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 IS 5 YEARS

Answer 1

A bond's yield to maturity (YTM) is the rate of return required for the present value of the future cash flows of the bond to equal the current bond price. It is expressed as an annual %.

a. for Bond no 1, based on the above calculation, the YTM is 3.96%. This can also be calculated using the excel function RATE;

RATE= (nper, pmt, pv , fv)

RATE = (5, 30, -957,1000)

nper- period

pmt- annual coupon rate

pv- present market value (expressed as (-)

fv- maturity value.

b. for Bond no 2; Using the same function: the YTM for bond b is 0.91%

RATE= (nper, pmt, pv , fv)

RATE = (5, 80, -1345,1000)

c. for zero coupon bond: YTM for bond b is 3.21%

RATE= (nper, pmt, pv , fv)

RATE = (5, 0, -854,1000)