Question

Both Bond Sam and Bond Dave have 8 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has 3 years to maturity, whereas Bond Dave has 15 years to maturity.

If interest rates suddenly rise by 4 percent, what is the percentage change in the price of Bond Sam?

If interest rates suddenly rise by 4 percent, what is the percentage change in the price of Bond Dave?

If rates were to suddenly fall by 4 percent instead, what would the percentage change in the price of Bond Sam be then?

If rates were to suddenly fall by 4 percent instead, what would the percentage change in the price of Bond Dave be then?

Answer 1

If interest rates suddenly rise by 4 percent

Bond Sam:-

If rates suddenly increase by 4%, the new YTM will be = 8% + 4% =12%

Then current price of bond is:

=PV(12%/2,3*2,80/2,1000)

=901.65

Change in price =901.65-1000/1000 = -9.83

Bond Dave:

If rates suddenly increase by 4%, the new YTM will be = 8% + 4% =12%

Then current price of bond is:

=PV(12%/2,15*2,80/2,1000)

=724.70

Change in price =724.70-1000/1000 = -27.53%

b)

Bond Sam:

If rates suddenly fall by 4%, the new YTM will be = 8% - 4% =4%

Then current price of bond is:

=PV(4%/2,3*2,80/2,1000)

=1112.03

Change in price =1112.03-1000/1000 = 11.20%

Bond Dave:

Then the current price of the bond is:

=PV(4%/2,15*2,80/2,1000)

=1447.93

Change in price =1447.93-1000/1000 = 44.79%