Contingent immunization example CFAI

[patso]

Contingent immunization example in CFAI material. We are told a firm has $500m and a 3-year investment horizon over which it must earn 3% and it can immunize its asset portfolio at 4.75%. I don’t understand the bit about dropping YTM to 3.75%.

 

[Galli]

Can you share a page number so we know what you’re referring to?

 

[broadex]

FIRST PART – EAST BIT:
Required terminal value =500*(1+0.03/2)2*3 =546.72
What is required to meet the terminal value at the prevailing rate - 546.72/(1+0.0475/2) 2*3=474.9
Cash at hand: 500
Dollar safety margin to play with = 500-474.9 = 25.1
SECOND PART - DIFFICULT PART:
If the manager invests the entire 500 million in 4.75%, 10-year notes at par and the YTM immediately changes to 3.75%, what will happen to the dollar safety margin?
Required terminal value =500*(1+0.03/2)2*3 =546.72
What is required to meet the terminal value at the prevailing rate 3.75%: 546.72/(1+0.0375/2) 2*3=489.06
Cash at hand: PV of PMT = 500 * .0475/2; N=10*2; FV = 500; I/Y = 3.75/2 = 541.36
Dollar safety margin to play with = 541.36-489.06 = 52.3
Hope this addresses your concern.

 

[hiteshsavanth]

Hey! When YTM drops to 3.75% the current portfolio value rises to 541.36, but to create 546.72 at 3.75% we need only 489.06, hence creating a buffer of 52.3! The buffer increased because the portfolio value sharply shot up (greater than the increase in required value from 474.9 to 489.06)… Not sure if I could satisfy your query fully though…