Convexity plays a crucial role in mortgage-backed securities (MBS) and other structured products, as it directly impacts the risk and return characteristics of these financial instruments. Understanding convexity is essential for investors, issuers, and risk managers involved in these markets.
Mortgage-backed securities are financial instruments that represent an ownership interest in a pool of mortgage loans. These loans are typically secured by
real estate properties and generate cash flows through monthly mortgage payments made by borrowers. MBS are structured in different ways, such as pass-through securities, collateralized mortgage obligations (CMOs), or real estate mortgage investment conduits (REMICs).
Convexity in MBS refers to the non-linear relationship between changes in interest rates and the price or value of the security. It measures the sensitivity of the MBS price to changes in interest rates, beyond what can be explained by duration alone. Duration is a measure of the average time it takes to receive the cash flows from an investment, and it provides an estimate of the price change for a given change in interest rates.
The presence of convexity in MBS arises due to prepayment options embedded in mortgage loans. Borrowers have the right to prepay their mortgages partially or fully before their scheduled maturity dates. When interest rates decline, borrowers tend to refinance their mortgages at lower rates, resulting in increased prepayments. Conversely, when interest rates rise, prepayments decrease as borrowers are less likely to refinance.
The impact of convexity on MBS can be understood by considering two scenarios: a decrease and an increase in interest rates. In the case of falling interest rates, the value of MBS increases due to the higher likelihood of prepayments. This is because the cash flows from the underlying mortgages are received earlier than expected, allowing investors to reinvest at higher rates. As a result, MBS exhibit positive convexity, which means that their prices rise more than proportionally to the decrease in interest rates.
Conversely, when interest rates rise, the value of MBS decreases due to the reduced likelihood of prepayments. This is because borrowers are less likely to refinance their mortgages at higher rates, resulting in delayed cash flows for investors. As a result, MBS exhibit negative convexity, which means that their prices decline more than proportionally to the increase in interest rates.
The presence of convexity in MBS has important implications for investors and risk managers. Positive convexity can provide a hedge against interest rate risk, as the increase in MBS prices during falling interest rate environments can offset losses from other fixed-income investments. This makes MBS attractive to investors seeking to manage their portfolio's interest rate exposure.
However, negative convexity introduces additional risks. As interest rates rise, the value of MBS declines more rapidly than duration alone would suggest, leading to potential losses for investors. This risk is particularly relevant for mortgage-backed securities with longer maturities or those backed by loans with low prepayment rates.
To manage the risks associated with convexity, issuers and investors may use various strategies. For example, issuers of MBS may structure tranches with different levels of convexity to cater to different investor preferences. Investors may also employ hedging techniques, such as using interest rate derivatives or dynamically adjusting their portfolios to maintain a desired level of convexity exposure.
In addition to mortgage-backed securities, convexity also plays a role in other structured products, such as asset-backed securities (ABS) and collateralized debt obligations (CDOs). These products often exhibit similar characteristics to MBS, including embedded options and varying levels of convexity. Understanding convexity is crucial for accurately assessing the risk and return profiles of these structured products.
In conclusion, convexity is a fundamental concept in mortgage-backed securities and other structured products. It captures the non-linear relationship between changes in interest rates and the price or value of these securities. Convexity arises due to prepayment options embedded in mortgage loans, and it has important implications for investors, issuers, and risk managers. By understanding and managing convexity, market participants can effectively navigate the risks and opportunities presented by these financial instruments.