Question

why occurrence change in bond price as a function of change in yield to maturity and discuss how duration impacts the sensitivity of a bond. why is the feature a concern? what does this mean for investors? can investors avoid this feature, why or why not?

Answer 1

As an example, lets take a case of a semi annual 10yr bond par value 1000 and coupon rate 6.5%
With 8.5% YTM
Par value or FV 1000
Years to maturity 10 * semi annual frequency = 20
Coupon rate 1000* (6.5%/2) =32.5
Frequency semi annual
Yield to maturity/ Market rate is (8.5%/ 2) semi annual = 0.0425
Bond Price formula = Coupon payment* [ 1- (1+r) ^-n] / r + FV/ (1+r) ^n ]
32.5 * ((1-(1+0.0425)^-20) / 0.0425 + 1000/((1+0.0425)^20)
867.06
OR
Method 2
You can use the PV function in excel
PV(rate,NPER,PMT,FV,TYPE)
PV(8.5%/2,20,32.5,1000)
867.06
with 7.90% YTM
Par value or FV 1000
Years to maturity 10 * semi annual frequency = 20
Coupon rate 1000* (6.5%/2) =32.5
Frequency semi annual
Yield to maturity/ Market rate is (7.90%/ 2) semi annual = 0.0395
Bond Price formula = Coupon payment* [ 1- (1+r) ^-n] / r + FV/ (1+r) ^n ]
32.5 * ((1-(1+0.0395)^-20) / 0.0395 + 1000/((1+0.0395)^20)
904.45
OR
Method 2
You can use the PV function in excel
PV(rate,NPER,PMT,FV,TYPE)
PV(7.9%/2,20,32.5,1000)
904.45

• This indicates that when market rate decreases, the bond with its fixed or unchanged coupon rate sells for a higher price

Duration:
Lets take the same example and alter the duration
As an example, lets take a case of a semi annual 10yr bond par value 1000 and coupon rate 6.5% with 8.5% YTM
we know that the bond price is 867.06
with 6yr duration and everything else remaining the same
PV(8.5%/2,12,32.5,1000) = 907.50

with 5yr duration and everything else remaining the same

PV(8.5%/2,10,32.5,1000) = 919.89

• The shorter the duration, the higher is the bond price
• The investor will have to undertsand these two features and do a calculation taking into account all these factors to decide whether to go ahead or not