Sharpe (1964) and Lintner (1965) propose the capital assets pricing model (CAPM) to find whether the stock has the excess return, and suggest that there is a linear relation between the expected returns on stocks and market βs and that the market β is the only factor that can explain the expected return on stocks. Since 1980s, some studies find that the rule of firm characteristics, like that firm size (Banz, 1981), book-to-market ratios (Rosenberg, Reid and Lanstein, 1985), and earnings-price ratios (Basu, 1983), leverage (Bhandari, 1988) etc., can explain the cross-section return, those firm characteristics are not concluded in CAPM.
However, in the empirical asset pricing literature, it has long been argued that the cross-section of stock returns is related to risk factors associated with systematic financial distress. The intertemporal capital asset pricing model (ICAPM) proposed by Merton (1973) and the arbitrage pricing theory (APT) proposed by Ross (1976), consider that there are many factors to affect the asset return, not only market risk. Chan, Chen, and Hsieh (1985) and Chen, Roll, and Ross (1986) find that a default factor, the spread between high- and low-grade bonds, has a significant contribution in explaining the cross-section of stock returns. Asset pricing theory claims stocks that underperform when the economy is in a high-distress state should reward the investors who hold them with higher expected returns as a compensation for bearing this non-diversifiable risk. Hence, these high returns would be partially unexplainable by a model that does not account for a distress factor, and therefore would be considered apparent mispricngs.
The existence of “pricing anomalies” such as the size and book-to-market effects has in fact been widely documented. The essence of the pricing anomalies lies in the fact that they cannot be justified by the return’s covariance with the market factor. The difference in market βs cannot explain the return differential between small and large firms, and between stocks with high and with low book-to-market values. Since market risk alone dose not price these stock, some other factors can explain the unexplained part. In their seminal papers, Fama and
French (1993) identify the two stock market factors related to size and book-to-market, i.e., SMB and HML, that in conjunction with the market factor form an impressive pricing model.
In a later paper, Fama and French (1995) find that firms with high book-to-market tend to be relatively distressed, coming from a persistent period of negative earnings, and conversely, low book-to-market firms is associated with sustained strong profitability. They suggest that size and in particular book-to-market capture a firm’s level of financial distress.
A number of studies have tried to link default risk and stock returns with mixed and contradictory results. Altman (1993) finds that for most distressed firms subsequent average returns are lower. Dichev (1998) finds that bankruptcy risk is not rewarded by higher returns and concludes that a distress factor cannot be at the origin of the size and book-to-market effect. In particular, he finds that portfolios formed on the basis of a distress measure, whether Altman’s Z-score or Ohlson’s O-score, have returns inversely related to bankruptcy risk, a high probability of default is associated with low average returns. After examining the cross-sectional relation between stock returns and bankruptcy measures, as well as size and book-to-market, he concludes that the fact that firms with low bankruptcy risk outperform firms with high bankruptcy risk can only be explained by a mispricing argument. Griffin and Lemmon (2002) measure bankruptcy risk by using the Ohlson’s O-score, and find that the low return of high default-risk firms is driven by low book-to-market stocks with extremely low returns. They attribute these very low returns to mispricing due to a high degree of information asymmetry proxied by low analyst coverage.
By contrary to above studies, Lang and Stulz (1992), and Denis and Denis (1995) find that bankruptcy risk is related to aggregate factors, which implies that bankruptcy risk may be systematic. Fama and French (1996) suggest that small value stocks tend to be firms in distress (with high financial leverage and earnings uncertainty), with higher returns due to a distress premium. Vassalou and Xing (2004) use the distance to default implied by the Merton (1974) model to conclude that the size and book-to-market effects exist only in the quintiles
defined by high default risk stocks. They also provide evidence that distress risk is priced in the cross-section and that the Fama and French (FF) factors capture some of the default-related information.
Our study investigates the relationship between SMB, HML, and financial distress risk in Taiwan stock market (exclude banking, security and insurance industries). We focus on testing the hypothesis that the Fama and French (1993) factors are related to a default risk measure.
The measurement of the expected default probability is critical in understanding how default risk related to stock return. We compare the performance of Logit model (Ohlson (1980)), Probit model (Zmijewski (1984)), and Discrete-Time Hazard model (Shumway (2001)) to predict default risk. Forecasting precision is imperative because we use the predicted probability of default to examine the relation between distress risk and stock returns. A more informative measure will give us a more complete understanding of what the FF factors represent. In our study, we establish a connection between the probability of default and factor loading. We anticipate that the return and default risk are related. A high probability of default should cause a stock to have high loading on the SMB and HML factors, thus delivering high returns which compensate the investor for holding default risk.
This study proceeds as follows. Relative researches are reviewed in section 2; the research methodologies are presented in section 3; the data employed are presented in section 4; the empirical results are presented and analyzed in section 5; conclusions are presented in section 6.