Should we know how to do contingent immunization?

CFA Level III Fixed Income
#1

Hi all, Should we know how to do contingent immunization please? I could not find any exercises on it (topic test, CFAI curriculum or mocks). Is this important? Thank you

#2

Yes. Very likely to be tested in my opinion. A question could involve calculating the initial safety margin, or taking it a step further, if rates increased and whether or not a manager could continue active management.

The curriculum actually presents a very good example of the steps involved.

#3

JayWill - is this good example in topic tests, or a blue box in the textbook?

I’ll have a look for some good practice - thanks!

#4

Great thanks JayWill. One question about the formula please.

Why does the formula is Tx2 please? And why do we divide the rate by 2? Is it because it is a semi annual coupon bond? If it were a quarterly bond I would multiply and divide by 4 instead?

Thank you

#5

Yes: BEY.

They won’t give you a quarterly pay bond in a contingent immunization question. That’s not the point of the question.

#6

Correct unless mentioned assume semi annual compounding.

#7

OK thanks a lot guys.

But then the way the formula is presented does not make sense because it assumes a semi annual coupon bond… Just saying :slight_smile:

#8

Sorry I was away for a bit (had to get to work). Page 40 of Reading 25 runs through it. Also, question 8-B of the 2013 AM exam required us to calculate the initial safety margin. Also, 8-C requires an explanation of why widening of credit spreads may require re-immunizing the portfolio again. Basically, question 8 hit these concepts pretty hard.

In regards to why we divide the rate by 2 and multiply the period by 2, you’ll see on the 2013 exam question mentioned above a note that says: “Assume semi-annual compounding”. This kind of stuff is pretty common I’ve found. They tend to be really clear on the actual exams.

#9

I’m fine with initial cushion spread and safety margin. But when rates change, still need to master that.

In page 41 it says: If YTM drops to 3.75…value = $541.36 … how is that worked out?

#10

FV = 500, PMT = 11.875, I/Y = 1.875, N = 20, CPT PV

#11

Ah great, got it now - thanks.

So we essentially can:

  • Work out cushion spread (% difference min return and immunized rate)

  • Work out initial safety margin: Difference between:

    • PV portfolio &
    • PV portfolio converted to FV (using min %) converted back to a PV (using imm %)

  • Invest in a bond - say 10 years, par, at imm rate

  • If YTM changes:

    • Work out new PV of bond (using new YTM, and previously agreed coupon rate)
    • FV of initial PV (using min % - from before), discount this back to today using new YTM to get a PV
    • Difference is new safety margin

Is this correct?

#12

Yep looks like you have it.

I kind of doubt we’d need to actually calculate a change in the YTM though, but if we do, yeah there you have it.

#13

It boils down to Time Value of Money calculation.

  1. If there is no cushion spread, then PV of assets = PV of liabilities or FV of assets = FV of liabilities

  2. If given immunized rate, you obtain the FV of liabilities and discount back to the PV

  3. Safety Margin = PV of assets using required return minus PV liabilities using immunized rate

#14

Was this covered in schweser notes? I have no recollection of this subject

#15

It is well covered in Schweser notes.

#16

Oops, thought I was replying about the surrender cost index. I clearly need coffee :slight_smile: right, immunization was definitely covered

#17

Oops, thought I was replying about the surrender cost index. I clearly need coffee :slight_smile: right, immunization was definitely covered

#18

Surrender cost is also covered in Schweser

#19

Yep. As well as Net Payment Index.