Contingent Immunization Safety Margin Calculation (CFAI vol 4, page 37)

CFA Level III Fixed Income
#1

Can anyone help me with this?

In CFAI, vol 4, page 37, middle of the page, it states: “If rates rise so that YTM is now 5.8% the portfolio value will be $460.55 million and the intial asset value required will be $460.52 million.” Where are these figures coming from?

For for first figure, I’m coming up with $460.58, not $460.55 using the following inputs: PMT: 11.875, FV: 546.72, N: 20, I: 2.9%

For the second figure, I’m calculating $460.55, not $460.52, using a straight discount forumula: 546.72/(1.029^6).

Did I misread something or make an error in building up my formulas? Thank you to whoever can straighten me out.

#2

it is a rounding issue. Book states portfolio value would be 541.36 - when I do

N=20, I=3.75/2, PV=? PMT=500*4.75%/2=11.875, FV=500

I get PV = 541.376.

your formulae are correct.

#3

Isn’t the book’s conclusion incorrect?

#4

nope. the value drops to almost 0 cushion at 5.8%. that is all they are trying to say.

#5

Why isn’t “I” 5.8%/2 or 2.9?

#6

I did it for the 3.75% case.

For the 5.8% case:

If rates rise so that the YTM is now 5.80 percent, the portfolio value will be $460.55 million and the initial asset value required will be $460.52 million. The dollar safety margin has gone to zero,

For the 5.8% case - it would be:

N=20, I=2.9, PV=? PMT=11.875, FV=500

PV = 460.583

500 * (1 + 0.03/2)^6 / (1.029^6) = 460.547

cushion has reduced to almost zero.

the numbers they have quoted are 460.55 and 460.52 respectively.