An empirical study of the diffusion process of securities and portfolios

The nature of the stochastic process generating the path of security prices through time plays an important role in dynamic theories of financial economics. An important consideration is the possible dependency of return variances on price levels. Using 55 years of data separated into five‐year intervals, this study demonstrates that, in general, security and portfolio variances are dependent on stock price levels and the relationship is a function of portfolio size. The relationship is unstable over time. The results suggest possible detrimental effects of diversification and financial models based on log‐normality are questionable.