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Topological Risk Parity
Dnyanesh Kulkarni / El Mehdi Ainasse / Revant Nayar
portfolio management / risk managementResource overview

Topological Risk Parity

Paper2026

by Dnyanesh Kulkarni, El Mehdi Ainasse, Revant Nayar

Tags
portfolio managementrisk management

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Understand this paper

Suggested foundations for portfolio construction and risk measurement and stress. Specialist prerequisites vary by paper.

Before you read

  1. Eigenvalues and Covariance Matrices

    Understand the covariance structure of portfolio risk.

  2. Constrained and Convex Optimisation

    Read objectives, constraints and optimality conditions.

  3. Random Variables and Distributions

    Represent losses as a distribution rather than one forecast.

  4. Expected Shortfall and Other Tail Risk Measures

    Distinguish a loss quantile from the average loss in the tail.

Go further

  1. Mean-Variance Optimisation

    Construct allocations and examine sensitivity to estimated inputs.

  2. Portfolio Constraints

    Turn mathematical weights into feasible portfolio decisions.

  3. VaR Estimation in Practice: Variance-Covariance, Historical Simulation, Monte Carlo

    Compare risk estimators and their assumptions.

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