The Behavior of Stock Returns: Is It Stationary or Evolutionary?

Empirical studies of the behavior of stock returns are important for several reasons. First, the nature of stock return behavior is fundamental to the formulation of the concept of “risk” (or “uncertainty”) in various financial theories and models. Second, the measurement of risk depends heavily on properties (such as the stationarity, long-tailedness, finiteness of the second and higher moments, etc.) of empirical stock return distributions. Third, various tests for the empirical validity of financial models [28] and the applications of these models (e.g., to the evaluation of investment performances [21], [22]) rely to a considerable extent on the steadiness over time of stock return distributions and the constancy of systematic risk. Fourth, several important pricing models for stock options, warrants, convertible debentures, and other similar financial instruments usually require explicit estimates of stock return variances [5]; the usefulness of such models depends largely on the adequacy (e.g., the finiteness, accuracy, etc.) and the stationarity of the variance measurements.