You hold $250m of a bond with modified duration 6.8 and the yield falls 7 basis points. What is the profit in dollars, and what does convexity of 60 add on a move that size?

You hold $250m of a bond with modified duration 6.8 and the yield falls 7 basis points. What is the profit in dollars, and what does convexity of 60 add on a move that size?

Approach: Compute the dollar value of one basis point from notional and modified duration, scale it by the yield move, then size the second order convexity term against it.

1190000. The DV01 is the dollar value of one basis point, equal to notional * modified duration * 0.0001, so 250000000 * 6.8 * 0.0001 = $170000 per basis point. A 7 basis point fall in yield is a gain of 7 * 170000, which is 1190000 dollars. The mental route is that 6.8 of modified duration on $250m is $1.7bn of duration dollars, and one basis point of that is $170000 because a basis point is one part in ten thousand. Convexity adds 0.5 * C * (dy)^2 * notional, which here is $3675, or 0.31% of the first order figure, small enough to ignore on a move this size.

Follow-up: Yields fall 150 basis points instead. What does the duration estimate miss, and what does convexity contribute now?

Key concepts: DV01, modified duration, basis point, convexity.