Capital structure arbitrageurs focus on individual issuers. They look for valuation differentials between a company's debt and equity securities.Arbitrage is when an asset (stocks, currencies, etc.) is bought in one market and sold in another for a higher price. Arbitrage is the simultaneous purchase and sale of the same asset in different markets in order to profit from a difference in its price. Arbitrage, at its most simplest, involves buying securities on one market for immediate resale on another market in order to profit from a price discrepancy. In this research paper, the benchmark is the market return, where we define the market as all bonds in the US IG or US HY index. An arbitrage opportunity is defined here as: a riskless trading strategy that generates a positive profit with no net investment of funds. We set up a mathematical framework for investment in a financial market with a fixed number of assets, thought of as stocks.