Question

Calculate the duration of a 2-year bond with 8% semiannual coupon selling at par

if interest rate decreases by 1 percentage point,by how much will the price of the bond change, based on the Duration model?

Answer #1

Macaulay duration of a par value bond (semi-annual coupon) = ((1+YTM/2)/YTM)*(1-1/((1+YTM/2)^(2*m)))

YTM = Yield to maturity = 8%

m = Number of years = 2

Macaulay duration of a par value bond (semi-annual coupon) = ((1+0.08/2)/0.08)*(1-1/((1+0.08/2)^(2*2)))

Macaulay duration of a par value bond (semi-annual coupon) = 1.8875455

Modified duration = Macaulay duration/(1+YTM/m)

Modified duration = 1.8875455/(1+0.08/2)

Modified duration = 1.814947596

Percentage change in bond price = -Modified duration *Change in interest rate

Percentage change in bond price = -1.814947596*(-0.01) = 0.0181497

Percentage change in bond price = 1.81497%

Hence, the bond price increases by 1.81497%

Show all work please.
a) What is the duration of a four-year semiannual coupon bond
with a 6 percent coupon rate selling at par?
b) What is the duration of a three-year semiannual coupon bond
with a 6 percent coupon rate selling at par?
c) What is the duration of a two-year semiannual coupon bond
with a 6 percent coupon rate selling at par?
d) Using these results, what conclusions can you draw about the
relationship between duration and maturity?

find with formulas
Modified Duration:
For this
bond: coupon interest rate: 5%. yield: 4%;
semiannual pay; 2 years.
a. find the bond price in decimal
format (as though principal is 1.0) and in percentage-of- par
format.
b. using that price find the Macauley
Duration.
c. using Macauley Duration find
Modified Duration

A 25-year semiannual bond has 10% coupon rate and par value
$1,000. The current YTM of the bond is 10%. Its Macaulay duration
is 9.58 years and convexity is 141.03.
(1) What is the bond’s modified duration? (2 points)
(2) What is the percentage price change if interest rate were to
fall 125 basis points considering both duration and convexity? (4
points)
(3) What is the estimated price with 125 basis points decrease
in yield? (4 points)

Consider the following.
a. What is the duration of a four-year Treasury bond with a 8
percent semiannual coupon selling at par?
b. What is the duration of a three-year Treasury bond with a 8
percent semiannual coupon selling at par?
c. What is the duration of a two-year Treasury bond with a 8
percent semiannual coupon selling at par? (For all requirements, do
not round intermediate calculations. Round your answers to 2
decimal places. (e.g., 32.16))
a
Duration of...

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A 5-year $100 par value bond bearing a 8% coupon rate payable
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22-years and convexity of 415. If the yield decreases by 2%, what
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52.3%
60.6%
80%
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1. What is the duration of a 10-year zero-coupon bond with a par
value of $1,000?
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with a duration of 10 years and a convexity of 135.5. If the
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A bond has a coupon rate of 8% (annualized) and pays semiannual
coupon. It has a par value of
$2000, and a yield of 6%.
It is due in 3 years.
A.Compute the price of the bond.
B.Compute Macaulay duration.
C.If the yield increases by 0.2% compute the approximate price
change using the
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D. If the Federal Reserve hikes rates what effect should it have
on the bond price
.

Please show how to solve using EXCEL ONLY.
10. Calculate the duration of a $1,000, 12‐year
zero coupon
bond using annual compounding and a current market rate
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12. Calculate the duration for a $1,000, 4‐year
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