The Skewness Effect: A Case for Nonstationary Return Distributions

Abstract

The objective of this thesis is to provide a general model for the behavior of stock price change distributions. Such distributions are assumed to be generated by individual perceptions of past returns and expectations about future returns in an efficient market. This paper seeks to explain how changes in the shape of the distribution, as measured by the statistics for the first three moments, provides capital markets with a dynamic mechanism by which equilibrium prices are determined. Further evidence will provide that the shape of the distribution is important information in determining investor strategy. As a result, expost returns are significantly related to the extante statistics of the return distribution's moments. Due to uncertainty of market participants, information may be fully reflected in the price, even though the market may not be in equilibrium. As a result, disequilibrium is shown to be a symptom of investor uncertainty about changing expectations, rather than an inefficiency in the market. This approach significantly differs from previous research for the following reasons: 1) Most research focuses on the first two moments, as measured by the mean and variance, as sources of information to individuals in the market. The following research incorporates skewness, the statistic for the third moment, as a measure of uncertainty stemming from changing expectations in the market. 2) Past research assumes that the market is efficient because it is in a static state of equilibrium. The past model provides no mechanism for investor expectations to adjust to new information, but asserts that prices and return distributions will adjust almost instantaneously to equilibrium. More importantly, the possibility of disequilibrium is ignored. In fact, the only satisfactory definition of a market for a stock in disequilibrium is the negation of the definition for equilibrium. 3) Research has been done on investor preference for skewness (Arditti, l967, 1971, 1975) and the effects of skewness (Merton and Scholes, l972). However, the past research has not investigated the causes of skewness or has merely incorporated it into current models as a static condition of equilibrium (or an exception to equilibrium). 4) The effect of nonstationary parameters upon equilibrium prices has been documented (Barry, l978). That research, however, only sought to explain discrepancies in estimates of the Capital Asset Pricing Model as static equilibrium points for a security's price. This paper associates non-stationarity with skewness to explain the adjustment of returns to equilibrium. 5) The equilibrium model assumes that all individuals are rational. Then, the speculator's economic behavior is deemed irrational and irrelevant. This attitude is kept even when the authors acknowledge that the speculator may be necessary to keep prices in equilibrium, and keep the market efficient. The concept of nonstationarity in return distributions incorporates the behavior of both investors and speculators. More importantly, the presence of skewness in a distribution explains how both strategies are rational. 6) Finally, in all previous research the difference between risk and uncertainty is dismissed. The justification being that most price generating processes studied are from efficient markets. As a result, price sequences tend to be repetitive and independent. The fact that unexpected results can destroy the market player's ability to estimate expected returns from repetitive processes is ignored.