If a 21030 butterfly spread goes down by 50 basis points a b

If a 2-10-30 butterfly spread goes down by 50 basis points, a bullet portfolio concentrated in the 10-year maturity:

a. will outperform a barbel portfolio
b. will underperform a barbel portfolio
c. will generate the same return as a barbel portfolio

Solution

Answer: b

b. will underperform a barbell portfolio.

When rates goes down 50 basis points the price of the bond portfolio will increase.

hence barbell is spread across 2 and 30 year maturity the price increase will be more when compared to 10 year concentrated bullet portfolio.

On the other hand, In the butterfly spread 2-10-30, bullet portfolio is concentrated (that is long) on 10 year maturity, and short at 2 and 30 year maturity which a barbell.

Hence the changes in the portfolio will offset each other because of long short combination in the event of a parallel yield curve shift( rates goes down by 50bps across 2-10-30).