The empirical frequency distributions of continuously-compounded monthly share returns on the Melbourne Stock Exchange over 1958-73 are studied for individual securities and portfolios. The typical distributional shape is observed and the stable Paretian and Student t distributions are fitted to the returns. The latter clearly is superior and even normality is a reasonable approximation for medium sized portfolios. The most likely explanation seems to be non-stationarity in the generating process for returns, rather than infinite-variance distributions or data errors. The implications for future empirical work and the theory of asset pricing are discussed.
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