What is Convexity Explained

The measure of the degree of the curve between the relationship of Bond prices and bond yields is known as Convexity.

Relation between Interest rates and Bond prices

Convexity helps us in demonstrating how the rate of interest changes with Bond. It is also used as a risk management tool by the portfolio managers to measure the portfolio’s exposure to the various risks of the interest rate.

To gain a better understanding of convexity, it’s important for us to know how bond prices relate to market interest rates.

The bond prices rise with a fall in the interest rates. Whereas, the rising interest rates lead to a gradual fall in the bond prices. This scenario is created due to the rising rates.

The bond yield is the return an investor can expect to make on purchasing a Bond or other debt holding.

There are several characteristics affecting the bond’s price. It includes the market interest rate and can change periodically.

As the market rates start rising, new bonds entering the market, also start raising its yields. The upcoming bonds get issued to new, higher rates. Also, the investors start demanding a higher yield from the purchased bonds with the increasing rates in the market.

Investors usually don’t demand a fixed-rate bond at current yields. They expect interest rates to go higher in the future. As a result, when interest rates eventually increase, the issuer of these debt cycles ought to raise their yields as well just for the sake to remain competitive.

Convexity and Duration

The core concept of convexity is built on the concept of measuring the sensitivity of the duration of a bond as a change in yields.

Concerning bond duration, convexity is a better way to measure interest rate risk. Here, the duration determines a linear relationship between interest rates and bond prices. Moreover, convexity also allows other factors to produce a slope.

The duration can be a good tool measure, how bond prices get affected due to small and sudden fluctuations in interest rates. The relationship between bond prices and yields is more sloppy and convex.

Thus, convexity is a more preferable measure for assessing the impact on bond prices in case of large fluctuations.

The systemic risk for exposing a portfolio is increased, with increasing convexity. During the financial crisis of 2008 systemic risk became a common term to the masses.The failure of one financial institution became a threat to others. However, this risk is applicable to all businesses, industries, and the economy as a whole

Negative and Positive Convexity

When a bond’s duration increases with yield increases, the bond is said to have negative convexity.

The bond price will decline by a greater rate if there’s a rise in yields instead of fallen yields. Thus, if a bond possesses negative convexity, the duration of the bond would tend to increase and eventually the price would fall.

If the interest rates rise, and the opposite becomes true.
The duration of bond prices rises when yields fall. This situation gives rise to positive convexity. When the yields fall the bond prices tend to rise by a greater value and duration.

Whereas Positive convexity leads to a major increase in bond prices. The bond l experiences a larger price yield if it happens to be a positive convexity.

Under normal market conditions, the higher the coupon rate, the lower a bond’s degree comparatively will be. There is lesser risk for the investor when a bond has a high coupon. Since the market rates would be to increase significantly to surpass the bond’s yield.

Hence, a portfolio of bonds with a maximum number of yields will have low convexity and eventually lesser risk of their existing yields.

Real-world examples


Mostly the mortgage-backed securities (MBS) will have a negative convexity because their yield is certainly higher than the traditional bonds. Henceforth, it will significantly rise in yields to help an existing holder of MBS in possessing a lower yield.

Let’s say for example, the SPDR Barclays Capital Mortgage Backed Bond ETF (MBG) offers a yield of 3.33% on March 26, 2019. Now If we compare the ETF’s yield in the current 10-year Treasury yield, trades out roughly at 2.45% interest rates which will rise substantially.

If the interest rate goes well above 3.33% for the MBG ETF, it will eventually have a risk of losing out on higher yields. To the conclusion, the ETF has negative convexity as any rise in yields would have less impact on existing investors.

Example Source: Investopedia.com

Final words

As bonds sell-off and the prices fall, the investor may wait for the interest rates to stop rising before getting back in the bond market via buying higher-yielding security.
As a result, the bond prices and yields move in the opposite direction.

We hope you liked the content and the content was able to solve your doubts on Convexity.

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