# Re-test contingent immunization Q

A portfolio manager has decided to pursue a contingent immunization strategy over a three-year time horizon. He just purchased at par \$93 million worth of 10.0% semiannual coupon, 12-year bonds. Current rates of return for immunized strategies are 10.0% and the portfolio manager is willing to accept a return of 8.5%. If interest rates rise to 11% immediately, what is the dollar safety margin ?

Around 303066?

^ i also get \$303,066 safety margin

PV assets = 86,884,460

Reequired assets = 86,581,393

same here

for similar questions, CFAI might make it even trickier by changing “interest rises immediately” to “rises in one year”.

make sure you use total return calculation to value your bond portfolio, not just the PV of your bond.

passme, if above was ‘change in one-year’, would that mean n just changes in the calc, or is there another step?

not only does n change, you also have to add to your calculated PV with 1 year worth of reinvestment return.

it is semi annual payment, so coupon+couponx(1+I/Y)^0.5 is added to arrive at total bond value.

I think the reinvestment I/Y to use is 10%.

Schweser had this in one of its practice exams.

^this

^this

remember this.(one year later q)

I often got wrong answer on contingent immuz question…Do you write down the formula or inputs for TVM first? Thanks.

Can someone show how they calculated this? I got a slightly different answer but probably making an obvious mistake. Thanks.

Why not show yours first?

For 1 year later , value of the bond =

Bond PV = N=22 , I/Y=5.5 , PMT=-4,650,000 , FV= -93,000,000 CPT PV= +87,148,826

Coupon Reinvestment = 4,650,000*(1.05)+4,650,000 = 9,532,500

Total Assets = 96,681,326

Liability = 93,000,000 * (1.0425^6)/(1.055^4) = 96,367,255

DSF = 96,681,326 - 96,367,255 = 314,070

I did this because I feel tremendously ashamed that I had forgotten how to do the first one . Biting my knuckles in fear

all above correct…303,066

Jana…its a good presentation…

can calculate liability as 119,382/(1.055^4) = 96,367

hope we can kill it in less than 3 minutes…

how do you get required assets of 86,581,393?

the terminal value = 93M(1.0425)^24 = 252,527,381.80

the required assets after the interest rate change = 252,527,381.80 / (1.055)^24 = 69.863,522.15

the new dollar safety margin i get = 86,884,460 - 68,863,522.15 = 18,020,937.85

do i have a wrong input?

the liability has only 3 years time horizon…

Gotcha, thanks for this refresher. It’s stupid mistakes like that that worry me.

If returns fall to the safety net return and you switch to passive management, do you earn the safety net return or the immunization rate? Schweser Book 3 page 33 says the “immunization mode is triggered to lock in the safety net return” (8%) but page page 35 says there is a “lack of assurance that the immunization rate (9%) will be achieved.”

And we always calculate the coupon reinvestment fv at the yield to maturity right? Which we may need to calculate if they do not purchase the bond at par and do not give it to us.

Reinvestment rate is given in the Schweser question. It may says that th yield curve is flat, then YTM=reinvestment rate.

page page 35 says there is a “lack of assurance that the immunization rate (9%) will be achieved.”

Now I notice it’s different from point 1. It may mean that: when the rate rises, the dollar safety margin is 0 and it switches to immunization mode. We have to consider the re-investment in this case, since the immunization rate is a total rate of return… Especially when the yield curve is upward sloping.

i think passive management earns the 9% immunization rate though?

that is the passive rate, why would you earn less than the passive rate of return in the market?

the safety net return of 8% is just locked in (i.e. you wont go lower than 8)