Question

5. Duration as an Approximation (Empirical) This question has two purposes. The first is to get you back in front of a computer and either coding the solution using a programming language or utilizing a spreadsheet to do the calcu- lations. Either is acceptable and a valid method of engaging with the question. The second is to have you more thoroughly explore the concept of duration. I will give you two bonds with different payment structures but the same time to maturity. What I want for you to do for each bond is to 1) Calculate the yield to maturity of the bond 2) Calculate the modified duration of the bond 3) Using our Duration expression from class P = -D* Ay graph the percentage change in price as a function of the change in yields 4). Calculate the actual change in price for the bond for the same percentage change in yields and graph the two functions on the same graph, using the fact that P = PV. (For the purposes of defining the domain of the above functions we will be graphing you want to go plus or minus 2 percentage points). (a) A coupon bond with a par value of $1000 and an annual coupon of 3 percent that's selling at a price of $957.
THE TIME TO MATURITY OF THE BONDS IS 5 YEARS

Answer 1

1.)

Yield To Maturity be r. - Catfag veture Present valuelt en tot where C= coupon payments (a) PV = 957 n=5 . FV = 1000 C=30 So, using Hatre equation o 957 = 30 + 30 + 30, + 30, + 30+10 to [112e (1rojo (1+r) T1+r) solding above equation we get r = 3.965 % PV = 134 5 FV = 1000 n - 5 C-80 c) PV=854 using equation 1345 = 80 + 80 , + 80 + 804 + 80-71000 Ho (1+² (1+rja (ltr). (1+r) solving above for a we get r='0.91 % for a zero coupon bond, to wield to Maturity - 1 591 10054 - 1 = 1. 032068-1 = 3.2068% Scanned with CamScanner