Some Properties of Absolute Return: An Alternative Measure of Risk

The expected absolute return belongs to a class of risk measure derived by Luce (1980) from axioms. The paper considers the time series properties of and also the marginal distribution properties, for various properties of ?. Using a long daily stock index series it is found that the autocorrelations decline slowly for all positive ? but this "long-memory" property is strongest for ? = 1, the absolute return. The moments of absolute returns, after removal of a few outliers, suggest that an exponential distribution is appropriate.