Question

12.Your pension fund is invested in $40 million worth of bonds with a duration of 5.5 years and $60 million worth of bonds with a duration of 8 years. The "target date" (the date that the fund needs to pay its contributors) is 6.909 years from now. To become duration-matched, the fund needs to shift how much of its money from 8-year duration bonds into 5.5-year duration bonds? Round your answer to the nearest dollar. HINT: This is a challenging one that requires several steps. First, remember that the duration of your portfolio is the weighted average of the durations of the bonds inside of it. You control the weights, which are the percentages you have invested in the different bonds, so think of them as Wa and Wb, where Wb = (1-Wa).

Duration-matching means making the portfolio's duration equal the target date: Wa*Da + Wb*Db = T. Substitute (1-Wa) in for Wb and go through the algebra to solve for Wa. The answer that you get is what the weight of A needs to be in order to become duration-matched. Just multiply that new weight by the total amount of money invested and that tells you how much money you will need to have in A. Compare that number to the current amount ($40 million) and you know how much more of A you need to add after selling the same amount of B.

Answer 1

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H w x 4x E: ENG 05:10 01-08-2020 66 B 35 Х V16 fx L M N o Р Q R S T U V W х Y z AA 2 3 4 TOTAL INVESTMENT IN 2 BONDS = 40 + 60 = 100 WA = 1-WA = WEIGHT OF 5.5 YEAR DURATION BOND WEIGHT OF 8 YEAR DURATION BOND 5 6 7 8 9 10 DA = IN YEARS 5.5 DURATION 8 DURATION DB = 11 WE NEED TO HAVE DURATION = 6.909 12 13 14 15 16 17 18 19 20 REQUIRED DURATION = WA*DA + (1-WA)*DB 6.909 = WA*5.5+ (1-WA)*8 6.909 = WA*5.5+ 8 - WA*8 1.091 = 2.5 (WA) WA = 0.4364 REVISED WEIGHT OF 5.5 YEAR DURATION BOND 1-WA 0.5636 REVISED WEIGHT OF 8 YEAR DURATION BOND 21 22 23 24 25 AS TOTAL AMOUNT OF BOND = 100 SO INVESTMENT IN 8 YEAR DURATION BOND NOW = 56.36 FUNDS NEED TO BE SHIFT FROM 8 YEAR DURATION BOND = ANSWER FUNDS NEED TO BE SHIFT FROM 8 YEAR DURATION BOND = 3.64 4 AS TOLD TO DO] LOAN EAIR OLIVER NOMINAL SBUX excel pv fv DAUTEN reinvest Sheets Sheet11 CASH FLOW royal EVA Sheets HAL... →