Question

For the same bonds in question 9, let us now turn to focus on the relationship between price and yield. Using the measures you calculated above, answer the following of questions. (a) Estimate the new price of the bonds for a 100 basis point increase in interest rates (using DV01) (b) Estimate the new price of the bonds for a 100 basis point increase in interest rates (using the modified duration) (c) Using both duration and convexity measures, estimate the price of the bonds for a 100 basis point increase in interest rates. (d) Now, using the bond pricing formula precisely calculate the new prices of both bonds for an increase in interest rates of 100 basis points. (e) Which of the approximations from parts (a) through (c) provides you with the closest approximation of the new prices that you obtained in part (d)? Why do you think that this measure works best? (f) Without working through calculations, indicate whether the duration of the two bonds would be higher or lower if the yield to maturity is 10% rather than 8%.

          For the same bonds in question 9, let us now turn to focus on the relationship between price
and yield. Using the measures you calculated above, answer the following of questions.
(a) Estimate the new price of the bonds for a 100 basis point increase in interest rates (using
DV01)
(b) Estimate the new price of the bonds for a 100 basis point increase in interest rates (using
the modified duration)
(c) Using both duration and convexity measures, estimate the price of the bonds for a 100
basis point increase in interest rates.
(d) Now, using the bond pricing formula precisely calculate the new prices of both bonds for
an increase in interest rates of 100 basis points.
(e) Which of the approximations from parts (a) through (c) provides you with the closest
approximation of the new prices that you obtained in part (d)? Why do you think that this
measure works best?
(f) Without working through calculations, indicate whether the duration of the two bonds
would be higher or lower if the yield to maturity is 10% rather than 8%.

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Added by Elizabeth P.

Horngren’s Cost Accounting

Srikant M. Datar, Madhav V. Rajan 16th Edition

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Solved by Expert Akash M

08/02/2023

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For the same bonds in question 9, let us now turn to focus on the relationship between price and yield. Using the measures you calculated above, answer the following of questions. (a) Estimate the new price of the bonds for a 100 basis point increase in interest rates (using DV01) (b) Estimate the new price of the bonds for a 100 basis point increase in interest rates (using the modified duration) (c) Using both duration and convexity measures, estimate the price of the bonds for a 100 basis point increase in interest rates. (d) Now, using the bond pricing formula precisely calculate the new prices of both bonds for an increase in interest rates of 100 basis points. (e) Which of the approximations from parts (a) through (c) provides you with the closest approximation of the new prices that you obtained in part (d)? Why do you think that this measure works best? (f) Without working through calculations, indicate whether the duration of the two bonds would be higher or lower if the yield to maturity is 10% rather than 8%.

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Transcript

00:03 Thing even though asking a question like what we need to calculate or compute macaulay duration and modify duration.

00:12 So first calculate macaulay duration d.

00:21 So how we can calculate c multiply by t divided by plus y to the power t.

00:30 M divided by 1 plus y to the power t.

00:36 So here it is the case now sees coupon annual coupon payment t time by yield of maturity m power value.

00:43 So let's put the values here 0 .06 multiply by 5 divided by 1 plus 0 .07 to the power 5 plus 1000 divided by 1 plus 0 .07 to the power 5 when we simplifying it we got 4 .396 now in this the second thing we need to calculate is modified duration md.

01:21 So this is macaulay duration which is represented by d divided by 1 plus y.

01:28 So here it is 4 .396 divided by 1 plus 0 .07.

01:34 So here it is 4 .109.

01:38 Now the second thing we need to calculate convexity and dollar convexity.

01:46 So convexity first we need to calculate here, which is shown by c capital c.

01:53 This is sigma.

01:54 Oh, this is sigma t multiply by t multiply by t plus 1 divided by 1 plus y to the power t.

02:06 So let's plug the values here 0 .06 multiply by 1 multiply by 2 divided by 1 plus 0 .07 to the power 1 plus 0 .06 multiply by 2 multiply by 3 divided by 1 plus 0 .07 to the power 2.

02:35 So this is for 5 years till 0 .06 multiply by 5 multiply by 6 divided by 1 plus 0 .07 to the power 5.

02:50 So when we sort this out, we got 22 .382 talk about dollar convexity.

03:05 So this is c plus which is 22 .3832 multiplied by 1 plus 0 .07 to the power 2.

03:16 So here it is 23 .931.

03:20 This is the second case answers...

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