Small Effect Firm

Applied Financial Economics, 1994, 4, 405-411

Stock market efficiency, the small firm effect and cointegration
PATRICIA L. CHELLEY-STEELEY^ and ERIC J. PENTECOST School of Management, University of Manchester, Institute of Science and Technology, Manchester, M60 IQD and Department of Economics, Loughborough University, Loughborough, Leicestershire, LEU 3TU, UK

The cointegration methodologycommonly used for testing the eflRciency of the foreign exchange market is applied to a sample of UK share prices. Specifically we test for static market efficiency in the share prices of small and large firms, using monthly data from January 1975 to December 1989. The empirical findings provide evidetice of market efficiency for portfolios of large firms but of inefficiency for small firmportfolios. These results are indicative of a small firm effect iti the UK stock market.

I.

INTRODUCTION

According to Fama (1970) a market is efficient if prices reflect all available information. In the case of the stock market the intrinsic value of a share is equivalent to the future discounted value of cash flows that will accrue to investors. If the stock market is efficient share pricesmust reflect all available information which is relevant for the evaluation of a company's future performance and therefore share prices must be the rational expectation of future discounted profits. Any new information which changes expectations of a company's future profitability must immediately be reflected in the share price since any delay in the diffusion of information to prices wouldsuggest irrationality, as some subset of available information could be used to improve the forecast of future profitability. In efficient markets rational share price variations must be a response only to changing beliefs about company profitability; that is, a reaction to information innovations. Since information arrives randomly, share prices must also fluctuate in a stochastic fashion. Thestochastic nature of share price variations has been associated with the random walk model which implies that stock markets have no memory, or that there is no persistence in stock returns. It is this hypothesis that this paper seeks to test for a sample of stock prices of different sized UK firms by the use of multivariate cointegration time series methods. In this context if stock prices

are foundto be cointegrated then they exhibit persistence and hence market inefficiency. Early empirical tests of the efficient markets hypothesis were based on serial correlation tests. Kendall (1953), for example, tested for serial independence in weekly price movements of price indexes from different sectors over a tenyear period and concluded that any correlation present was so weak as to be unhelpfulfor prediction purposes. In the USA Fama (1965) investigated the serial correlations between successive changes in the logarithms of prices for each of the shares making up the Dow Jones Industrial Average index over the period 1957-62 and found that the correlations were close to zero and hence consistent with the random walk hypothesis of share prices.^ More recent tests of market efficiency haveused variance ratio tests to identify mean reversion and mean revision tests. Variance ratio tests use the fact that the variance of yearly sampled returns must be twelve times as large as the variance of monthly sampled returns if share prices are generated by a random walk. Lo and MacKinlay (1988) and Porterba and Summers (1988) have found evidence of positive serial correlation inshort-horizon returns with the use of variance ratio statistics, although share returns appear to follow a mean-reverting pattern and suggest a predominance of negative autocorrelations over long investment horizons of up to five years. Mean reversion exists when there is an initial overreaction or overshooting of stock

This paper was started while the author was a lecturer in the economics department of...