Approximately 5% of stocks have negative book equities. Such stocks have a greater chance of financial distress. Due to difficulties in sorting these stocks into portfolios, they are omitted from most existing research, and the most important Fama French's value premium, HML, is no exception. Accepting the value premium is generated because book-to-market ratio acts as a default risk, documented widely in the finance literature, exclusion of these negative book equity stocks from data sample may result in weakening modeling representative, to say the least, as there are no other stocks in greater default risk than these negative book equity stocks. This study takes the Fama and French (1993) as a benchmark. The study first replicates their portfolio construction and obtains the value premium. It then includes the negative book equity stocks by using a novel clustering model, Brown's GSC. The study allocates these negative book equity stocks into predetermined portfolios and reconstructs a new value premium. In doing so, it finds that the new HML factor is statistically, economically, and significantly different from the old HML. The new HML replicating portfolio has a higher annualized return, which means that a practitioner may trade these negative book equity stocks and obtain an enhanced return. The results of this study show that the value premium exhibits a downward trend in the 1990s, but contradicts its explanation as the value premium gradually increases beyond the 1990s.

The Fama and French three factor model (FF3) has become the most important asset pricing model in finance. FF3 incorporates one of the most well-documented stock returns anomalies - the value premium. Fama and French (1992) demonstrate that the book-to-market ratio (BE/ME) has more explanatory power than other traditional measures such as market beta in CAPM for predicting the cross-section of average stock returns. In other words, value stocks earn high average returns than growth stocks (Graham et al., 1953; Rosenberg et al., 1985; and Lakonishok et al., 1994).

There are mainly two competing explanations for the value premium⁵. One perspective, offered by DeBondt and Thaler (1987), and Lakonishok et al. (1994), views the value premium as evidence of systematic mispricing in which investors incorrectly extrapolate stocks' past performance. The argument is that investors are optimistic (pessimistic) about strong (weak) companies, driving their values irrationally high (low) and, the eventual price correction results in previously strong (weak) companies experiencing subsequent lower (higher) returns.

In addition, DeBondt and Thaler conclude that investors overreact to the recent past events. Ball and Watts (1972) and others, however, find that the actual pattern of changes in annual corporate earnings corresponds to a random walk. In addition, Bauman and Miller (1997) observe that the EPS growth rate has a mean-reversion tendency, over time, in which the high growth rates associated with growth stocks subsequently tend to decline whereas the low growth rates associated with value stocks tend to increase. As a result, investors systematically overestimate the future EPS of growth stocks relative to value stocks, therefore, growth stocks appear to experience lower returns subsequently. Proponents of this view regard the value premium as evidence contradicting the efficient market hypothesis.

Applied Finance Journal, Negative Book Equity, Finance Literature, Asset Pricing Model, Center for Research in Security Prices, CRSP, New York Stock Exchange, NYSE, Statistic Techniques, Portfolio Management, Stock Market Seasonality, Financial Economics, Generalized Style Classification.