Semi-Deviation
Semi-deviation is the standard deviation of the daily portfolio returns that fall below the mean return. Days above the mean do not count, so it measures only downside dispersion.
Mathematical Formulation
Definition
The denominator is T - 1, the same Bessel correction as volatility.
As reported
P is the run's periods per year.
Reading it
The Sortino ratio's downside deviation is a different quantity: it measures shortfall below the daily cash return, not below the mean, and divides by T.
For a symmetric distribution, semi-deviation is the volatility divided by the square root of 2.
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_deviation: annualized by the square root of the periods per year.
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.
skfolio's semi_deviation (unbiased) and riskfolio-lib 7.0.1's SemiDeviation both divide by T - 1; FolioLab's value agrees with both to rounding.
References
- Markowitz, H. M. (1959). Portfolio Selection: Efficient Diversification of Investments. John Wiley & Sons, Chapter 9.
- Estrada, J. (2006). "Downside Risk in Practice." Journal of Applied Corporate Finance, 18(1), 117-125.
Not investment advice. Past performance is not indicative of future results.