Question

a) First, consider a 10 year bond with a coupon rate of 7% and annual coupon payments. Draw a graph showing the relationship between the price and the interest on this bond. The price should be on the y- axis and the interest rate on the x-axis. To compute the various prices, consider interest rates between 2% and 12% (use 0.5% increments). So your x-axis should go from 2%, then 2.5% ... until 11.5% and then 12%.

Is the relationship linear (i.e. is the slope constant)? Start at 7%. If interest rates go up or down by 0.5% is the price changing by the same amount? What type of relationship do we observe between prices and interest rates (liner, concave, convex or something else)?

b) Now consider the same bond with 10 year maturity, a face value or $1,000, a coupon rate of 7% (coupon is paid annually) and assume that the yield to maturity on the bond is 7%. Compute the duration of this bond.

c) Next, we are going to analyze the effect of time to maturity on the duration of the bond. Compute the duration of a bond with a face value of $1,000, a coupon rate of 7% (coupon is paid annually) and a yield to maturity of 7% for maturities of 2 to 18 years in 1-year increments (so here we are going to vary the time to maturity and see how duration changes if N=2, 3 ... etc.). What happens to duration as maturity increases?

d) Next, we are going to analyze the effect of the yield to maturity on the duration of the bond. Compute the duration of a bond with a face value of $1,000, a coupon rate of 7% (coupon is paid annually) and a maturity of 10 years as the interest rate (or yield to maturity) on the bond changes from 2% to 12% (consider increments of 1% - so you need to compute the duration for various yields to maturity 2%, 3%, ..., 12%) . What happens to duration as the interest rate increases?

e) Finally, we are going to analyze the effect of the coupon payment on the duration of the bond. Compute the duration of a bond with a face value of $1,000, a maturity of 10 years and a yield to maturity of 7%. Compute the duration for coupon rates ranging from 2% to 12% (in increments of 1%). What happens to duration as the coupon rate increases?

Answer #1

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Part-4

Consider a 10 year bond with a coupon rate of 7% and annual
coupon payments. Draw a graph showing the relationship between the
price and the interest on this bond. The price should be on the
y-axis and the interest rate on the x-axis. To compute the various
prices, consider interest rates between 2% and 12% (use 0.5%
increments). So your x-axis should go from 2%, then 2.5% … until
11.5% and then 12%. Is the relationship linear (i.e. is...

Consider two bonds, both pay annual interest. Bond C
has a coupon rate of 7% annually, with 5 years to maturity. Bond D
has a coupon rate of 8% annually with 5 years to maturity. The
yield to maturity today for these bonds is 6%.
What is the Modified duration for Bond C

Consider a 2-year bond with 6% coupon rate and a yield to
maturity of 7%. Calculate the duration of the bond.

Consider a 7-year semi-annual bond with an annual coupon rate of
9% and a bond equivalent yield (BEY) of 12%. If interest rates
remain constant, one year from now the bond’s price will be
__________.
None of the above.
It depends if it is a semi-annual or an annual bond.
Higher.
The same.
Lower.

A bond with a 2-year maturity has a coupon rate of 13% and a
face value of $1,000. The coupons are paid annually and the next
coupon is due in one year. The bond’s yield to maturity is 13%.
What is this bond’s Modified Duration?

Consider two bonds: bond XY and bond ZW . Bond XY has a face
value of $1,000 and 10 years to maturity and has just been issued
at par. It bears the current market interest rate of 7% (i.e. this
is the yield to maturity for this bond). Bond ZW was issued 5 years
ago when interest rates were much higher. Bond ZW has face value of
$1,000 and pays a 13% coupon rate. When issued, this bond had a...

Consider two bonds: bond XY and bond ZW . Bond XY has a face
value of $1,000 and 10 years to maturity and has just been issued
at par. It bears the current market interest rate of 7% (i.e. this
is the yield to maturity for this bond). Bond ZW was issued 5 years
ago when interest rates were much higher. Bond ZW has face value of
$1,000 and pays a 13% coupon rate. When issued, this bond had a...

A semi-annual coupon bond with 2 years to maturity and 8% per
annum coupon rate has a face value of $1,000 with a yield to
maturity of 12% per annum (compounded semi-annually). Using the
bond’s modified duration, estimate the new bond price when the
yield to maturity immediately changes from 12% per annum to 8% per
annum.
Select one:
a. 66.27 dollars.
b. 996.97 dollars.
c. 930.70 dollars.
d. 864.43 dollars.
e. None of the statements is true.

Consider a 10 year bond with face value $1,000, pays 6% coupon
annually and has a yield-to-maturity of 7%. How much would the
approximate percentage change in the price of bond if interest rate
in the economy decreases by 0.80% per year?
increase by 5.55%
increase by 5.55%
increase by 5.98%
decrease by 5.98%

A bond with a 3-year maturity has a coupon rate of 6% and a face
value of $1,000. The coupons are paid annually and the next coupon
is due in one year. The bond’s yield to maturity is 9%. What is its
Macaulay Duration?

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