 # Immunization ques

AUF has been directed to pursue a contingent immunization strategy for a portfolio MV \$100. Trustees not wiling to accept below 6% return for 5 years the length of time when liability must be paid. Trustees stated that belive an immunization rate of 8% is attainable in today’s market. Portfolio manager has decided to implement this strategy by purchasing \$100 mil in 10 years bonds with an annual coupon bond of 8% semiannually

1. Assuming an immediate (today) increase in the immunized rate to 11%, the portfolio reuired return that would most likely make Price turn to an immunization strategy is closest to:

a) 11%

b) 11.7%

c) 12.5%

b. 11.7%

Can u also show how u arrived at the answer?

I also get 11.7%

TV = 100(1.03)^10 = 134.39

PV of terminal value = 78.676, calculated:

FV = 134.39

n = 10

i/y = 5.5

solve for PV => 78.676

next solve forcurrent MV of portfolio:

FV = 100

PV (from above) = -78.676

n = 20

PMT = 4

solve for I/Y => 5.834% x 2 = 11.7%

mcap11 - all the payments are annual. just so you notice that in this problem.

whether you do annual or semi-annual you end up with a pretty close answer…

CP is there an easier way to solve this? i dont get the logic.

thanks CPK = just assumed since I have never seen an annual coupn bond anywhere in the CFAI texts or exams…must ne a Schweser question!

first case - PV(Liabilities) = 100*1.06^5/1.11^5 = 79.417 Mill

You have 100 Mill Bond available - and that should equal this (at the least) otherwise you will have to end up with immunization.

FV=100, PMT=8, N=10, PV=-79.417

Solve for I/Y => 11.58

If the rate is above that - you will be in a state with zero cushion.Closest = 11.7% (first closest rate).

I am getting 11.58050309

Ans is B?

and where is this question from?

right its B…you guys are amazing…

pls explain “the portfolio required return that would most likely make Price turn to an immunization strategy is closest to:”

10 years bonds with an annual coupon bond of 8% semiannually. So the coupon is paid semiannually.

This questions threw me off – I was wondering what it’s asking for. It asks to calculate I/Y (a required return, but not a discount rate?).

question is asking you for the breakeven point, where your dollar safety margin would be zero.

iso you must solve for the I/Y of the bond portfolio that will get you the same PV as your required terminal value

so in this particular question, the initial immunization rate of 8% is not even needed?

it was needed to know that 100 Mill in bonds were invested to start with. Otherwise you could not have known that. And that 100 Mill was used in the 2nd step.

Thanks CP Seems mcap11’s answer is correct (11.7%) since this is a semiannual bond. Further in the absence of infromation, i auume all 100 initially invested in the bond.

^ the question is technically flawed in a blatant way…

“…purchasing \$100 mil in 10 years bonds with an annual coupon bond of 8% semiannually…”

The bolded part is very confusing.

it is only missing the word “paid” before semi-annually. Also, you know 100 is invested in the bond because its an 8% bond when rates are 8%, so it’s par.