This repository contains the code for solving constrained risk budgeting with generalized standard deviation-based risk measure:
This formulation encompasses Gaussian value-at-risk and Gaussian expected shortfall and the volatility. The algorithm supports bounds constraints and inequality constraints. It is is efficient for large dimension and suitable for backtesting.
A description can be found in Constrained Risk Budgeting Portfolios: Theory, Algorithms, Applications & Puzzles by Jean-Charles Richard and Thierry Roncalli.
Can be done using
pip install git+https://github.com/jcrichard/pyrb
from pyrb import EqualRiskContribution ERC = EqualRiskContribution(cov) ERC.solve() ERC.get_risk_contributions() ERC.get_volatility()
Griveau-Billion, T., Richard, J-C., and Roncalli, T. (2013), A Fast Algorithm for Computing High-dimensional Risk Parity Portfolios, SSRN.
Maillard, S., Roncalli, T. and Teiletche, J. (2010), The Properties of Equally Weighted Risk Contribution Portfolios, Journal of Portfolio Management, 36(4), pp. 60-70.
Richard, J-C., and Roncalli, T. (2015), Smart Beta: Managing Diversification of Minimum Variance Portfolios, in Jurczenko, E. (Ed.), Risk-based and Factor Investing, ISTE Press -- Elsevier.
Richard, J-C., and Roncalli, T. (2019), Constrained Risk Budgeting Portfolios: Theory, Algorithms, Applications & Puzzles, SSRN.
Roncalli, T. (2015), Introducing Expected Returns into Risk Parity Portfolios: A New Framework for Asset Allocation, Bankers, Markets & Investors, 138, pp. 18-28.