Contingent Immunization

CFA Level III Fixed Income
#1

A portfolio manager has decided to pursue a contingent immunization strategy over a three-year time horizon. She just purchased at par $84 million worth of 9.2% semi-annual coupon, 10-year bonds. Current rates of return for immunized strategies are 9.2% and the portfolio manager is willing to accept a return of 8.5%. Given that the required terminal value is $107,829,022, and if interest rates rise to 11% immediately, which of the following is most accurate? The dollar safety margin is

negative (-$3,237,038) and the manager must switch to immunization. B) positive ($1,486,948) and the manager can continue with contingent immunization. C) negative (-$3,237,038) and the manager can continue with contingent immunization.

We are given the required terminal value of $107,829,022. Next, we calculate the current value of the bond portfolio: PMT=($84,000,000)(.046)=$3,864,000, N=20, I/Y=11/2=5.5%, and FV=$84,000,000, CPT → PV=$74,965,511.

Next, compute the present value of the required terminal value at the new interest rate: FV=$107,829,022, PMT=0, N=6, I/Y=11/2=5.5%, CPT → PV=$78,202,549.

Alternatively ($107,829,022) / (1.055)6 = $78,202,548

The dollar safety margin is negative ($74,965,511 − $78,202,549 = -3,237,038) and the manager can no longer employ contingent immunization.

Therefore, a switch to immunization is necessary.

Why is there a need to take back liability with new rate of 11% to 78202548?? In schweser lecture notes there is example of same kind with PV of libility remains the same with original immunization rate…Please clarify should we always take back PVLiability with new rate to find out new safety margin?

#2

Would we actually be required to calculate contingent immunization, the LOS just says Describe. Am I missing something?

#3

OK you received cash to give it back with some interest at some future dates. You invest this cash in a bond portfolio OK?

Safety margin is difference between the actualized Value of your liability against your investments (that you’ll be using to pay back your liability)

Both figures are dependent on interest rates, so I’d say Yes we need to capture these two new values according to Delta interest rates.

Specifically on the above example the two values deflate while your bond portfolio loses more value than your actualized liability

It means that if rates stay as they are …your are currently “under water” you won’t be able to cope with your future liabilities.

#4

I think Immunization rate is the discount rate use to calculate PV of liability, so when the interest rate changes, you must take back PV of liability.

#5

I believe hung is correct, but would add that the original required $107 would have had to have been calculated based on the minimum rate of 8.5%.

Shrubaks, can you please post the Schweser lecture notes question you reference in your question that doesn’t discount this back? Perhaps it’ll be easier to see what the difference between these two situations is

#6

Also confusing that you use 11% to discount both a 3 year item (the liability) and 10 year item (your bonds). Assumes flat yield curve. Wish they made that more obvious.

#7

They did, it says par and immunization rate

#8

Because interest rates go up, then the PV of the liabilities drop down as well, so your new immunization rate changes (the one that sets the PV of the liability equal to the market value).