标题: Qbank: Two puzzles on Dollar safety margin Q [打印本页] 作者: AnalystForum 时间: 2011-7-11 19:10 标题: Qbank: Two puzzles on Dollar safety margin Q
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:
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Answer by Qbank:
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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.
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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.作者: wake2000 时间: 2011-7-11 19:10
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作者: jmh530 时间: 2011-7-11 19:10
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.作者: susana 时间: 2011-7-11 19:10
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.
