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# What is Bond Convexity?

Justin Riche
Justin Riche

Bond convexity is normally a measure used to analyze bonds, and it helps the bond analyst estimate the interest rate risk and return associated with certain bonds. The bond convexity measure is used to make up for errors that other measures can present, especially when yields change significantly. Interest rate risk is a typical issue for bond investors because when interest rates rise as a result of inflation or other factors, bond values will be affected. Thus, measuring the convexity of bonds can help investors manage the risk caused by fluctuating interest rates. Moreover, bond convexity can be represented graphically to display the yield and price relationship of a bond.

In the bond market, prevailing market interest rates will go up or down for different reasons, which will affect the value of many types of bonds. All bonds are not created equal, so this rise and fall of rates will affect their values in different ways. Thus, bond investors use a measure such as bond convexity to analyze any similarities or differences that might exist between two or more bonds. This can help them select bonds that can serve their needs in particular conditions.

Generally, in a volatile market, some traders and investors might prefer a higher degree bond convexity because it is perceived that this type will produce better returns than the kind that is less convex. Typically, this is because the curvier the convexity of a bond, the better it might do when market interest rates decline remarkably. When interest rates are rising, its price will not be affected by the same degree as when they fall, even if the percentage of the rise and fall of the interest rates is equal. Stated differently, when interest rates fall by a certain percentage, the bond price will rise by a greater amount, compared to when the rates rise by the same percentage — the price will fall by a relatively smaller amount.

Using the bond convexity formula, the analyst will be able to quantify the effect that the change in interest rates will have on the value of the bond. Hypothetically speaking, he or she can see that a 1 percent decline in interest rates might result in the bond price rising by \$50 US Dollars (USD), for example. If the interest rates were to rise by 1 percent, however, the price will not drop by \$50 USD but might instead drop by \$25 USD.

Theoretically, a measure such as duration will show that the simultaneous rise and fall of bond prices and yields are linear, meaning that they will fall and rise somewhat proportionally, which applies only when this decline and rise is of a small degree. When the prices and yields rise and fall in a significant manner, however, there will be errors as represented by the duration measure. This is when the bond convexity measure comes in and helps correct these errors, and it can be used together with the duration measure for a better overall estimation.

Moreover, bond convexity illustrates the relationship between bond prices and yield, which is usually plotted on a graph to show what is called a convex curve. The degree of the curvature, as represented on the graph, demonstrates the manner in which a bond's yield reacts to a change in the bond's price — that is, as the price rises, the yield falls, and vice versa. This curve will also visually show how price and yield react to each other's changes and how they do not follow a linear form.

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