A Note on "Quarterly Returns to Investment in Ordinary Shares, 1919-1970": Two Tests of Market Efficiency

Abstract

This note analyses the data of Foldes and Watson (1982a). It gives some statistics to test for weak-form efficiency (Fama, 1976) for quarterly returns, xt, for a valueand equally weighted equity portfolio, and for 2' per cent Consols gross and net of tax. All series show a very high degree of randomness, which implies a high quality in index construction. The second test has returns for shares and Consols regressed on inflation for the whole period and for five sub-periods to see if they account for inflation. Foldes and Watson (1982b), in an excellent and detailed paper, have examined UK and US equity portfolio returns over 1926-1970 for normality, stationarity, seasonal variation, autocorrelation and a variance curve. The autocorrelation section uses spectral analysis, integrated spectra and a firstorder autoregression for the United States to see if the series are random. It used only one UK equity portfolio, value-weighted, money terms, gross of tax, but the spectra of this and value weights, real terms, and equal weights, money terms, were similar. Spectral analysis is the least reliable method of testing for dependence in financial returns given the very small samples used here and the need for covariance stationarity for return data. This is discussed in Praetz (1979) with the very difficult problem of testing for a flat spectrum. The time domain tests using serial correlations and a runs test are much more powerful and easier to understand. Table 1 comprises 12 quarterly serial correlation coefficients, r(l)-r(12); an omnibus test of them-chi-squared (24) =124 r(j)2; Durbin-Watson (DW) statistic-DW = (xt xt_1)2/ X2; and z (runs), a standardized statistic of the number of runs minus its expectation over the standard deviation of runs. It has value-weighted and equally weighted equity portfolios and 24 per cent Consols gross and net of tax for whole period. A 1 per cent significance level is used because of the large sample; however, not one statistic is significant, supporting a very high degree of randomness. A quarterly seasonal pattern (Praetz, 1975) would have large positive values at r(4), r(8), etc., which is clearly not the case here. Weak-form efficiency means that a market cannot be exploited systematically for economic profit, which is supported by the very low values of the statistics in Table 1. Cooper (1982) has studied the UK and other countries for randomness, but at daily, weekly and monthly intervals, so the quarterly data used here are for a much longer period of time. The only other index with dividends added over a comparable period is the de Zoete Equity Index, which has much more dependence in its returns over time (Benjamin, 1980). The stock returns and inflation are related to market efficiency. In an efficient market, all relevant public information such as inflation should be reflected in market prices. This is the semi-strong form of market efficiency.