contingent immunization - dollar saftey margin question

CFA Level III
#1

Hi, i would be extremely grateful if you could walk me through exactly how to calculate the below question - totally lost here and truly hope it doesn’t come up! thanks so much in advance!

A portfolio manager has decided to pursue a contingent immunization strategy over a four-year time horizon. He just purchased at par $26 million worth of 6% semiannual coupon, 8-year bonds. Current rates of return for immunized strategies are 6% and the portfolio manager is willing to accept a return of 5%. Given that the required terminal value is $31,678,475, and if the immunized rates rise to 7% immediately, which of the following is most accurate? The dollar safety margin is:

A) negative (-$1,423,980) and the portfolio manager must switch to immunization. B) positive ($6,158,602) and the portfolio manager can continue with contingent immunization. C) positive ($370,765) and the portfolio manager can continue with contingent immunization

#2

c is correct

FV=-31 678 475

I/Y= 3.5

N=8

CPT PV= 24 057 000

This is how much you need to have to be able to fund your liabilities (if you have more now, then you will be able to pursue contingent immunization)

Now lets calculate what you have

FV=-26 000 000

PMT=-0.03*26 000 000=-780 000

N=16

I/Y=3.5

CPT PV= 24 427 764

24 427 764 this is how much your portfolio is worth. Now substruct 24 057 000 (what you need to have to fund your liabilities) and you get 370 765

#3

thank you so much - just what i needed!

#4

i have a question though, was the initial cushion 992719?

it makes sense to me that it dropped from the above mentioned value to 370765 because immunization rate increased however is the number correct?

thanks

#5

Yes it was 992719.

#6

amazing thanks a lot.

#7

I was wondering if you get the same as the CFA page 37 v4 using the way you showed above. (rates go up to 5.8%). I cannot seem to get the 460.52 that they say they get.

I get 460.58…

#8

rounding errors. depends on how your calculator is set. I get 460.54 I wouldn’t worry about it. In the exam the difference between answers will be clear.

#9

by the way, 1 trick they could use by not giving us the purchase price and thus we need to find:

1- price of the bond first

2- getting terminal required value

3- finding 1st cushion

4- Interest rates change thus we need to find the new pv of the bond

5- new liability too at different interest rate

6-new cushion

7- find decrease / increase in cushion depending on the question posed.

#10

Why do you use the immunized rate of return for the YTM when calculating the PV of assets? Unless I’m missing something, this is a poor worded question. If it says you purchased $26MM worth of bonds at par, isn’t the coupon the YTM? Isn’t your asset value 26MM so that you subtract the PV of liabilities from that 26MM for your dollar margin? I’m confused…

#11

Because YTM on bonds and imunnized rate are the same 6% you assume that they will move in line.

#12

Interesting - is that in the curiculum?

#13

That is my understanding based on the example in the curriculum mentioned earlier p.37 vol4