Duration/Convexity

On the below question, why isn’t the first term positive? It seems to me it should be (-7.8*-0.01)

). Their answer keeps the negative outside of term. Can someone please explain why

Thanks

A 9-year corporate bond with a 3.25% coupon is priced at €103.96. This bond’s duration and convexity are 7.8 and 69.8. If the bond’s credit spread widens by 100 basis points, the impact on the bondholder’s return is closest to:

A) −7.80%. B) +8.15%. C) −7.45%.

Return impact ≈ −(Duration × ΔSpread) + (1/2) × (Convexity × (ΔSpread))2 ≈ −(7.8 × 0.0100) + (1/2) × (69.8) × (0.0100)2 ≈ −0.0780 + 0.0035 ≈ −0.0745 or −7.45%

Using logic, a widening of the credit spread should either decrease your return, or increase the required rate of retrun.

Having the negative term outside means that only one of the terms (the first term in this case) should be negative, but not both. The second term measures the difference between spreads.

A credit spread widening of 100bp means that

(By the way, the formula you have above:

Return impact ≈ −(Duration × ΔSpread) + ½ × (Convexity × (ΔSpread))²

is incorrect: you show it squaring the convexity. The correct formula is:

Return impact ≈ −(Duration × ΔSpread) + ½ × Convexity × (ΔSpread)²

Be careful.)

Thanks guys

My pleasure.