Abstract
Large negative stock and equity portfolio rates of return occur more frequently than they should under the Gaussian normal distribution. They tend to be kurtotic, roughly as if they were drawn from Student T-distributions with 2 to 5 degrees of freedom. A very easy adjustment to help assess the probability of losses is to work with a transformed Z score, Z ′ = − 1.25 − log ( − Z ) . For example, one should expect a stock return that is 17 standard deviations below the mean under the empirical distribution as often as one would expect to see a draw that is Z ′ = | – 1.25 − log ( 17 ) ≈ − 4 | standard deviations below the mean under the idealized normal distribution.
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