Question

Consider a zero-coupon bond with $100 face value that matures in seven years and has a yield of 7%.

i) What is the price when we assume that the (discrete) compounding frequency is semiannual?

ii) What is the bond’s modified duration?

iii) Use the modified duration to find the approximate changes in price if the bond yield rises by 10, 20, 50, 100 and 200 basis points.

iv) evaluate the same bond price if rates changes by -200 bps, -100 -50 -10 -5 0 +5. +200 (bps: 1/10,000 % ie. 200 bps= 2% ) use dp/P approximation=-D (dr) then use convexity adjustment to correct the approximation error?

Answer #1

(i, ii)

(iii)

(excel) Consider a 8% coupon bond
making annual coupon payments with 4 years until maturity
and a yield to maturity of 10%.
What is the modified duration of this bond?
If the market yield increases by 75 basis points, what is the
actual percentage change in the bond’s
price? [Actual, not approximation]
Given that this bond’s convexity is 14.13, what price would you
predict using the duration-with-convexity
approximation for this bond at this new yield?
What is the percentage error?

A 20-year, 6.500% annual payment bond settles on a coupon date.
The bond's yield to maturity is 9.400%.
(a) What is the bond’s Macauley Duration (show your
work, like you did in problem (16) above.)
(b) What is the bond’s approximate modified duration? Use yield
changes of +/- 30 bps around the yield to maturity for your
calculations.
(c) Calculate the approximate convexity for the bond.
(d) Calculate the change in the full bond price for a 40 bps
change...

You happen to have a 20yr bond with 7.5% annual payment which
settles on a coupon date. Bond yield to maturity is 9.4%.
1.What is the bonds Macauley Duration
2. Whats the bond’s approximate modified duration in this
example? Please use yield changes of +/- 30 bps around the yield to
maturity
3.what is the convexity for the bond (approx.)
4. Find the change in the full bond price for a 40 bps change in
yield.

An 8% semiannual coupon bond matures in 5 years. The bond has a
face value of $1,000 and a current yield of 8.21%. What are the
bond’s price and YTM?
calculate using a financial calculator

Given a zero coupon bond with maturity of 5 years and yield of
2% (in annualized units)
Calculate the price of this bond in a continuous and discrete
models
What are the durations and convexity of this bond in discrete
and continuous models?
Assume that the yield goes up by 0.5% calculate the returns
directly and using duration convexity approximation

Consider a 3-year 8% semiannual coupon bond. The YTM of this
bond is 6%. Compute the following
a) Macaulay Duration (use Mac Duration
b) Modified Duration
c) Effective duration (assume a ±50 BP change of Yield)
d) Convexity Factor (use
e) Effective Convexity Factor (assume a ±50 BP change of
Yield)

19. A 20-year, 6.500% annual payment bond settles on a coupon
date. The bond's yield to maturity is 9.400%.
(a) What is the bond’s Macauley Duration (show your
work, like you did in problem (16) above.)
(b) What is the bond’s approximate modified duration? Use yield
changes of +/- 30 bps around the yield to maturity for your
calculations.
20. Consider the bond from problem (19) above.
(a) Calculate the approximate convexity for the bond.
(b) Calculate the change in...

Suppose a 6-year zero-coupon bond with a face value of $100 trades
at $76.235. If the yield increases by 125 basis points, what is the
magnitude of the error between the exact new bond price and the
first-order approximation of the new bond price using the Modified
Duration?

An 8% semiannual coupon bond matures in 6 years. The bond has a
face value of $1,000 and a current yield of 8.3977%. What are the
bond's price and YTM? (Hint: Refer to Footnote 6 for the definition
of the current yield and to Table 7.1) Do not round intermediate
calculations. Round your answer for the bond's price to the
nearest cent and for YTM to two decimal places.
Bond’s price: $ =
YTM: =

a) An HSBC bond has a face value of 1000, a coupon rate of 8%, 3
years until maturity and a yield to maturity of 7%. Calculate bond
duration. D= ? *[cash flowt/(1+YTM)t]}/price of bond where t is
time to maturity and YTM stands for yield to maturity. N.B: You
need to show how you have calculated duration. A single value will
not suffice.
b) HSBC has issued a 9-year bond with YTM of 10% and duration of
7.194 years....

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