Why is bond immunization necessary?

I don’t seem to grab this concept no matter how many times i read it. It is stated that immunization is a strategy to minimize the interest rate risk.

“Suppose you have a liability that must be paid off at the end of five years. So you would like to form a bond portfolio that will fully fund it. However you are concerned about the effect of interest rate risk that will have on the ending value of your portfolio.”

Isn’t the simple solution to let the bond mature and pay off one’s liability? Can someone explain me why matching duration of bonds to duration of liabilties are necessary and why should a portfolio manager concerned about the effect of interest rate risk?


you are not answering the big what if --> you planned today for your bond to meet the liability when it became due on a prediction that the bond’s YTM is achieved consistently over the next 5 years.

What if the YTM is not achieved - and you suddenly got an increase in market rates - which would raise the YTM. You end up getting higher coupons - but your END value DROPS … and the big “balloon” (Principal) you expected at the end - may not be achieved.

Reinvestment rate risk is what you are trying to minimize by immunization.

Question. If you invest in a 5 yr fixed bond and rates increase do you receive higher coupons? I thought your coupons would be fixed based on the rate at inception?

just need clarity, thanks!

if it were floating coupons …

Can someone explain me why matching duration of bonds to duration of liabilties are necessary and why should a portfolio manager concerned about the effect of interest rate risk?

To answer this:

The duration of this liability is 5yrs and Lets assume the value of liabitliy is $1 Million.

If you dont match this duration and say you buy a 6yrs bond instead of 5yr, you would have to liquidate this bond when the liability is due, i.e., @ 5yrs. What happens if the Interest rate prevaling during that time is high ? your bond value would be low and when you sell this bond you would END up getting a lower value say $970,000 and would fail to fully match the liability amount of $1 Million.

Hopefully this helps.

Interest rate risk is primarily a concern if you are managing a portoflio against a liability. The uncertainty of the liability can be in terms of amount or timing or both.

Duration measures sensitivity to changes in interest rates. If the duration of your bond portfolio is longer/more than the duration of the liabilities then a rise in interest rates will cause your asset to decline by more than the laibility, possibly leading to a funding shortfall when the laibility is due be paid. Alternatively, if the duration of the asset portfolio is shorter then a fall in interest rates will call the liability to rise by more.

Immunization is designed to ensure that the rise/fall in income is precisely offset by the fall/rise in asset value but only works for a short time and that inroduces the need for rebalancing.

Ganeshrpl, like your answer but why would anybody buy a bond with a maturity that differed from the liability they’re attempting to match? Seems like a simple solution: buy a 5-year note or a bond with 5 years left, no?

my two cents:

immunization is in essence balancing reinvestment risk (of the fixed coupons) vs. price risk (of the principal) in order for the bond asset to retire in full the bond liability.

it just follows to match their duration (their changes in value in response to change in interest rates) so the bond asset and liability values will respond to the same degree to changes in interest rates

You’re suppose to match both duration and convexity.

The base case is a parallel shift in the yield curve as is in the assumption of classical immunization.

Then we can extend to non-parallel shift but it’s getting much more complicated to illustrate.

I understand that portfolio price (value) can fall if interest rates increase, but i’m not sure i understand why price risk is important in the big picture. You know what the face amount will be upon maturity (assuming you hold it the whole time), so who cares if the price fluctuates during the horizon. Seems like the reinvestment risk is the real concern bc you don’t necessarily know what that will be upon maturity.

Can someone help me understand then why price (ie price risk) is such a big deal then?

Thank you in advance!

Only in the case of a guaranteed investment contract is the price guaranteed at the horizon.

If it were a bond (the traditional kind that you were investing in) - the normal behavior would be when rates increase - price drops. This is the reason price risk is important. The same thing is seen in the contingent immunization calculations too if you see them now.

And the purpose of classical immunization is to ensure that the price risk = reinvestment risk.

Here’s the way I’m thinking about it. Say you have a liability due in 5 yrs. You buy a 5-year bond at $1,000 face. Disregarding whether or not the total return was actually earned (which I know can be affected by the available reinvestment rates), you know at year 5 you will get the $1,000 principal. So who cares if the price fluctuated during the 5 years? Seems like the reason for any shortfall would be solely do to reinvestment income.

Isn’t the duration for 5 year bond ALWAYS smaller than 5 years because of coupon payment? (Duration of 5 y Zerobond would be 5?). Therefore if you do have a 5 year liability you would probably have to buy something like 6 year bond…Then at t=5 you have price risk for bond when you repay liability but this would be offset by higher reinvestment income of bond?

Guys, what is reinvestment risk ? Trouble in reinvesting the PREPAYMENTS made by the borrower when the interest rates are low and you not able to earn the intial assumed return. So as guys above have posted, if in 5yrs, say we have a liability of 1000$, u say, simply buy a 5yr bond and hold till maturity to get back the 1000$ on maturity. My question is what happens, if the borrower starts to repay part of the principal say 50$ at 1.5yrs, another 75$ at 2.5yrs and say 65$ at end the end of 3rd year( Assume, no prepayments are made after this) due to very low interest rates. Now you wont be getting the assumed 1000$ at maturity. Rather approx 810$ [1000-( 75+50+65)]. Now you have a risk of not meeting the 1000$ liability as you get only 810$ @ maturity + what ever is the accrued total money, from the reinvestment made on the prinicpal prepayments. The “market value movement of the bonds” & “reinvesment returns” move in opposite directions. That is, as interest rates increase, prices fall but reinvestment rates rise. As interest rates decrease, prices rise but reinvestment rates fall. So they have “OPPOSITE EFFECTS”. Hence its very very important to keep balancing such that the increase in one, offsets the decrease in the other. Therefore, we have to make “Principal risk = reinvestment risk” Hope this puts the basics in perspective.

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Awesome, Dirk. That’s a great example. Thank you and CPK for the help.

That also helps, ganeshrpl. Thanks.

It seems like a change in price could / will have a larger impact than a change in reinvestment rates. Is that generally the case, wrong, or does it depend? I tend to think that investors are more concerned with price movement than what reinvestment rates will be, maybe i’m wrong there.

However, at least in the discussion regarding immunization risk, it seems like reinvestment risk is the larger concern. Not sure if it matters. Maybe it’s best to just know the risks related to each and how to mitigate, instead of which one is the greater of the two risks.

No matter which one is higher or lower, the bottom line is to have them both equal so that they compensate each other’s opposite movement equally and keep us( as a portfolio mgr. managing this portfolio) Immune to any interest rate fluctuation smiley

Not sure if that’s actually right though. CFA Book text has immunisation with bond of same maturity as liability-which to me doesn’t make sense as durations wouldn’t be the same (page 26). So easiest way to see if that’s true would be to calculate duration of 5 year bond and then “make up” liability with same maturity and see what happens if rates change just after t=o. Maybe somebody can just tell me if I’m on right track?

I guess i need to brush up on my duration understanding, but how is it that duration (as the measurement of price sensitivity to interest rates) equals or roughly equals duration (as a weighted average time of future cash flows).

I understand how time relates / effects duration but I just don’t understand how the two measurements (which measure two different things) are essentially equal. Anyone?