Question

A bond has a 7.5% annual coupon rate with 4 years to maturity and pays annual coupon. par value is $1000

1.1 What is the price of the bond if the yield to maturity is 5%

1.2 What is price of the bond if the yield to maturity increases by 0.2%?

1.3 What is the % change in the price of the bond when yield increases by 0.2%?

1.4 What is the bond duration? (YTM 5%)

1.4 What is the modified duration? (prevailing bond yield 5%)

1.5 Using the modified duration, what is the percentage change in the price if the yield increases by 0.2%

1.6 What can you conclude regarding the error-estimate based on the modified duration?

Answer 1

1.1 Inflow (Coupon payment ) = $1000 * 7.5% = $75

Year Inflows Pvf at 5% Present value

1 75 0.952381 71.43

2 75 0.907029 68.03

3 75 0.863838 64.79

4 75 0.822702 61.70

4 1000 0.822702 822.70

Total 1,088.65

Price of Bond, when yield to maturity is 5% = $1088.65

1.2 Year Inflows Pvf at 5.2% Present value

1 75 0.95057 71.29

2 75 0.9035839 67.77

3 75 0.85892 64.42

4 75 0.816464 61.23

4 1000 0.816464 816.46

Total 1,081.18

Price of Bond, when yield to maturity is 5.2% =$1081.18

1.3 Change in price of Bond = (Decrease in price of bond / price of bond ) * 100

= $7.47 / 1088.65 *100

= 0.69%

Change in price of Bond when yield increases by 0.2%( i.e Decrease in price of bond)

= $1088.65 - $ 1081.18

= $7.47

1.4 Year Inflows Pvf at 5% P. value Year*P. value

1 75 0.9523809 71.43 71.43

2 75 0.907029 68.03 136.05

3 75 0.863838 64.79 194.36

4 75 0.822702 61.70 246.81

4 1000 0.822702 822.70 3,290.81

Total 1,088.65 3,939.47

Modified duration = Bond duration / ( 1+YTM)

= 3.6187 / ( 1+0.05)

= 3.446

Bond Duration = Sum of (PV of inflows) / Sum of (Year*PV of inflows)

= $3,939.47 / $1088.65

= $3.6187

1.5 % Change in price of bond = (-1 * Modified duration * % change in YTM in term of basis point)

= ( -1 * 3.446 * 0.2)

= -0.69 %