Cont (2001) listed the following statistical properties common to most financial assets (assets returns and exchange rates):

• Absence of autocorrelations
• Heavy tails
• Gain/loss asymmetry
• Aggregational Gaussianity
• Intermittency
• Volatility clustering
• Conditional heavy tails
• Slow decay of autocorrelation in absolute returns
• Leverage effect
• Volume/volatility correlation
• Asymmetry in time scales

Reference

Cont, R. (2001). Empirical properties of asset returns: Stylized facts and statistical issues. Quantitative Finance, 1(1), 223-236. [pdf]