Abstract
The paper reviews the currently held and quite persistent assumptions about the statistical distributions behind financial market returns used to make inferences for the purposes of risk management. We use data from 30 years of daily observations from the 15 largest and oldest stock price indices around the world and test the return data against the most popularly assumed distributions, breaking the data arrays into 100, 250, 750, and 250-day estimation windows at 0.95 and 0.99 confidence levels. We find returns in different estimation windows to be inconsistent with single distributions. When returns in short windows fit Gaussian distributions better, returns in longer estimation windows do not fit any suggested distributions at all. The normal distribution seems to be a better choice for 100-day windows, with longer window rejection rates for all suggested distributions being too high for reliable inference.
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