Mortgage (MBS) Convexity – Negative Convexity & Impact on Bond Markets and Global Macroeconomics
Mortgage-Backed Securities (MBS) are financial instruments that have been at the heart of the fixed-income market for decades.
They pool together mortgage loans from various borrowers and allow investors to participate in the real estate market indirectly.
MBS pricing and risk are closely related to the concept of convexity, which measures the sensitivity of bond prices to changes in interest rates.
In this article, we will focus on MBS convexity, particularly negative convexity, and how it impacts bond markets and global macroeconomics.
And for those curious why they may not be allowed to prepay their mortgage, this article will give some reasons why.
Key Takeaways – Mortgage (MBS) Convexity
- Mortgage-Backed Securities (MBS) exhibit negative convexity due to the embedded prepayment option in mortgage loans.
- This means that MBS prices do not rise as much as other fixed-income securities when interest rates fall, and they can experience sharper price declines when interest rates rise.
- Negative gamma, which is the rate of change of convexity, worsens the negative convexity of MBS as interest rates change. This can lead to higher volatility in bond markets, amplifying price declines in rising interest rate environments and dampening price appreciation in falling interest rate environments.
- The presence of negative convexity and negative gamma in MBS can create systemic risks in financial markets and have implications on global macroeconomics.
- They can contribute to liquidity crunches, sharp price corrections, and spillover effects on the broader financial system, making them a crucial consideration for investors and central banks when managing interest rate risk and implementing monetary policy.
Mortgage-Backed Securities and Convexity
Convexity is an essential concept in fixed-income markets, as it determines the price sensitivity of a bond in response to interest rate fluctuations.
For most bonds, convexity is positive, meaning that the bond price will rise more quickly for a decrease in interest rates than it will fall for an increase in interest rates of equal magnitude.
Positive convexity is desirable, as it provides a natural hedge against interest rate risk.
However, MBS have a unique feature called negative convexity.
Negative convexity arises due to the embedded prepayment option in mortgage loans, which allows borrowers to prepay their loans before maturity.
When interest rates fall, homeowners are more likely to refinance their mortgages, leading to higher prepayment rates.
This causes MBS investors to receive principal payments sooner than expected, effectively shortening the duration of their investments and reducing the price gains associated with falling interest rates.
Conversely, when interest rates rise, prepayment rates decrease, extending the duration of MBS and amplifying price declines.
How “Convexity” Impacts Bond Yields
Negative Gamma and Its Impact on Momentum Moves in Bond Markets
Negative gamma is a concept related to negative convexity, and it refers to the rate of change of convexity concerning interest rate fluctuations.
In the context of MBS, negative gamma implies that the negative convexity of these securities worsens as interest rates change.
This means that MBS investors face increasing risks in managing their interest rate exposures, as their hedges become less effective and require constant readjustment.
Negative gamma can have a significant impact on momentum moves in bond markets.
When interest rates rise, negative gamma can amplify the selling pressure on MBS, as traders/investors work to hedge their interest rate exposures.
This, in turn, can lead to higher volatility in the bond market, creating a feedback loop that exacerbates price declines.
In a falling interest rate environment, negative gamma can dampen the price appreciation of MBS, as investors are forced to sell other fixed-income securities to rebalance their portfolios.
Global Macroeconomic Implications
Negative convexity and negative gamma can have far-reaching consequences on global macroeconomics.
The presence of negative convexity in MBS can create systemic risks in financial markets, as the increased price sensitivity and hedging requirements can lead to liquidity crunches and sharp price corrections.
This was exemplified during the 2008 financial crisis when the collapse of the MBS market played a significant role in the broader economic downturn.
Furthermore, central banks need to be mindful of the negative convexity dynamics in MBS when implementing monetary policy.
As MBS make up a substantial portion of the fixed-income market, central banks need to consider the potential spillover effects of interest rate changes on MBS pricing and the broader financial system.
If not managed appropriately, these effects can lead to financial instability and exacerbate economic downturns.
FAQs – Mortgage (MBS) Convexity
What is the duration and convexity of a mortgage?
Duration and convexity are important concepts for understanding the behavior of fixed-income securities, including mortgages, in response to changes in interest rates.
Both duration and convexity help assess the sensitivity of a mortgage or mortgage-backed security (MBS) to interest rate fluctuations.
Duration
Duration is a measure of the weighted average time to receive all the cash flows from a fixed-income security, such as a bond or mortgage.
It is used to estimate the percentage change in the price of a security for a given change in interest rates.
The higher the duration, the more sensitive the security’s price is to interest rate changes.
For a mortgage, duration depends on factors such as the loan’s term, interest rate, and the timing and size of cash flows (principal and interest payments).
Mortgages typically have lower durations than their actual terms, as principal and interest payments are made throughout the life of the loan, not just at maturity.
For example, the 30-year fixed-rate mortgage – a staple of the US housing market – has a duration that is lower than that 30 years but is highly uncertain because borrowers can prepay their mortgages.
Convexity
Convexity measures the rate of change of duration with respect to interest rate fluctuations.
It helps capture the non-linear relationship between bond prices and interest rates, offering a more accurate estimate of price sensitivity for larger interest rate changes.
For most fixed-income securities, convexity is positive, meaning that bond prices increase at an increasing rate when interest rates fall and decrease at a decreasing rate when interest rates rise.
However, mortgages and mortgage-backed securities exhibit negative convexity due to the embedded prepayment option, which allows borrowers to refinance or prepay their loans when interest rates fall.
The duration and convexity of a mortgage can vary significantly over time due to factors such as changes in interest rates, prepayment behavior, and the remaining term of the loan.
This variability makes managing interest rate risk for mortgages and mortgage-backed securities more complex compared to other fixed-income instruments.
How do you know if prepayments are likely to impact MBS duration?
You look at the interest rates on existing mortgages relative to current interest rates (mortgage rates).
If current interest rates are higher than existing mortgages, there is little refinancing, and therefore not a lot of prepayments.
When existing mortgage rates are lower than most mortgages, you can expect more refinancing.
What is the difference between duration and convexity in the context of MBS?
Duration is a measure of the sensitivity of a fixed-income security’s price to changes in interest rates, while convexity measures the rate of change of duration with respect to interest rate fluctuations.
In the context of MBS, duration helps estimate the price change for small interest rate movements, while convexity has to do with the non-linear relationship between bond prices and interest rates for larger interest rate changes.
Why do MBS exhibit negative convexity?
Negative convexity in MBS arises due to the embedded prepayment option in mortgage loans. This allows borrowers to refinance or prepay their loans when interest rates fall.
This prepayment behavior causes MBS investors to receive principal payments sooner than expected. It effectively shortens the duration of their investments and reduces the price gains associated with falling interest rates.
How does negative convexity impact MBS investors?
Negative convexity impacts MBS investors by making their investments more sensitive to interest rate changes compared to other fixed-income securities.
When interest rates rise, MBS prices can fall more sharply due to the increased likelihood of borrowers holding onto their mortgages, effectively extending the duration of the MBS.
Conversely, when interest rates fall, MBS prices may not appreciate as much as other fixed-income securities due to increased prepayment rates.
What is negative gamma, and how does it impact bond markets?
Negative gamma is a concept related to negative convexity, referring to the rate of change of convexity concerning interest rate fluctuations.
In the context of MBS, negative gamma implies that the negative convexity of these securities worsens as interest rates change.
This can lead to higher volatility in bond markets, as MBS investors need to constantly readjust their hedges, potentially exacerbating price declines in rising interest rate environments and dampening price appreciation in falling interest rate environments.
How do negative convexity and negative gamma influence global macroeconomics?
Negative convexity and negative gamma can create systemic risks in financial markets, as the increased price sensitivity and hedging requirements can lead to liquidity crunches and sharp price corrections.
Central banks also need to be mindful of the negative convexity dynamics in MBS when implementing monetary policy, as MBS make up a substantial portion of the fixed-income market, and interest rate changes can have spillover effects on MBS pricing and the broader financial system.
How can investors manage negative convexity in their MBS portfolios?
Investors can manage negative convexity in their MBS portfolios by diversifying their fixed-income investments, incorporating other types of bonds with positive convexity, or employing hedging strategies such as interest rate swaps, options, or futures.
Additionally, investors can consider investing in MBS with different prepayment risk profiles, such as those backed by loans with prepayment penalties or restricted refinancing options.
Conclusion
Understanding the mechanics of mortgage-backed securities convexity, particularly negative convexity and negative gamma, is important for investors, policymakers, and financial market participants.
The unique characteristics of MBS can have big implications on bond markets and global macro.