L-Moments
L-moments describe the shape of a distribution with linear combinations of the sorted sample instead of powers of it. The third measures asymmetry and the fourth measures tail weight, like skewness and kurtosis, but one extreme day moves them much less.
Mathematical Formulation
As an ordered weighted average
x_(t) is the t-th smallest daily return. These are Hosking's unbiased sample L-moments.
Ratios
FolioLab reports the numerators. The second L-moment is half the Gini mean difference, so the ratios follow from the gini_mean_difference field.
Reading it
A negative third L-moment means a longer left tail: large losses are more common than large gains of the same size.
Both are daily, in return units, and small, so they are shown in scientific notation.
Like every metric on FolioLab, this value describes the run window. It is a measurement of past returns, not a forecast of future ones.
Where FolioLab reports it
results.<method>.performance.l_moment_3: daily, over the run window.results.<method>.performance.l_moment_4: daily, over the run window.
Each value appears on the result page under Further Risk Measures, in the PDF and Excel reports, in the compare view and through the MCP explain_metric tool. A run stored before this measure existed does not carry it.
Only riskfolio-lib has this measure. FolioLab lifts its owa_l_moment weights under the BSD-3 licence and matches riskfolio-lib 7.0.1's L_Moment to rounding.
References
- Hosking, J. R. M. (1990). "L-moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics." Journal of the Royal Statistical Society, Series B, 52(1), 105-124.
Not investment advice. Past performance is not indicative of future results.