Question

this is a problem from actuary class, please give brief reasoning and complete steps, thank you

Unless otherwise specified, questions involving duration assume a flat term structure. I 7.1.2 Suppose that the yield rate and coupon rate on an n-coupon bond are the same. Show that the Macaulay duration is än valued at the yield rate. Find the Macaulay duration of a 6-coupon bond with coupon rate 10% per coupon period and yield rate 10% per coupon period.

"mathematics of investment and credit"

Answer 1

1. Macuglay Deration is calculated by using I duesent value of a bond's cash flows, weighted by length of time to receept and divided by bond's current market value 1. So, first row will be colulated using belowtable. Ideeaed po of cash How Tu of $1 prof Period y X preciod - at 10% cash eash flow x cash H 100 100 100 100 100 100 1000 .909 .827 .751 .683 .621 .565 0564 $ 90.9 § 827 $ 75.1 $68.3 $6201 $ 56.5 & 564 100 200 300 400 soo 600 6000 90.9 165.4 225.3 273-2 310.5 339 3384 47883 f to the by calce, late sum of cement $1000. macaulay auration, we then divide reseat value of these aash How bond rice (adlich we are gosuming (2) macaulay duretion = 4788.3/ 1000 7 4.79