This study reviews the literature concerned with the apparent historical negative relationship between stock returns and inflation. Seven possible explanations for the negative relationship are compared and tested. These include the rational expectations based explanations of Fama and of Geske and Roll, the risk-premium explanation, a tax-related explanation and two portfolio adjustment explanations, one derived from monetarist theory and the other from Tobin. The irrational investor hypothesis of Modigliani and Cohn is also examined. Testing methodology includes Box-Jenkins ARIMA techniques with transfer functions.