Question

16. A portfolio manager owns S 15 million par value of bond ABC. The bond is trading at 80 and has a modified duration of 5. The portfolio manager is considering swapping out of bond ABC and into bond XYZ. The price of this bond is 85 and it has a modified duration of 4 Answer the below questions. (a) What is the dollar duration of bond ABC per 100-basis-point change in yield? b) What does that mean? Explain e) What is the dollar duration for the $15 million position of bond ABC? d) How much in market value of bond XYZ should be purchased so that the dollar duration of bond XYZ will be approximately the same as that for bond ABC?

Answer 1

a). Change in yield = 100 bp = 100*0.01 = 1 percent

Change in price = price*(-modified duration)*change in yield

= 80*(-5)*(-1%) = 4

New price = 80 + 4 = 84

Dollar duration = - change in price/ change in yield in decimal = - (84 - 80)/(-1) = $4

b). Dollar duration is the actual dollar amount by which a bond price changes when interest rate change.

c). Market value of 15 million par value = (80/100)*15 = 12 million

Modified duration = 5 so for a 100 bp change in yield, price will change by 0.01*5 = 0.05

Dollar duration of 12 million = 0.05*12 = 0.60 million or 600,000

d). Let D_ABC = dollar duration for 100 bp change in yield for bond ABC

MD_XYZ = Modified duration for bond XYZ

MV_XYZ = market value of bond XYZ at which it will have the same dollar duration as bond ABC

D_ABC = (MD_XYZ/100)*MV_XYZ

MV_XYZ = (100*D_ABC)/MD_XYZ

MV_XYZ = (100*600,000)/4 = 15,000,000

Market value of bond XYZ which should be purchased to equal the dollar duration of bond ABC is 15 million.