Efficient management of bankruptcy risk requires treating distant-to-default (DD) stochastically as long as historical stock prices move randomly and, thus, do not guarantee that history may repeat itself. Using long-term data that date back to 1952–2023, including the nonfinancial companies listed in the Dow Jones Industrial Average and National Association of Securities Dealers Automated Quotations indexes, this study estimates the historical and stochastic DDs via the geometric Brownian motion (GBM). The results show that (a) the association between the debt-to-equity ratio and the stochastic DD can be used as an indicator of excessive debt financing; (b) debt tax savings have a positive effect on stochastic DD; (c) bankruptcy costs have negative effects on stochastic DD; (d) in terms of the size of the company being proxied by sales revenue and the equity market value of the company, the DD is a reliable measure of bankruptcy costs; (e) in terms of macroeconomic influences, increases in the percentage change in manufacturing output are associated with lower observed and stochastic DD; and (f) in terms of the influences of industry, the stochastic DD is affected by the industry average retail inventory to sales. This paper contributes to related studies in terms of focusing on the indicators that a company’s management can focus on to address the stochastic patterns inherent in the estimation of the DD.

Welfare quality is usually a stochastic outcome, as attempts at improving social welfare cannot be predicted in advance. The advances in stock market participation conclude that equity market performance is able to reflect investors’ mass reactions and therefore can fairly reflect the empiricism of welfare quality. In this paper, the pillars of the Happy Planet Index (hereinafter HPI) are used as proxies for countries’ welfare quality. The data cover 57 countries where equity markets exist over the annual period of 2006–2020. The results indicate that (a) the three pillars of HPIs have historical positive impacts on market capitalization and stock turnover; (b) stochastically, life satisfaction has an expected positive impact on market capitalization and stock turnover; (c) firms located in high (low) HPIs, life satisfaction, and life expectancy have significant (insignificant) stochastic impacts on market capitalization; and (d) the historical ecological footprints have positive impacts on market capitalization and stock turnover, whereas stochastic impacts are statistically insignificant.