You hold $50m of a bond with modified duration 7.0 and convexity 60. Yields rise 25 basis points. What is the loss to first order, what is the DV01, and how much does convexity give back?

You hold $50m of a bond with modified duration 7.0 and convexity 60. Yields rise 25 basis points. What is the loss to first order, what is the DV01, and how much does convexity give back?

Approach: Apply the first order duration term to the market value, then convert it to a one basis point figure and add the second order correction.

$875,000. The first order price change is market value times modified duration times the yield move, so 50m*7.0*0.0025 = $875,000 of loss. The DV01 is the same expression at one basis point, 50m*7.0*0.0001 = $35,000, and 25*35,000 reproduces the figure by construction. Convexity gives some back: 0.5*60*0.0025^2 = 0.0188% of market value, or $9,375, so the true loss is nearer $866,000. The correction is 1% of the answer at 25 basis points and 10% at 250 basis points, so duration alone is adequate for hedging small moves and misleading for stress scenarios.

Follow-up: What is the DV01 of a swap where you receive fixed on $50m for 7 years against a 3% flat curve?

Key concepts: modified duration, dv01, convexity, basis point.