Transparency is a feature. This page explains what these shape and tail descriptors measure and why we compute them — in plain terms. The precise formulas and numeric conventions are documented in our internal methodology; the summary here is deliberate, not an omission.
These are five descriptors of the shape of a return series — the picture beyond its average return and its typical variability. The first two read the symmetry and the tail-heaviness of the distribution as a whole; the last three focus on the balance between the up-side and the down-side. All are scale-free in the sense that they describe shape rather than magnitude, so the size of the returns does not distort them. Each period return is treated as a simple decimal fraction of the prior value.
Skewness measures the asymmetry of the return distribution — whether the series leans left or right. A positive value means a longer or fatter right tail (occasional large gains); a negative value means a longer or fatter left tail (occasional large losses); zero means the up- and down-sides are balanced. We report the standard Fisher-Pearson measure without a small-sample bias correction. It needs at least two observations, and a perfectly flat (constant) series has no shape to describe, so no value can be reported.
Kurtosis measures tail-heaviness and peakedness — how much of the action lives in rare, extreme moves rather than in the middle of the distribution. By default we report it in excess form, meaning it is centered so that a normal (bell-curve) distribution lands at zero; a positive number then signals fatter-than-normal tails, and a negative number thinner tails. A raw (non-excess) form is also available. Like skewness, it needs at least two observations and cannot be defined for a perfectly flat series.
The Omega ratio compares the total amount of gain above a chosen threshold to the total amount of loss below it. Its appeal is that it uses the entire distribution — every gain and every loss, of every size — rather than just the mean and variance, so it captures shape that simpler ratios miss. The threshold defaults to zero, so by default only positive returns count as gains. A value above one means the gain side outweighs the loss side at that threshold. It is undefined when there are no returns below the threshold (nothing on the loss side to divide by).
The tail ratio compares the size of the right (upside) tail to the size of the left (downside) tail, using a high percentile of the returns against a low one. A value above one means the upside extreme is larger than the downside extreme; below one means the downside dominates. The percentiles are read with the same standard linear-interpolation convention used by the other historical tail metrics in the terminal, and the downside figure is taken in absolute terms so the comparison is like-for-like. It is undefined in the rare case where the downside percentile is exactly zero.
The gain-to-pain ratio expresses the net total return earned per unit of cumulative loss — the "pain" being the summed magnitude of only the losing periods. A value of one means the net return exactly equals the total downside suffered along the way; a value of zero means gains and losses netted out to nothing. It is signed, so it can go negative when the series ends net-down over the window. It is undefined when there were no losing periods at all, since there is then no pain to divide by.
