30 year maturities

[patso]

What does this really mean in baby language “The 30-year maturities provide investors with extra positive convexity for a modest increase in effective (or modified-adjusted) duration.”

 

[S2000magician]

It means that the duration of a 30-year bond is only slightly higher than that of, say, a 20-year bond, but its convexity is higher.
For example, consider two bonds with 6% coupons and 6% YTM: one a 20-year bond, the other a 30-year bond.

• 20-year: modified duration = 11.6 years, modified convexity = 186.8 years²
• 30-year: modified duration = 13.8 years, modified convexity = 296.5 years²

So, for a 19.7% increase in duration, you get a 58.7% increase in convexity.

 

[patso]

Thanks Magician. I understand the longer the maturity the higher the convexity and the duration but why should this be positive convexity (why not negative??).

 

[S2000magician]

You’re welcome.
Fixed-coupon, option-free bonds always have positive convexity. Take a look at any price/yield curve.
(Note: higher convexity is always better, whether it’s -100 vs. -150, or 0 vs. -100, or 50 vs. -50, or 150 vs 50.)

 

[Galli]

Wouldn’t negative convexity mean it’s concave?

 

[S2000magician]

Yes.