Question

Both Bond Sam and Bond Dave have 7 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has 4 years to maturity, whereas Bond Dave has 16 years to maturity.

a) If interest rates suddenly rise by 5 percent, what is the percentage change in the price of Bond Sam?

b) If interest rates suddenly rise by 5 percent, what is the percentage change in the price of Bond Dave?

c) If rates were to suddenly fall by 5 percent instead, what would the percentage change in the price of Bond Sam be then?

d) If rates were to suddenly fall by 5 percent instead, what would the percentage change in the price of Bond Dave be then?

Answer 1

a)

Bond Sam:

If rates suddenly increase by 5%, the new YTM will be = 7% + 5% =12%

Then current price of bond is:

=PV(12%/2,4*2,70/2,1000)

=844.76

Change in price =844.76-1000/1000 = -15.52%

Bond Dave:

If rates suddenly increase by 5%, the new YTM will be = 7% + 5% =12%

Then current price of bond is:

=PV(12%/2,16*2,70/2,1000)

=647.90

Change in price =647.90-1000/1000 = -35.21%

b)

Bond Sam:

If rates suddenly fall by 5%, the new YTM will be = 7% - 5% =2%

Then current price of bond is:

=PV(2%/2,4*2,70/2,1000)

=1191.29

Change in price =1191.29-1000/1000 = 19.13%

Bond Dave:

Then the current price of the bond is:

=PV(2%/2,16*2,70/2,1000)

=1681.74

Change in price =1681.74-1000/1000 = 68.17%