Value-at-Risk-Based Portfolio Insurance: Performance Evaluation and Benchmarking Against CPPI in a Markov-Modulated Regime-Switching Market

ArXiv ID: 2305.12539 “View on arXiv”

Authors: Unknown

Abstract

Designing dynamic portfolio insurance strategies under market conditions switching between two or more regimes is a challenging task in financial economics. Recently, a promising approach employing the value-at-risk (VaR) measure to assign weights to risky and riskless assets has been proposed in [“Jiang C., Ma Y. and An Y. “The effectiveness of the VaR-based portfolio insurance strategy: An empirical analysis” , International Review of Financial Analysis 18(4) (2009): 185-197”]. In their study, the risky asset follows a geometric Brownian motion with constant drift and diffusion coefficients. In this paper, we first extend their idea to a regime-switching framework in which the expected return of the risky asset and its volatility depend on an unobservable Markovian term which describes the cyclical nature of asset returns in modern financial markets. We then analyze and compare the resulting VaR-based portfolio insurance (VBPI) strategy with the well-known constant proportion portfolio insurance (CPPI) strategy. In this respect, we employ a variety of performance evaluation criteria such as Sharpe, Omega and Kappa ratios to compare the two methods. Our results indicate that the CPPI strategy has a better risk-return tradeoff in most of the scenarios analyzed and maintains a relatively stable return profile for the resulting portfolio at the maturity.

Keywords: Portfolio Insurance, Regime Switching, Value-at-Risk (VaR), Constant Proportion Portfolio Insurance (CPPI), Markov Model, Equities

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced stochastic calculus and Markov-modulated regime-switching models, involving SDEs and matrix exponentials, which indicates high mathematical complexity. However, it relies on Monte Carlo simulations for evaluation rather than real-world data, backtesting, or live implementation details, placing it lower on empirical rigor.

  flowchart TD
    A["Research Goal<br>Design & Compare Portfolio<br>Insurance Strategies in<br>Regime-Switching Market"] --> B["Modeling Phase<br>Regime-Switching Framework"]
    
    B --> C["Data & Inputs<br>Simulated Risky Asset<br>Markovian Regimes<br>Initial Portfolio Value"]
    
    C --> D{"Strategy Formulation"}
    D --> E["VBPI Strategy<br>Weight = (VaR - T)/S<br>Dynamic allocation via VaR"]
    D --> F["CPPI Strategy<br>Weight = (Floor - Cash)/S<br>Constant multiplier approach"]
    
    E & F --> G["Performance Evaluation<br>Sharpe Ratio<br>Omega Ratio<br>Kappa Ratio<br>Return Profile Stability"]
    
    G --> H["Key Findings<br>CPPI shows better risk-return<br>tradeoff in most scenarios<br>CPPI maintains stable<br>return profile at maturity<br>VBPI effective under<br>certain market regimes"]
    
    style A fill:#e1f5fe
    style H fill:#e8f5e8