Question about Contigent Immunization

Question about Notes, Book 3, page 34.

a) if interest rate increase, a switch to immunization is necessary? Why?

b) Why the question assume the bond is purchased at par, what if it is not? How will the calculation differs?


If reinvestment allowed at I/y then it doesn’t matter that coupon not = I/y . You can always derive a PV if you know coupon , I/y, and N and FV . If interest rate changes then contingent immunization will not work to meet the liability at the horizon . You will have negative dollar safety margin . So you switch to full immunization

int rates rise = safety cushion goes down to zero or negative = must switch back to full immun

Why safety cusion goes down?

If interest increases, shouldnt both liability and immunized portfolio values goes down?

Why the second goes down faster then?

Yea. I get the logic. But Why the immunized portfolio decrease faster than the liability when interest increases?Is it becasue of the coupon payment?

If coupon Not =I/Y. What is the required terminal value? Should I use notional or PV here?

Also, I dont understand: Why PMT=0 when calculating asset required for immunization, yet PMT=coupon rate when calculating current Val of portfolio at current immunization rate?

the liability is a fixed obligation. you owe money, period.

do you think that when interest rates rise, the mortgage you owe on your house goes down? or is it the same money owed to the bank?

No, I think that is wrong.

For example, as a pension fund, the liability is the obligation to future pension benefit(in terms of PV). In this case, its value varies with interest rate. That is th whole point of hedge a single liability by duration.

I can only say you are missing the point (and arguing unnecessarily at this point in time)

on a liability basis, the FV is a fixed number. period. just like the principal of the bond is a fixed number on the asset side (face value of $1000 or whatever)

whatever you discount some fixed number at, is obviously going to change depending on the discount rate. the PV could be any number – depending on the discount rate.

if you owe me $100 in 10 years and will pay me with proceeds from a bond what to you think will happen if int rates go up?

you still owe me $100 but your bond is worth less

The reason the assets fall faster is because the durations of the assets vs the liabilities are not matched. In active management of a bond portfolio a manager will adjust the duration of the portfolio away from the duration of the benchmark (in this case the liability) to reflect their current investment opinion. The situations in the book assume that the duration of the assets are longer than the durations of the liabilities; in this situation when interest rates rise the market value of the assets will fall faster than the market value of the liabilities. In this situation there is a possibility of reducing the cushion spread to 0 and a need to convert to full immunization.

If the manager had correctly positioned the portfolio for an increase in interest rates (eg he had shortened the duration of his assets) then his liabilities would fall faster than his assets. However, this situation increases the cushion spread and does not get the point of possibly having to convert back to full immunization across.


Agree with Finninja. Yea, this is what I thought initially. Guess I missed the assumption that asset duration>liability duration. I read notes only. Is this more explicitly explained in the book?

Another question, pension liability on a firm’s balance sheet, shouldnt that be the PV of future obligations?

That’s why I disagree with Prophet as the definition of a liability.

Thanks, everyone.

you’re wrong, because you are confusing several issues together

lol why dont these people search the forum before they ask these questions… waste of time

and this is why i don’t bother explaining… guy puts in minimal effort, gets minimal response.

^ Good call at this point in the game