A Modeling Approach of Return and Volatility of Structured Investment Products with Caps and Floors

ArXiv ID: 2311.06282 “View on arXiv”

Authors: Unknown

Abstract

Popular investment structured products in Puerto Rico are stock market tied Individual Retirement Accounts (IRA), which offer some stock market growth while protecting the principal. The performance of these retirement strategies has not been studied. This work examines the expected return and risk of Puerto Rico stock market IRA (PRIRAs) and compares their statistical properties with other investment instruments before and after tax. We propose a parametric modeling approach for structured products and apply it to PRIRAs. Our method first estimates the conditional expected return (and variance) of PRIRA assets from which we extract marginal moments through the Law of Iterated Expectation. Our results indicate that PRIRAs underperform against investing directly in the stock market while still carrying substantial risk. The expected return of the stock market IRA from Popular Bank (PRIRA1) after tax is slightly greater than that of investing in U.S. bonds, while PRIRA1 has almost two times the risk. The stock market IRA from Universal (PRIRA2) performs similarly to PRIRA1, while PRIRA2 has a lower risk than PRIRA1. PRIRAs may be reasonable for some risk-averse investors due to their principal protection and tax deferral.

Keywords: Structured Products, Parametric Modeling, Law of Iterated Expectation, Principal Protection, Risk-Return Analysis, Retirement Accounts/Equities

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats
  • Why: The paper employs advanced mathematical concepts like the law of iterated expectation, total variance, and truncated normal distributions, scoring high in math complexity. However, it lacks backtests or real-time implementation details, relying on historical data analysis and theoretical modeling rather than actionable trading strategies, resulting in lower empirical rigor.
  flowchart TD
    A["Research Goal:<br>Model & Analyze Puerto Rico IRAs"] --> B["Data & Inputs:<br>PRIRA Historical Performance Data"]
    B --> C["Methodology:<br>Parametric Modeling Approach"]
    C --> D{"Computational Process:<br>Law of Iterated Expectations"}
    D --> E["Calculate Conditional<br>Expected Return & Variance"]
    E --> F["Extract Marginal Moments<br>from Asset Data"]
    F --> G["Key Findings/Outcomes:<br>Risk-Return Analysis vs. Benchmarks"]
    
    G --> H1["PRIRAs < Market Portfolio<br>Higher Risk vs Bonds"]
    G --> H2["PRIRA2 < PRIRA1<br>Lower Risk Profile"]
    G --> H3["Principal Protection + Tax Deferral<br>Viable for Risk-Averse"]