Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

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 %

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.