# contingent immunization mock question

i thought i had this topic nailed, but i’ve got a Boston Society Mock question that’s got me all worked up! It asks for the required terminal value:

cushion spread: 1.5%, safety net return 4%, required initial portfolio amount \$279m, time horizon 2 years

i thought the terminal value is the FV liability at the required return ie.279m * (1+(0.04/2))^4 = 301.9, but the solution uses the cushion rate of 5.5% per annum i.e. 279 * (1+(0.055/2))^4 = 311m. I thought the liability is calculated based on the safety net rate of return, rather than the immunized rate.

Cushion spread = Immunization rate - Safety return on portfolio. If cushion spread is given and is 1,5 % if safety return is 4%, than immunization rate is 5,5%.

To calculate TV you first have compound initial amount with safety return and then discount back by immunization rate to get PVL.

I don’t remember for Boston society case but the second equation looks like an error, 301.9 should be discounted by immunization rate and such steps are required in each official material question.

thanks, but i thought TV is the FVL, rather than the PV of the FVL at the immunized rate.

From which test is this Boston Society? Cannot find that.

It is, you’re correct. Looks like an error by the author to me. It should be …

279 * (1+(0.04/2))^4 = 301.9 (

301.9 / (1+(0.055/2))^4 = 270.85

Initial Dollar Safety Margin = 279 - 270.85 = 8.15

Thank you all. A little disappointing that they made a mistake- it was CFA Boston Society 2017 Q28 afternoon

they have been known to make plenty of mistakes (BSAS).