Question

Elliot Karlin is a 35-year-old bank executive who has just inherited a large sum of money. Having spent several years in the bank's investments department, he's well aware of the concept of duration and decides to apply it to his bond portfolio. In particular, Elliot intends to use $1 million of his inheritance to purchase four U.S. Treasury bonds:

Bond 1 An 8.67%​, ​13-year bond​ that's priced at $1,099.60 to yield 7.46%.

Bond 2 7.849 % ​15-year bond​ that's priced at $ 1026.57 to yield 7.55%.

Bond 3 20-year stripped Treasury​ (zero coupon)​ that's priced at $ 199.67 to yield 8.22%.

Bone 4 24-year,7.49 % bond​ that's priced at $ 960.33 to yield 7.86%.

QUESTIONS: thumbs up for correct answers

A. Find the duration of the whole bond portfolio if Elliot puts $ 250,000 into each of the 4 U.S. Treasury bonds.

The duration of this portfolio is (blank) years ?

B.  Find the duration of the portfolio if Elliot puts $330,000 each into bonds 1 and 3 and $170,000 each into bonds 2 and 4.

The duration of this portfolio is (blank) years ?

C. Which portfolio - the portfolio in part b or the portfolio in part c—should Elliot select if he thinks rates are about to head up and he wants to avoid as much price volatility as​possible? ​(Choose the best answer​ below.)

a. He should invest in either portfolio. The portfolio in part c has a higher duration than the portfolio part b If rates are about to​ rise, then it is equally safe to invest in either​ portfolio, because both portfolios would be equally price volatile

b. He should invest in the portfolio in part c. The portfolio in part c has a higher duration than the portfolio in part b If rates are about to​ rise, then it is riskier to invest in the portfolio in part b because it would be more price volatile than the other portfolio.

c. He should invest in the portfolio in part b. The portfolio in part c has a higher duration than the portfolio in part b If rates are about to​ rise, then it is safer to invest in the portfolio in part b because it would be less price volatile than the other portfolio.

d. He should invest in the portfolio in part c. The portfolio in part b has a higher duration than the portfolio in part c If rates are about to​ rise, then it is safer to invest in the portfolio in part b because it would be less price volatile than the other portfolio.

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

A B C D E F G H I 1 Bond Maturity Settlement in years date 13 Maturity Par value date 1/1/2013 $1,000.00 1/1/2015 $1,000.00 1/1/2020 $1,000.00 1/1/2024 $1,000.00 Annual Coupon rate Duration Price YTM (Semi-annual payment) (in years) 8.670% $1,099.607.46% 8.2849 7.849% $1,026.577.55% 9.1494 0.000% $199.67 8.22% 20.0000 7.490% $960.33 7.86% 11.2432 15 20 1/1/2000 1/1/2000 1/1/2000 Bond Weight Duration (in years) 8.2849 9.1494 20.0000 11.2432 Amount invested $250,000 $250,000 $250,000 $250,000 $1,000,000 0.25 0.25 0.25 0.25 Duration of Portfolio 12.1694 years Bond Weight Duration (in years) 8.2849 9.1494 20.0000 11.2432 Amount invested $330,000 $170,000 $330,000 $170,000 $1,000,000 0.33 0.17 0.33 0.17 4 Duration of Portfolio 12.8007 years 28 C. 29 30 31 Correct option: c. He should invest in the portfolio in part b. The portfolio in part c has a higher duration than the portfolio in part b If rates are about to rise, then it is safer to invest in the portfolio in part b because it would be less price volatile than the other portfolio. 32 34

Cell reference -

2 A B Bond Maturity in years Settlement date Maturity date 13 15 =DATE(2000,1,1) |=DATE(2000,1,1) =DATE(2000,1,1) =DATE(2000,1,1) =DATE(2000+C4,1,1) =DATE(2000+C5,1,1) =DATE(2000+C6,1,1) =DATE(2000+C7,1,1) Par value Annual Coupon rate (Semi-annual payment) Price YTM Duration (in years) 1000 0.0867 1099.6 0.0746 =DURATION(D4, E4, G4,14,2,3) 1000 0.07849 1026.57 0.0755 =DURATION(D5, E5, G5,15,2,3) 10000 199.67_ 0.0822 =DURATION(D6, E6,66,16,2,3) | 1000 0.0749 960.33 0.0786 =DURATION(D7,E7,67,17,2,3) | 20 24 Bond Duration (in years) Amount invested Weight =J4 =J5 250000 250000 250000 250000 =SUM(D11:014) =D11/$D$15 =D12/$D$15 =D13/$D$15 =D14/$D$15 =J6 =J7 Duration of Portfolio =SUMPRODUCT(C11:C14, E11:E14) years Bond Duration (in years) Amount invested Weight =J4 330000 =J5 =D20/$D$15 =D21/$D$15 =D22/$D$15 =D23/$D$15 170000 330000 170000 =SUM(D20:D23) =J6 =J7 Duration of Portfolio =SUMPRODUCT(C20:C23, E20:E23) years Correct option: c. He should invest in the portfolio in part b. The portfolio in part c has a higher duration than the portfolio in part b If rates are about to rise, then it is safer to invest in the portfolio in part b because it would be less price volatile than the other portfolio.

Please note :

Portfolio in part b = Elliot puts $ 250,000 into each of the 4 U.S. Treasury bonds.

Portfolio in part c =  Elliot puts $330,000 each into bonds 1 and 3 and $170,000 each into bonds 2 and 4.

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.