Decomposition of risk for small size and low book-to-market stocks

Abstract

We investigate whether the size and book-to-market ratio fully capture the financial distress risk of firms within the small/low group of stocks. Size and BE/ME ratio struggle to explain the distress risk of small/low firms because they are usually analyzed together with small declining firms in factor analysis models. Using the Fama–French 3 factor model, we identify small (size) and low (BE/ME ratio) stocks and sort them further based on their financial distress risk. Using thirteen different proxies of financial distress risk, we find that the significant intercept of the Fama–French 3 factor model is statistically insignificant for firms with low financial distress risk. We also show that the low-high portfolios earn statistically significant positive returns when sorting on distress risk. Our results are robust to changes in the distress risk proxy and sorting methods (terciles/quintiles/deciles). We further find that cash flow-based proxies of distress risk generate the highest abnormal returns, followed by analyst coverage and net income.

Appendices

Appendix A: variable descriptions

Proxy	Definition
Cash flow from operations	The OANCF variable taken from Compustat
Coverage	Distress risk proxy presented in Hong et al. (2000). It is the unique number of analysts covering the firm as of the end of the fiscal year in the previous year
Change in cash flow from operations	Calculated as current year cash flow from operations less cash flow from operations for the previous year
Change in gross profit	Calculated as current year gross profit less gross profit for the previous year
Change in income before extraordinary items	Change in the IB variable as taken from Compustat. It is calculated as the current year IB less IB for the previous year
Change in net income	Change in the NI variable as taken from Compustat. It is calculated as the current year NI less NI for the previous year
Gross profit	The GP variable as calculated from Compustat (sales less cost of goods sold)
Income before extraordinary items	IB variable as taken from Compustat
Lagged coverage	Lagged coverage is the lagged value of analyst coverage as calculated above
Net income	NI variable as taken from Compustat
O-score	Distress risk proxy as presented in Ohlson (1980). It is calculated as, $-1.32-0.407\text{log}\left(\frac{\text{Total Assets}}{\text{GNP}}\right)+6.03\left(\frac{\text{Total Liabilities}}{\text{Total Assets}}\right)-1.43 \left(\frac{\text{Working Capital}}{\text{Total Assets}}\right)+0.0757 \left(\frac{\text{Current Liabilities}}{\text{Current Assets}}\right)-1.72 X-2.37 \left(\frac{\text{Net Income}}{\text{Total Assets}}\right)-1.83 \left(\frac{\text{Funds from operations}}{\text{Total Liabilities}}\right)+0.285 Y-0.521 (\frac{\Delta \text{Net Income}}{\left|\text{NI}\right|+\left|\text{Lagged Net income}\right|})$ where $X = 1\;{\text{if Total Liabilities}} > {\text{Total}}\;{\text{Assets}},\;{\text{and}}\;{ }0\;{\text{otherwise}}$ $Y = 1\;{\text{if net loss for past two years}},\;{\text{and}}\;0\;{\text{otherwise}}$
Sales	SALE variable obtained from Compustat
Tobin's q	Market value of assets/book value of assets
Decline	Following Dickinson (2011), indicator variable takes a value of 1 if cash flow from operations is negative and cash flow from investing is positive
Growth	Following Dickinson (2011), indicator variable takes a value of 1 if cash flow from operations is positive, cash flow from investing is negative, and cash flow from financing is positive

Appendix B: financial distress risk relation

Proxy	Relation
Cash flow from operations	1=H
Coverage	1=H
Change in cash flow from operations	1=H
Change in gross profit	1=H
Change in income before extraordinary items	1=H
Change in net income	1=H
Gross profit	1=H
Income before extraordinary items	1=H
Lagged coverage	1=H
Net income	1=H
O-score	1=L
Sales	1=H
Tobin’s q	1=L
Decline	1=H
Growth	1=L