From the course: Fixed Income Fundamentals

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Convexity

Convexity

From the course: Fixed Income Fundamentals

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Convexity

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- [Instructor] Next we're going to talk about convexity. The relationship between price and yield for any given bond is not linear. That is prices rise at an increasing rate as yields fall and prices fall at a decreasing rate as yields increase. Let's look at this graphically. The shape of the curve is bowed from the origin and the shape is called convex, as you can see on this purple line. Hence, duration at any given yield is only an approximation as it's only a tangent to the curve and works well only for very small changes in yield. Convexity is a measure of the degree of curvature of a bond's price yield relationship, and it differs from bond to bond. For largest changes in yield, convexity produces a change in price as well in addition to the duration effects, we call that the convexity adjustment. The formula for convexity in years is as shown on the screen. We use C in this case to denote convexity, and convexity is equal to one over one plus Y over F, all squared multiplied…

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