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This paper reports the results of various tests of the efficient markets hypothesis (EMH) using daily observations on the Statex Actuaries' Price Index for Australia and the NZSE–40 Index for New Zealand for the period 1975–92. The weak form of the EMH is examined by testing the log of the price for each country for stationarity and by examining the autocorrelation structure of returns. The autocorrelations provide evidence of return predictability, although the stationarity results are consistent with the weak form of the EMH. Results are similar across countries. Semi-strong efficiency is addressed by testing for cointegration between Australian and New Zealand share prices and for Granger causality between the two countries' rates of return. Robustness of the results is assessed in various ways. First, similar tests are carried out for both weekly and monthly data. Second, similar tests are conducted for various subsamples of the original sample and by trimming outlying observations. Third, the expected euilibrium return is modelled using interest rates as an alternative to the common assumption of constancy. Finally, several alternative indexes are used: the Statex Actuaries' Accumulation Index and the All Ordinaries Price and Accumulation Indexes in place of the Statex Actuaries' Price Index and the NZ Gross Index in place of the NZSE–40
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