Análise Matemática da Marcação a Mercado de 2020 a 2025 dos Títulos Prefixados 26 e 29 e Títulos IPCA+ 26 e IPCA+ 29 do Tesouro Direto

Abstract

This study presents an analysis of mark-to-market applied to Brazilian Treasury Direct public bonds, focusing on the Fixed-Rate Treasury Bonds (Tesouros Prefixados) 2026 and 2029, and the IPCA-linked Treasury Bonds (Tesouros IPCA+) 2026 and 2029. Although fixed income is often perceived as an investment with predictable returns, the dynamics of mark-to-market reveal a fluctuation that many investors, especially beginners, are unaware of or have limited understanding of. This lack of comprehension can compromise their investment decisions and lead to unexpected losses or missed gain opportunities when disposing of bonds before maturity. The research adopts a quantitative, descriptive, and longitudinal approach, collecting and analyzing daily historical Unit Price (PU) data for these bonds, as well as macroeconomic indicators such as the Selic rate, CDI, and IPCA, over the period from 2020 to 2025. The results demonstrate that mark-to-market is a crucial mechanism that daily updates asset prices and reflects market conditions, revealing that fixed income is not inherently "fixed." An inversely proportional relationship was observed between market interest rates (influenced by the Selic rate) and the PU of fixed-rate bonds: when rates rise, the PU falls, and vice-versa, generating opportunities for profit or loss in early redemptions. For IPCA-linked bonds, profitability is influenced by both inflation adjustment (IPCA) and the fixed-rate component, which also undergoes mark-to-market, making them sensitive to real interest rate expectations. Comparative analysis showed that bonds with longer maturity periods tend to exhibit greater fluctuation and are more susceptible to the effects of mark-to-market. It is concluded that a deep understanding of mark-to-market and the interrelation among economic indicators is fundamental for active management of fixed income portfolios, empowering investors to identify windows of opportunity to maximize returns and mitigate risks, and contributing to the strengthening of financial education in Brazil.