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Chapter 3: Q.23I (page 362)

Find the convexity of a seven-year maturity, 6% coupon bond selling at a yield to maturity of 8%. The bond pays its coupons annually.

( Hint: You can use the spreadsheet from this chapter’s Excel Application on Convexity, setting cash flows after year 7 equal to zero. The spreadsheet is available at www.mhhe.com/bkm; link to Chapter 11 material.)

Short Answer

Expert verified

Answer

Convexity = 37.6310570

Step by step solution

01

Step by Step Solution Step 1: Given information

Coupon = 6%

YTM = 8%

Maturity = 7 years

02

Calculation of Convexity

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Most popular questions from this chapter

You own a fixed-income asset with a duration of five years. If the level of interest rates, which is currently 8%, goes down by ten basis points, how much do you expect the asset price to go up (in percentage terms)?

a. Use a spreadsheet to calculate the duration of the two bonds in Spreadsheet 11.1 if the interest rate increases to 12%. Why does the duration of the coupon bond fall while that of the zero remains unchanged?

(Hint: Examine what happens to the weights computed in column E.)

b. Use the same spreadsheet to calculate the duration of the coupon bond if the coupon were 12% instead of 8%. Explain why the duration is lower. (Again, start by looking at column E.)

Currently, the term structure is as follows: One-year bonds yield 7%, two-year bonds yield 8%, three-year bonds and greater maturity bonds all yield 9%. You are choosing between one-, two-, and three-year maturity bonds all paying annual coupons of 8%, once a year. Which bond should you buy if you strongly believe that at year-end the yield curve will be flat at 9%?

Return to Table 10.1 and calculate both the real and nominal rates of return on the TIPS bond in the second and third years.

Time

Inflation in Year just ended

Par Value

Coupon Payment

Coupon Payment + Principal payment

Total Payment

0


\( 1000 .00




1

2

\) 1020.00

\( 40.80

0

\) 40.80

2

3

\( 1050. 60

\) 42.02

0

\( 42.02

3

1

\) 1061.11

\( 42.44

\) 1061.11

1103.54

Question: A newly issued bond pays its coupons once a year. Its coupon rate is 5%, its maturity is 20 years, and its yield to maturity is 8%.

a. Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 7% by the end of the year.

b. If you sell the bond after one year when its yield is 7%, what taxes will you owe if the tax rate on interest income is 40% and the tax rate on capital gains income is 30%? The bond is subject to original-issue discount (OID) tax treatment.

c. What is the after-tax holding-period return on the bond?

d. Find the realized compound yield before taxes for a two-year holding period, assuming that (i) you sell the bond after two years, (ii) the bond yield is 7% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 3% interest rate.

e. Use the tax rates in part ( b ) to compute the after-tax two-year realized compound yield. Remember to take account of OID tax rules.
See all solutions

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