Convexity and dispersion of laddered portfolio

CFA Level III Fixed Income
#1

Hi all,

Convexity of Bullet < Convexity of Laddered portfolio < convexity of Barbell Portfolio

But why

Cashflow dispersion of Bullet < Cashflow dispersion of Barbell Portfolio < Cashflow dispersion of Laddered portfolio

I thought dispersion positive related to convexity ?

#2

that statement is not correct

#3

C =( malcau-duration2 + malcau-duration + dispersion) / (1+ cashflow yield)2.

Therefore, theres no way the bullet could have higher convexity.

Another way to look at it, the bonds with the difference of the lowest maturity and highest maturity will have the higher convexity.

#4

Reread what he wrote; he didn’t say that the bullet has higher convexity.

#5

You’re comparing cash flow dispersion to convexity here, which makes no sense.

#6

I guess this is what OP wants to say…

You could technically construct a barbell with 1 short end and 1 long end. The convexity of which should be closer to a bullet.

vs

Laddered ie the security maturities are stacked through out. You can gain a lot more advantage of the convexity in $ terms simply due to number I guess

Probably S2K can correct me.

#7

LOL responding to posts at 4AM is a good way to get things mixed up!

#8

Amen!

Been there, done that.

#9

Sorry, I meant Cashflow dispersion of Bullet < Cashflow dispersion of Barbell Portfolio

#10

“The laddered portfolio would provide better diversification over the interest rate cycle compared with the other portfolio styles.”

I would have thought the BARBELL portfolio would provide a better diversification than both the bullet and the ladder.

Unless “diversification” in this context means something else than dispersion.

Could someone please explain?

#11

Diversification means a little bit of everything… No one single maturity is going to win or kill ya. Since ladder bonds have a sliver of everything, you’re going to be more diversified.

How can barbell be better diverficiation since it is highly concentrated on the long and shorts? If the curve steepens, you’re screwed.

#12

sell calls and buy puts!!!

#13

Thanks 125mph, I think I did not correctly interpret diversification here. True laddered is the best if we are unsure whether the YC is gonna steepen or flatten.

Only I had in my mind that barbell is the best choice in case of higher volatility expectation.