Portfolio Optimization with Relative Tail Risk

Paper: arXiv 2303.12209

Authors: Young Shin Kim

Abstract

This paper proposes analytic forms of portfolio CoVaR and CoCVaR on the normal tempered stable market model. Since CoCVaR captures the relative risk of the portfolio with respect to a benchmark return, we apply it to the relative portfolio optimization. Moreover, we derive analytic forms for the marginal contribution to CoVaR and the marginal contribution to CoCVaR. We discuss the Monte-Carlo simulation method to calculate CoCVaR and the marginal contributions of CoVaR and CoCVaR. As the empirical illustration, we show relative portfolio optimization with thirty stocks under the distress condition of the Dow Jones Industrial Average. Finally, we perform the risk budgeting method to reduce the CoVaR and CoCVaR of the portfolio based on the marginal contributions to CoVaR and CoCVaR.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 5.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents strong theoretical contributions by deriving closed-form analytic expressions for portfolio CoVaR and CoCVaR using a normal tempered stable model. However, the empirical section is limited to a small illustrative example with 30 stocks rather than a comprehensive historical backtest.

Research Flowchart

  flowchart TD
    A[Goal: Relative Portfolio Optimization & Risk Budgeting via CoVaR/CoCVaR] --> B[Model Framework: Normal Tempered Stable NTS Model]
    B --> C[Derive Analytic Forms & Marginal Contributions for CoVaR/CoCVaR]
    D[Data: 30 Stocks & DJIA Index Benchmark] --> E[Monte-Carlo Simulation & Empirical Analysis]
    C --> E
    E --> F[Outcomes: Optimized Relative Portfolios & Risk Budgeting Allocations]