# Return Impact !!! Bond Convexity Spread (-Sign)

The formula says:

Return impact = modified duration * change in spread.

In a schweser problem, the spread narrows and it’s shown as a negative sign??? why is this the case?

If the spread had widen, would this be a +positive sign for the spread change?

My reasoning: if the spread narrows, the return impact will be an increase in bond price due to a lower denominator.

Post the question, Rasec.

An 8-year semiannual-pay corporate bond with a 5.75% coupon is priced at \$ 1 0 8.32. This bond’s duration and reported convexity are 6.4 and 0.5. The bond’s credit spread narrows by 75 basis points due to a credit rating upgrade. Estimate the return impact with and without the convexity adjustment.

Dear Rasec,

The spread narrowing means that your YTM is dropping, so that’s why its sign is negative; if spreads increase, then the change in spread is positive and the YTM is rising.

As well, while it may be market convention to state duration as a positive number, mathematically it is a negative number (remember, interest rates and bond prices are inversely related). I’ve seen the return impact formula listed with and without a negative sign, depending on the sign of the modified duration. If modified duration is listed as a negative number, then your formula above works fine; if modified duration is listed as a positive number, then you need a negative sign in front of your formula.

Is this the whole question? I am assuming when they say duration, they mean modified duration. Since the spread narrows, the spread adjustment is negative.

Return Impact = -(Duration x Spread) + 0.5 x Convexity x Spread^2 = -(6.4 x -0.0075 ) + 0.5 x 50.0 x -0.0075^2 = 0.0494 or +4.94%.

Spread narrows > interest rates decrease > price goes up.

What is Schweser’s explanation for the answer?

Right! I have to be careful here!

return impact w/o convexity = 4.80%

with convexity = 4.94%

I had a typo in my scaling factor for convexity. 0.5 convexity results in a rescaled convexity of 50, not 5.0. After accounting for this (updated my original post), the answers match with Schweser’s.

So based on what breadmaker said and the calculation above, does it make sense?

yes sir!

Thanks fellows!

Hi Guys,

I have a doubt in this topic:

The fucntion is correct :

Return Impact = -(Duration x Spread) + 0.5 x Convexity x Spread^2

however, I can not see a consensus when I check in investopedia or other place.

Return Impact = -(Duration x Spread) + Convexity x Spread^2

Without the 0.5 !!

Which one is the correct one ?

Best,

Daniel

Careful with this: you always need the negative sign. If they give you a modified duration that’s negative, it means that the duration is negative: _ when yields decline, the price drops, and when yields rise, the price increases _. The most common example of a bond having a negative duration is an IO strip when yields are low so prepayments are high.