Bias in Small Sample Tests of Stock Price Rationality

This paper demonstrates a severe small sample bias in the use of sample variances to test stock price variance bounds, under the maintained assumption that prices and dividends follow stationary and ergodic stochastic processes. This bias is due to the smoothness of the perfect foresight price, which is used to construct the variance bound. However, the small sample bias demonstrated here seems insufficient to explain the empirical apparent gross violations of the stock price variance inequality, in contrast to the result for variance bounds tested with bonds.