Folio Lab/Documentation

Risk Budgeting

A generalisation of risk parity that allocates a chosen risk measure across assets according to user-specified budgets. Equal budgets recover risk parity; unequal budgets allow tactical tilts on where you take risk.

Overview

Risk Budgeting answers the question: given a portfolio risk measure, how do I allocate its decomposition across assets in a specified proportion? Unlike Equal Risk Contribution (a special case where every asset contributes the same), risk budgeting permits an explicit budget vector — for example, allocating 60% of risk to equity and 40% to credit-like exposures.

Folio Lab's implementation uses skfolio's RiskBudgeting estimator with the CVaR risk measure by default. Other risk measures (variance, semi-variance, EVaR, EDaR, CDaR, drawdown) are also available through the same machinery.

Mathematical Formulation

Let be a positively-homogeneous risk measure and the risk contribution of asset :

Given a budget vector with , the risk-budgeting portfolio solves:

For variance, the contribution is ; for CVaR it is the conditional expectation of the loss attributable to asset . Setting recovers equal risk contribution (risk parity).

Advantages & Limitations

Advantages

  • Explicit risk control: You choose where the risk goes, not where the dollars go.
  • Flexible risk measure: Variance, CVaR, EVaR, drawdown — all compatible.
  • Reduces concentration: Naturally avoids one asset dominating risk.
  • No expected returns required: Depends only on the risk model.

Limitations

  • Implicit return view: Equal-risk implies equal Sharpe across assets.
  • Solver-dependent: CVaR and EVaR require conic solvers.
  • Risk-measure sensitivity: Different measures can give materially different weights.
  • Budget design: Choosing budgets is a soft form of view-setting.

References

  • Roncalli, T. (2013). Introduction to Risk Parity and Budgeting. CRC Press.
  • Bruder, B., & Roncalli, T. (2012). "Managing Risk Exposures using the Risk Budgeting Approach."
  • skfolio documentation — skfolio.optimization.RiskBudgeting.