Hit by Convexity

Photograph by Michael Gottschalk/AP Photo

Convexity is a measure of the curvature or 2nd derivative of how the price of a bond varies with the interest rate, i.e. how the duration of a bond changes as the interest rate changes. Specifically, one assumes that the interest rate is constant across the life of the bond and that changes in interest rates occur evenly. Using these assumptions, duration can be formulated as the first derivative of the price function of the bond with respect to the interest rate in question. Then the convexity would be the second derivative of the price function with respect to the interest rate.

-Wikipedia, Bond Convexity

These are uneven times. Even better, the increasing dearth of “evenly” means these are convex times.

How do we know? Take any given Bloomberg function (particularly any on the joy in Europe, my recent fav is .PORGER10 INDEX) and plot it arithmetically. Even better, get more “even” results by plotting, say, EUR-USD logarithmically, on the y-axis. The chart points peripherally South, with curvature.

If the semi-log time series curves convex, that’s convexity, and that’s acceleration, and that’s market participants reacting in an even manner, with uneven applied panic, to the nonlinearity of all things Europe.

Be bold. Bone up on duration, convexity, and its chart application to the singular crisis that is Athens, Madrid, Rome, and distant linear Oslo.

In crisis, convexity matters. President Hollande’s chariot was struck by lightning. He and the elites of Europe are being hit by convexity. Discuss.

Before it's here, it's on the Bloomberg Terminal.