3.1 Relative profitability
There is no basis in finance theory to justify the power of an accounting ratio to explain the cross section of average stock returns. There is only the possibility, if the phenomenon is risk-based, that BE/ME
10Mean annual HML returns for the sample period observed in Fama and French (1992) compared to HML returns for the subsequent fifteen years, 1994 to 2008. The t-statistic testing the hypothesis that the mean annual return is different from zero is 2.60 for the 30 year period tested by Fama and French, but only 1.11 for the shorter, more recent 15 year period. The standard deviation of annual HML returns, however, increases to 15.6 for the 15 year period likely reflecting the increased volatility associated with the dotcom boom and bust period.
11This example hints at the problem faced by risk-based explanations of the statistical value premium. Industry participants are likely to find the logic in the example bewildering based on commonly held beliefs about relative risks.
proxies for an underlying economic fundamental and that it has somehow successfully captured this risk in econometric tests across the statistical spectrum of low to high BE/ME company fundamentals.
Fama and French (1993) conjecture that relative profitability might be the economic fundamental that explains the common risk factor driving the relationship between book-to-market and average returns. The authors find that HML regression slopes for portfolios formed on E/P follow the pattern of average monthly returns and are similar to slopes of portfolios formed on size and BE/ME, thus indicating that average returns are a function of loadings on the HML factor.
Fama and French (1995) observe that portfolios formed on high BE/ME signal persistent low earnings. Indeed, high BE/ME value stocks are associated with persistently low returns on assets while low BE/ME growth stocks are associated with persistently high returns on assets. Consistent with these findings, Chen and Zhang (1998) find that stocks with high BE/ME characteristics typically exhibit persistent low returns on equity while stocks with low BE/ME characteristics typically exhibit high ROE.
3.2 The value premium and the risk of bankruptcy
Distress factors in Chen and Zhang (1998) representing dividends, earnings, and debt are clearly more informative descriptors of risk than the relationship between the market and book valuation of a company’s equity. Common distress factors such as earnings and debt provide investors a better intuitive understanding of the conditions under which they may use their stock screens - to include or exclude stocks that could generate premium returns. It would thus be ideal for investors to use a statistical rating index to find these distressed stocks rather than pouring over piles of income and balance sheet statements. One such easily accessible tool is the Z-score, a characteristics-based business failure classification model developed in Altman (1968), designed to indicate the risk of company bankruptcy within the next 2 years.12 A company’s Z-score is a weighted sum of several accounting ratios: working capital to total assets, retained earnings to total assets, EBIT to total assets, market value of equity to book value of liabilities and sales to total assets.13 Since BE/ME is a related construction to the accounting items in the Z-score, it would not be unexpected to see a relationship between the two data series, and thus operationally useful to investors.
Griffin and Lemmon (2002) briefly evaluate the Z-score as a proxy for distress. They find that high BE/ME stocks that exhibit the highest distress (lowest Z-score) generate a superior average return of almost 12% per annum over low BE/ME stocks. Using the O-score, a similar bankruptcy prediction
12Not to be confused with a standard score, or Z-score, in the field of statistics.
13The S&P Research Insight concept for Z-Score is 1.2*(WCAP/AT)+1.4*(RE/AT)+ 3.3*(EBIT/AT)+ .6*(@VALUE(PRCCF*CSHO,CEQ)+ PSTK)/(AT-CEQ-PSTK)+.999*(SALE/AT)
tool, the authors successfully show the value effect to be associated with high distress. The authors suggest, however, that the superior returns of these stocks are not a function of risk as suggested by Fama and French but of mispricing. Griffin and Lemmon observe that the returns between high and low BE/ME stocks in the most distressed quintiles are unusually high when compared to other quintiles and could not, in their opinion, be fully explained by the Fama and French 3-factor model or by other fundamental characteristics such as leverage.
Table 8 shows the median Z-Score for the smallest ME quintile of stocks trading on the NYSE, AMEX, and NASDAQ markets between June 2001 and June 2006. The sample of small stocks is used in this instance because prior research has indicated that the value premium – potentially generated as a function of distress – is statistically larger in the lowest size deciles. It is expected, therefore, that distress could be better differentiated within this size strata.
If the value premium is a function of risks associated with distress, then value stocks would be expected to systematically reflect a lower Z-Score than growth stocks. Results in Table 8 clearly show that BE/ME is indeed inversely related to a company’s Z-Score, indicating a positive relationship between value stock returns and the risk of bankruptcy over the next two years. High BE/ME value stocks exhibit the lowest average Z-Score (Z = 1.85). The low Z-score for the most extreme portfolio of value stocks indicates considerable financial and operating distress – and high probability of bankruptcy over the next two years. Conversely, growth stock portfolios with the lowest median BE/ME characteristic exhibit the highest average Z-Score (Z = 5.82). A high Z-score suggests that stocks are experiencing low operating and financial distress and have a low probability of bankruptcy over the next two years. The correlation between the Z-score and portfolio BE/ME characteristics is negative, very
high, and statistically significant (ρ = -0.89, t = -5.52). Therefore, results show a strong positive
relationship between book-to-market and the risk of bankruptcy during the observation period, consistent with findings for the O-Score by Griffin and Lemmon.
Contrary to arguments by Fama and French, both Dichev (1998) and Agarwal and Taffler (2003) find that distressed stocks earn lower post-formation returns than non-distressed firms. Dichev argues this outcome is contrary to conditions of market efficiency but Agarwal and Taffler disagree saying pricing of bankruptcy risk is rational when the nature of the risk is evaluated under varying economic conditions. Hwang and George (2008) find that the counter-intuitive negative relationship between high company distress and low returns observed in the two earlier studies evaporates when controlled for leverage.
TABLE 8: Median Z-score for portfolios of small cap stocks sorted on BE/ME. June 2001 to June 2006 Z-scores, BE/ME and ME for all NYSE, AMEX and NASDAQ stocks are sourced from Standard and Poor’s Research Insight and observed at June of each year beginning 2001 and ending June 2006. Stocks without computed Z- scores, primarily banks and financials, were eliminated from the sample. Stocks are sorted for each year to form 10 portfolio s on BE/ME. Medians are computed from the aggregated annual data for each decile. Since the sample in this exercise is screened to include only those stocks up to the smallest 20% Fama-French ME breakpoint for December 2006, $754 million in market value, it is therefore only necessary to sort the data for BE/ME. The BE/ME deciles are fixed over time and represent the average of the breakpoints for each 10thpercentile over the six years as found at the website of Kenneth French. Results for Z-score, BE/ME and ME are expressed as medians of each portfolio.
Small cap portfolios sorted on BEME
Z-SCORE* BE/ME ME Stocks
GROWTH 5.82 0.12 82.10 1593 2 4.41 0.26 105.00 964 3 4.40 0.36 126.48 811 4 4.04 0.44 121.36 703 5 3.53 0.53 120.23 764 6 3.32 0.62 100.24 675 7 3.24 0.73 74.01 718 8 3.06 0.89 61.01 864 9 2.63 1.17 42.23 991 VALUE 1.85 2.03 18.03 1243
* Z-Score less than 1.81 indicates a high probability of bankruptcy over the next two years; a Z-Score greater than 3.00 indicates a low probability of bankruptcy over the next two years.
More interesting to the question here, Agarwal and Taffler determine that SMB and HML are not influenced by a bankruptcy factor, thus suggesting SMB and HML are not proxies for bankruptcy or financial distress. Penman, Richardson and Tuna (2007) and Hwang and George (2008) may have formulated a resolution to the conflict. Consistent with what is hinted at by Argawal and Taffler, both Penman et al. and Hwang and George argue thatfinancialdistress andoperatingdistress are separately priced by the market and that they are captured separately by leverage and BE/ME respectively. Therefore, the book-to-market effect (and the value premium) may be a function of operating distress and not financial distress.