Risk Contribution by Measure
Risk contribution by measure splits three portfolio risk figures across the assets: CVaR (95%), the uncompounded CDaR (95%) and the mean absolute deviation. Each set of shares sums exactly to the figure it splits.
Mathematical Formulation
Euler allocation
All three measures scale with the weights, so the shares w_i times the partial derivative add up to the figure.
CVaR
The tail days and their weights q_t are the ones CVaR (95%) averages, so asset i's share is its average loss on the portfolio's worst days, times its weight.
MAD
Annualized by the square root of P, like the mad field.
Reading it
The derivatives are exact, not finite differences, so each set sums to its figure to rounding. riskfolio-lib and skfolio compute the same split by central differences, and FolioLab's shares agree with riskfolio-lib 7.0.1's to their step size.
The CDaR split uses uncompounded drawdowns because a compounded drawdown does not scale with the weights, so it has no exact split.
A negative share means the asset lowered the measure: on the portfolio's worst days it gained, on average.
The shares are in results.<method>.risk_contribution_by_measure, in the PDF report beside the variance attribution, in the Excel Risk Attribution sheet, and in the MCP get_job_result section of the same name.
Like every metric on FolioLab, this value describes the run window. It is a measurement of past returns, not a forecast of future ones.
References
- Tasche, D. (1999). "Risk Contributions and Performance Measurement." Working Paper, Technische Universität München.
- Rockafellar, R. T., & Uryasev, S. (2002). "Conditional Value-at-Risk for General Loss Distributions." Journal of Banking & Finance, 26(7), 1443-1471.
Not investment advice. Past performance is not indicative of future results.