Portfolio Insurance

On the optimal design of a new class of proportional portfolio insurance strategies in a jump-diffusion framework ArXiv ID: 2407.21148 “View on arXiv” Authors: Unknown Abstract In this paper, we investigate an optimal investment problem associated with proportional portfolio insurance (PPI) strategies in the presence of jumps in the underlying dynamics. PPI strategies enable investors to mitigate downside risk while still retaining the potential for upside gains. This is achieved by maintaining an exposure to risky assets proportional to the difference between the portfolio value and the present value of the guaranteed amount. While PPI strategies are known to be free of downside risk in diffusion modeling frameworks with continuous trading, see e.g., Cont and Tankov (2009), real market applications exhibit a significant non-negligible risk, known as gap risk, which increases with the multiplier value. The goal of this paper is to determine the optimal PPI strategy in a setting where gap risk may occur, due to downward jumps in the asset price dynamics. We consider a loss-averse agent who aims at maximizing the expected utility of the terminal wealth exceeding a minimum guarantee. Technically, we model agent’s preferences with an S-shaped utility functions to accommodate the possibility that gap risk occurs, and address the optimization problem via a generalization of the martingale approach that turns to be valid under market incompleteness in a jump-diffusion framework. ...

Optimal Management of DC Pension Plan with Inflation Risk and Tail VaR Constraint ArXiv ID: 2309.01936 “View on arXiv” Authors: Unknown Abstract This paper investigates an optimal investment problem under the tail Value at Risk (tail VaR, also known as expected shortfall, conditional VaR, average VaR) and portfolio insurance constraints confronted by a defined-contribution pension member. The member’s aim is to maximize the expected utility from the terminal wealth exceeding the minimum guarantee by investing his wealth in a cash bond, an inflation-linked bond and a stock. Due to the presence of the tail VaR constraint, the problem cannot be tackled by standard control tools. We apply the Lagrange method along with quantile optimization techniques to solve the problem. Through delicate analysis, the optimal investment output in closed-form and optimal investment strategy are derived. A numerical analysis is also provided to show how the constraints impact the optimal investment output and strategy. ...

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. ...