Abnormal statistical properties of stock indexes during a financial crash

• Stock indexes have dual fractal structure which is consistent with previous studies. • The return distribution of emerging markets shows abnormal dual power-law exponents. • External shock of a crisis affects different markets at distinct stages. a b s t r a c t We investigate minute indexes of stock markets in 10 countries during financial crashes by dividing them into several stages according to their stock price tendencies: plunging stage (stage 1), fluctuating or rebounding stage (stage 2), and soaring stage (stage 3). The tail distributions of the returns satisfy a power law for developed markets but show a dual power-law structure for emerging markets. Prominent dual fractal structures are found during the plunging stage in developed markets, and after the plunging stage in emerging markets. The fractal analysis on the sign series of the returns yields similar dual fractal properties. The magnitude series of the returns provides surprising results during a crash. We find that developed markets have strong and weak long-range persistence in plunging and soaring stage respectively, while emerging markets behave oppositely. These results indicate that different types of markets are influenced strongly by the external shock of a crisis at different stages.