Introduction

In the world of fixed income securities, understanding arbitrage opportunities is essential for both traders and investors. Arbitrage is the practice of exploiting price differences in similar or identical assets to make a risk-free profit. In this chapter, we will explore how arbitrage opportunities can arise in the context of fixed income securities with certain cash flows. We’ll explain these opportunities using arbitrage arguments and demonstrate how these concepts are applied to bond pricing.

Identifying Arbitrage Opportunities

Arbitrage opportunities arise when there is a discrepancy in the pricing of fixed income securities with identical or very similar cash flows. These opportunities can be categorized into two main types:

• Cash Flow Arbitrage: This type of arbitrage involves exploiting differences in cash flows between two or more fixed income securities. For example, consider two bonds with the same maturity date and credit quality, but one offers a higher coupon rate than the other. By purchasing the bond with the higher coupon rate and shorting the one with the lower coupon rate, an arbitrageur can lock in a profit equal to the difference in coupon payments.

• Yield Arbitrage: Yield arbitrage involves exploiting differences in yields (or interest rates) between fixed income securities. For instance, if a corporate bond offers a yield higher than that of a government bond with a similar maturity and credit risk, arbitrageurs may buy the corporate bond and simultaneously sell short the government bond. This strategy allows them to profit from the yield spread.

Using an Arbitrage Argument

Arbitrage arguments are logical demonstrations of how price discrepancies violate the law of one price. This law states that identical assets should have the same price in an efficient market. Here’s how we can use arbitrage arguments to illustrate arbitrage opportunities:

Example: Let’s say there are two bonds, A and B, with the same maturity date. Bond A pays a semi-annual coupon of 5%, while Bond B pays a semi-annual coupon of 4%. Both bonds have a face value of USD 1,000.

• Bond A’s cash flow: USD 25 every six months for five years.
• Bond B’s cash flow: USD 20 every six months for five years.

An arbitrageur could buy Bond A and short Bond B. Over five years, they would receive USD 250 in coupon payments from Bond A and pay out USD 200 in coupon payments for Bond B. At maturity, they would receive USD 1,000 from Bond A and pay out USD 1,000 for Bond B. The result is a risk-free profit of USD 50.

Applying Arbitrage to Bond Pricing

Arbitrage plays a crucial role in bond pricing because it helps maintain price consistency in the market. When arbitrageurs identify pricing discrepancies between bonds with similar characteristics, they engage in trading activities that drive prices back to equilibrium.

For instance, if a corporate bond is priced too low compared to government bonds with similar risk profiles, arbitrageurs will buy the corporate bond, increasing its demand and driving its price up. Conversely, they may short the overpriced government bond, causing its price to fall. These actions align the prices of the two bonds with their respective yields and risk levels.