Bullet vs Barbell

CFA Level III Fixed Income
#1

Little confused about immunization risk.

From the text Page 43. [content removed by moderator]

I don’t think this is true all the time. How can that even be the case?

My logic below.

Example (Short rates decline and Long rates increase)

Both experience a decline of the portfolio value at the end of the investment horizon below the target investment value for two reasons:

  1. Lower reinvestment rates.

  2. Experience a capital loss.

BUT, decline substantially higher for barbells for two reasons:

  1. Barbell experiences lower reinvestment rates longer than the bullet portfolio does.

  2. More of the barbell is outstanding at the end of the investment horizon leading to a larger capital loss.

Summary: the bullet portfolio here has less exposure to changes in the interest rate structure (same as CFA books)

Then, this is where I’m at a loss. Example (short rates increase and long rates decrease)

In this case wouldn’t the barbell portfolio have less risk then an bullet portfolio?

I would think

decline substantially higher for BULLETS (Therefor Riskier)- the opposite of the above reasons. With longer duration, the capital gain by the barbell would be greater than a bullet and the barbell would experience higher reinvestment rates for a longer time.

Along with that, would BOTH experience an increase in portfolio value at the end of the investment horizon above the target investment value?

Read it enough times where I’m just confused now. Any help is much appreciated. Thanks

#2

Or is the point, that even in the second case of short rate increase and long rate decrease that:

  • the reinvestment risk is still higher for the barbell (due to high dispersion of CF’s around the horizon date) but that the barbell strategy is better off return wise BUT again still is riskier?
#3

The barbell portfolio still bears greater reinvestment risk - it is irrelevant to the slope of the yield curve. The first statement: "…the effect on the value of the two portfolios differs - the barbell portfolio is riskier than the bullet portfolio”

You are conflating value with risk - just because an asset increases in value doesn’t mean there is less risk.

#4

perfect.

Much appreciated.