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There have been only three studies of the distribution of returns for index futures.
The way in which returns are defined can have important consequences for the distribution of returns.
He found the distribution of returns was non-normal, with leptokurtosis and positive skewness.
The model assumes that the probability beliefs of active and potential shareholders match the true distribution of returns.
Fair Chain aims to establish a fairer distribution of returns in a production chain.
The NIG-distribution is now widely used to describe the distribution of returns from financial assets.
This metric measures abnormalities in the distribution of returns that indicate the presence of bias in subjective pricing.
Hence, tests of this relationship have had to use historical data and have had to assume that the distribution of returns has remained stable over time.
The statistical relationship on which the model is based may be spurious, or may break down due to changes in the distribution of returns on the underlying assets.
Investors have an accurate conception of possible returns, i.e., the probability beliefs of investors match the true distribution of returns.
However, it should be stressed that this implementation requires the assumption that the distribution of returns in the past is stable and an accurate proxy for future returns.
Chan, Chan and Karolyi (1991) found that the distribution of returns over five-minute intervals for S&P500 futures from 1984 to 1989 was leptokurtic with fat tails.
Practitioners have advanced and regulators have accepted a financial risk management technique called value at risk (VAR), which examines the tail end of a distribution of returns for changes in exchange rates to highlight the outcomes with the worst returns.
Even if some money managers are consistently observed to beat the market, no refutation even of strong-form efficiency follows: with hundreds of thousands of fund managers worldwide, even a normal distribution of returns (as efficiency predicts) should be expected to produce a few dozen "star" performers.