first 11 months of the preceding year (UMD*), and gross profits-to-assets (PMU*), and are demeaned by the average characteristic for firms in the same industry (Fama-French 49). Residual market exposure is hedged with offsetting positions in value-weighted industry portfolios (alternatively, each "stocks" position in the strategy can be viewed as a long stock position and a short position in the stock's industry).

HML* excludes firms with negative book equity.

PMU* includes financials, because the gross profits-to-assets is demeaned by industry.

Accounting data are assumed available at the end of June for fiscal years ending on or before the end of December of the preceding calendar year.