May 23

Premium bond, duration and DV01 - Practice Question (Par 4)

by David Harper, CFA, FRM, CIPM

FRM |

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This question touches on some key bond relationships. Assume the following bond:

  • $100 par
  • 12% semiannual-pay coupon.
  • 8% yield (YTM)
  • 10 years to maturity

Questions:

  • What is the bond's price? (before calculations, you recognize it is a premium bond-yes?)
  • What happens directionally (up or down) to the bond price if the maturity is extended; e.g., to 30 years?
  • What happens directionally (up or down) to the bond's duration if the maturity is extended?
  • What happens directionally to the bond's DV01 if maturity is extended? (This is tricky)
  • Ceteris paribus, what happens to bond duration/DV01 if yield drops to 6%
  • Ceteris paribus, what happens to bond duration/DV01 if bond's credit rating is upgraded?

 

(please try before peeking)

 

 

 

 

 

 

 

 

 

 

Answers:

(i)

Price = $127.18

(ii)

Price goes up (conversely, a discounted bond's price goes down with longer maturity). Yesterday I got a question on the member page about this: why does price increase with maturity for a premium bond. Please look at the graph below - this is related to the bond as it pulls to par. The coupon exceeds the yield, so the longer the maturity, the more the buyer must pay because the buyer will be receiving more above-yield coupons.

(iii)

Duration goes up (Macaulay or modified) with longer maturity

(iv)

DV01 goes up with longer maturity, too. But recall this is tricky because DV01 is a function of duration and price: DV01 =(P)(D)/10,000. In this case of a premium bond, they are both increasing; but if the bond were a discount bond, the effects are offsetting and the DV01 is not always increasing.

(v)

As yield drops, both DV01 and duration increase. The intuition? The yield is the discount rate; to lower it is to increase the present value of the bond's future cash flows. But the distant cash flows will increase more, relative to whole bond. And they have the higher weight in duration.

(vi)

An upgrade will lower the bond's yield, so the same logic above applies: duration increases.

 

Here is an editgrid showing the bond's pulling to par. Note the premium bond as it's price is an increasing function of maturity.

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