Constrained and Unconstrained Risk Budgeting Allocation in Python

This repository contains the code for solving constrained risk budgeting with generalized standard deviation-based risk measure:

<a href="https://www.codecogs.com/eqnedit.php?latex=R(x)&space;=&space;-&space;\pi^T&space;x&space;&plus;&space;c&space;\sqrt{&space;x^T&space;\Sigma&space;x}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?R(x)&space;=&space;-&space;\pi^T&space;x&space;&plus;&space;c&space;\sqrt{&space;x^T&space;\Sigma&space;x}" title="R(x) = - \pi^T x + c \sqrt{ x^T \Sigma x}" /></a>

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.

You can solve

• Equally risk contribution
• Risk budgeting
• Risk parity with expected return
• Constrained Risk parity

Installation

Can be done using pip:

pip install git+https://github.com/jcrichard/pyrb

Usage

from pyrb import EqualRiskContribution

ERC = EqualRiskContribution(cov)
ERC.solve()
ERC.get_risk_contributions()
ERC.get_volatility()

References

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.