Semi-Kurtosis
Semi-kurtosis is the square root of the fourth moment of the daily returns below their mean. The fourth power makes it far more sensitive to the largest below-mean days than semi-deviation is.
Mathematical Formulation
Definition
Daily, and in squared return units, so it is small: near 1e-4 for a typical equity book.
Reading it
It is not standardized. The kurtosis field divides by the variance squared and has no units; semi-kurtosis does not, so it changes with the scale of the returns.
skfolio reports the fourth lower partial moment itself, which is the square of this value.
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.semi_kurtosis: 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.
riskfolio-lib 7.0.1's SemiKurtosis is this definition, and skfolio's fourth_lower_partial_moment is its square; FolioLab agrees with both to rounding.
References
- Cajas, D. (2021). Riskfolio-Lib documentation - risk measures, semi-kurtosis.
- Fishburn, P. C. (1977). "Mean-Risk Analysis with Risk Associated with Below-Target Returns." American Economic Review, 67(2), 116-126.
Not investment advice. Past performance is not indicative of future results.