Mean Absolute Deviation
Mean absolute deviation (MAD) is the average distance of a daily portfolio return from the mean daily return. It measures dispersion like volatility does, but it weights each deviation by its size rather than by its square.
Mathematical Formulation
Definition
x_t is the portfolio return on day t of the run window and T is the number of days.
As reported
P is the run's periods per year, the same P that annualizes volatility.
Reading it
For normally distributed returns, MAD equals the standard deviation times the square root of 2 over pi, about 0.80. A ratio of MAD to volatility well below 0.80 indicates heavier tails than the normal.
MinMAD minimizes this quantity, and the risk contribution by measure splits it across the assets.
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.mad: 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 mean_absolute_deviation and riskfolio-lib 7.0.1's MAD use the same formula; FolioLab's value agrees with both to rounding.
References
- Konno, H., & Yamazaki, H. (1991). "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market." Management Science, 37(5), 519-531.
Not investment advice. Past performance is not indicative of future results.