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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?

Sagot :

Tundexi

Answer:

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 %

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