Contingent Immunization the most confusing shi* in FI.

CFA Level III Fixed Income
#1

Qbank question:

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

Can someone kindly help breakdown the general idea of what steps should be taken in Contingent Immunization and then show me the steps required to answer this question please? No matter how many questions I have done, there is some different way that I get confused which means I am missing the basic understanding of this bloody concept.

#2

It’s A right?

  • The dollar safety margin is the difference between the current value of the portfolio and the PV of the required terminal value (discounted at the available immunization rate)
  • PV of required terminal value = 31,678,475/(1.035^8) = 24,057,000
  • Bonds have changed in value due to the shift in rates
  • New PV of bonds: N = 16, I/Y = 3.5, PMT = -780,000, FV = -26,000,000
  • CPT PV = 24,427,765
  • Dollar Safety Margin = 24,427,765 - 24,057,000 = 370,765
  • As this is a positive value the manager can continue with contingent immunization
#3

A

1: Calculate the current value of the bond portfolio

2: Calculate present value of the required terminal value at the new interest rate Dollar saftey margin = 1-2

#4

It’s C. Swiftly, you discounted the terminal value by 8 years instead of 16 periods.

#5

Why is the new immunized rate used instead of the minimum acceptable return?

#6
#7

He was right. You discount it for the immunization period, not the maturity of the bonds. The immunization period is 4 years with semiannual periods.

#8

because we want to figure out the differential between the PV of the immunized asset base and the PV of our portfolio. Terminal Value/(1.035^16) gives us the Minimum PV where we can immunize. The PV of the assets less the PV terminal value is positive which means we have a positive safety margin.

#9

I agree it’s A and follow swifty

#10

Sh!t. You’re right.

#11

Thanks!

So when do we use the minimum required return then?

#12

I want to know why we use the immunization rate for the bond’s new present value I/Y input - you are supposed to use the yield to maturity for the calculation.

#13

The minimum required return is the rate at which you want your current portfolio to grow and equate your liability in the future. The immunized rate is simply what available in the market.

#14

But the YTM for our bond and the immunization rate in the market is likely going to be differen, so why do I care what the available rate in the market is to get the present value of the bond that I own? I guess you can assume that because your bond was at the 6% immunization rate that it’s YTM has changed in line with the market, but this is often incorrect. There is a blue box question that addresses noting this difference specifically, which makes me think this is really a poor QBank question

#15

Just to not be misleading the answer is indeed A. Thanks for everyones input, will study this again after work.

QBANK Answer:

We are given the required terminal value of $31,678,475.

Next, we calculate the current value of the bond portfolio: PMT = ($26,000,000)(0.03) = $780,000; N = 16; I/Y = 7/2 = 3.5%; and FV = $26,000,000; CPT → PV = $24,427,765.

Next, compute the present value of the required terminal value at the new interest rate: FV = $31,678,475; PMT = 0; N = 8; I/Y = 7/2 = 3.5%; CPT → PV = $24,057,000.

Alternatively $31,678,475 / (1.035)8 = $24,057,000

The dollar safety margin is positive ($24,427,765 − $24,057,000 = $370,765) and the manager can continue to employ contingent immunization.

#16

Alright if you bought today a bond at par where the coupon equal the current market rate. two days later the new interest rate increased and you felt so bad because your coupon is stuck with the lower rate. Your bond will immediately decrease in price because no one would buy it from you at par since your coupon is less than current market rate. So always the bonds must be valused using the current YTM aka current market rate.

#17

2013AM Q8B, another good example. Very easy to do it wrong on exam day…

#18

Thanks for the heads up Frank. I did the 2010AM mock last weekend. Will aim for 2011AM and 2012AM this weekend (long weekend here in Canada) and 2013AM the following weekend - this seems like such a testable topic, its almost inevitable that it will be on the exam.

Do you think the best way to approach these problems is to understand the basic relationship you explained above?

PV of Asset available MINUS PV of Terminal Value (or Liability) required

#19

Yes, I like to start from here, PV of Asset available MINUS PV of Terminal Value (or Liability) required.

Most of the questions fit this approach and it makes sense.

#20

Cheers Frank.