# 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: " 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

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

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 is, you should use N=8*2.

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.

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.

markCFAIL’s post for “puzzle 1” is reflected in (QID#:91632).