# Performance of credit risky bonds vs. default-free bonds

Schweser Notes Page. 191 - LOS 50.f

“When credit spreads narrows, credit risky bonds will outperform default-free bonds. Overall, lower rated bonds to benefit more than higher rated bonds from narrowing of credit spreads (their yields fall more). Conversely, when credit spreads widen, higher rated bonds will outperform lower rated bonds on a relative basis (because their yields will rise less).”

Can someone elaborate and explain further the above please?

Suppose that the risk-free rate is 3% and the spread on the risky bond is 100 bp, and, to make things even simpler, both the risk-free bond and the risky bond have a modified duration of 4.5 years.

If the risk-free rate doesn’t change but the spread narrows by 20 bp, then the risk-free bond’s price won’t change, but the risky bond’s price will increase by approximately 0.2% × 4.5 = 0.9%. Therefore, the risky bond outperforms (i.e., has a higher return than) the risk-free bond.

If the risk-free rate decreases by, say, 30 bp and the spread narrows by 20 bp, then the risk-free bond’s price will increase by approximately 0.3% × 4.5 = 1.35% and the risky bond’s price will increase by approximately (0.3% + 0.2%) × 4.5 = 2.25%. Once again, the risky bond outperforms the risk-free bond.

I’ll leave the rest to you, but you get the idea.

Thank you sir!

My pleasure.