Qbank: Two puzzles on Dollar safety margin Q following, willing, manager, decided, required

AnalystForum

Q:
"A portfolio manager has decided to pursue a contingent immunization strategy over a four-year time horizon. He just purchased at par $26 million worth of 6% semiannual coupon, 8-year bonds. Current rates of return for immunized strategies are 6% and the portfolio manager is willing to accept a return of 5%. Given that the required terminal value is $31,678,475, and if the immunized rates rise to 7% immediately, which of the following is most accurate? The dollar safety margin is:
"

Answer by Qbank:
"
We are given the required terminal value of $31,678,475.

Next, we calculate the current value of the bond portfolio: PMT = ($26,000,000)(0.03) = $780,000; N = 16; I/Y = 7/2 = 3.5%; and FV = $26,000,000; CPT → PV = $24,427,765.

Next, compute the present value of the required terminal value at the new interest rate: FV = $31,678,475; PMT = 0; N = 16; I/Y = 7/2 = 3.5%; CPT → PV = $18,269,163.

The dollar safety margin is positive ($24,427,765 − $18,269,163 = $6,158,602) and the manager can continue to employ contingent immunization.
"

Puzzle 1: why it use N=16 for the present value of the required terminal value? It should be:
FV = $31,678,475; PMT = 0; N = 8; I/Y = 7/2 = 3.5%; CPT → PV

Puzzle 2: It seems we always assume semi annual compound here?
why not:
FV = $31,678,475; PMT = 0; N = 4; I/Y = 7%; CPT → PV



Edited 1 time(s). Last edit at Sunday, May 1, 2011 at 11:35PM by hellscream.

wake2000

I think both your puzzles are addressing the same issue. When dealing with bonds, we always use semi annual compounding unless otherwise stated.

NO EXCUSES

jmh530

hellscream; I think you think that N should be 8 because the immunization term is 4 years. But the question says that the par value of the bond, whose maturity is 8 years, is $26 million. So, in order to discount it, you should use N=8*2.

susana

I think puzzle 1 is an error and should be 8, because we are discounting the required terminal value (which was compounded as the PV of the bond at the MAR over the immunization period, or 4 years, for 8 periods semiannually). In puzzle 1 we are not valuing the bond, so i don't see why 16 is used, we are valuing the terminal value over the immunization period which is not 16 periods, but 8.

Puzzle 2 is not really a puzzle, it says that we use semiannual bond so you need to use semiannual rates when constructing immunization for consistency.