# Should we know how to do contingent immunization?

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

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.

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!

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

Yes: BEY.

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

Correct unless mentioned assume semi annual compounding.

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

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.

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?

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

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?

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.

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

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

It is well covered in Schweser notes.

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

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

Surrender cost is also covered in Schweser

Yep. As well as Net Payment Index.