Why mortgages have negative convexity

Create a personalised content profile. Measure ad performance. Select basic ads. Create a personalised ads profile. Select personalised ads. Apply market research to generate audience insights. Measure content performance. Develop and improve products. List of Partners vendors. Convexity is a measure of the curvature, or the degree of the curve, in the relationship between bond prices and bond yields. Convexity demonstrates how the duration of a bond changes as the interest rate changes. Portfolio managers will use convexity as a risk-management tool, to measure and manage the portfolio's exposure to interest rate risk.

In the example figure shown below, Bond A has a higher convexity than Bond B, which indicates that all else being equal, Bond A will always have a higher price than Bond B as interest rates rise or fall. Before explaining convexity, it's important to know how bond prices and market interest rates relate to one another. As interest rates fall, bond prices rise. Conversely, rising market interest rates lead to falling bond prices. This opposite reaction is because as rates rise, the bond may fall behind in the payout they offer a potential investor in comparison to other securities.

The bond yield is the earnings or returns an investor can expect to make by buying and holding that particular security. The price of the bond depends on several characteristics including the market interest rate and can change regularly. For example, if market rates rise, or are expected to rise, new bond issues must also have higher rates to satisfy investor demand for lending the issuer their money.

However, the price of bonds returning less than that rate will fall as there would be very little demand for them as bondholders will look to sell their existing bonds and opt for bonds, most likely newer issues, paying higher yields. Eventually, the price of these bonds with the lower coupon rates will drop to a level where the rate of return is equal to the prevailing market interest rates. Bond duration measures the change in a bond's price when interest rates fluctuate. If the duration of a bond is high, it means the bond's price will move to a greater degree in the opposite direction of interest rates.

Conversely, when this figure is low the debt instrument will show less movement to the change in interest rates. Essentially, the higher a bond's duration, the larger the change in its price when interest rates change. In other words, the greater its interest rate risk. So, if an investor believes that interest rates are going to rise, they should consider bonds with a lower duration. But it can be a pretty vicious move. Spreads on year U. That spread was last at 7 basis points. To be sure, convexity flows, even in the last few years, have not been as large as those seen in the run-up to the global financial crisis in From the point of view of MBS investors, the lack of refinancing of the underlying mortgages lengthens the expected time needed to be fully repaid, thereby increasing the duration of the corresponding MBS.

Furthermore, the increase in MBS duration will be larger the higher interest rates rise. This feature of MBS is called negative convexity and causes their price to fall more than that of Treasury bonds when yields rise. To control this risk within a portfolio, investors can hedge their MBS exposures, for example by buying Treasury bonds, thereby reducing the sensitivity of the portfolio to a rise in market yields.

However, due to MBS negative convexity, a large movement in yields makes it necessary to recalibrate the hedging in order to keep the overall duration of the portfolio close to the desired levels. If yields rise, the increase in portfolio duration due to MBS holdings must be offset by selling Treasuries, accentuating the upward trend in government bond yields. Such episodes were observed in and , coinciding with reversals of US monetary policy, and to a lesser extent during the taper tantrum.

To assess how high is the risk of another US Treasury selloff triggered by convexity hedging, it is useful to monitor the interest rates on new mortgages, which are typically of year maturity.

Data from the Mortgage Bankers Association of America confirm the very close relationship between changes in mortgage interest rates and refinancing activity see Chart 2. Currently, the rate on new year mortgages is 3.

However, refinancing activity has already decreased in March compared to a year ago and it is very likely to remain weak in the remainder of As mortgage rates fell until December to a low of 2.

This suggests that the risk of higher Treasury yields due to convexity hedging may intensify. The risk of adverse consequences on the government bond market will be mitigated by the reduced importance in the MBS market of investors who intensively hedge convexity risk, such as GSEs, pension funds, insurance companies and REITs see Chart 3. The share of banks and foreigners, two other categories of investors that do not hedge MBS convexity, has also increased in recent years.

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What Is Negative Convexity?