Question

Suppose you own $1,000 worth of two-year zero-coupon bonds. (

a) what position would you need to take in 20-year zero coupon bonds to get duration neutral?

(b) Suppose you took the position in 20-year from part (a). Using the duration approximation, what would be the approximate change in the value of your portfolio if the yield curve steepened1%

• I.e., what happens if the 20-year rate increases 100 basis points more than the 2-year rate?• Assume the yield curve started ?at at 5.26% (i.e., y=1/19)

Answer #1

As per given Question

You own Zero coupon Bond for 2 years at $ 1000

**P = M / (1+r) ^{n}**

where:

P = price

M = maturity value

r = investor's required annual yield

n = number of years until maturity

As per given calculation , Price for this zero coupon bond will be P = 1000/1+5.26%)^2

Hence Price for 2 years Bond will be $902.55

Now,

If the same bond issue for 20 years it will be $358.70

A) To keep duration nuetral Bond rate would be )0.495 %

B) In case rate increased to 1 % = 1.495% then for 20 years bond price will be $742.62

There are two bonds in a portfolio. One is a 5-year zero-coupon
bond with a face value of $5,000, the other is a 10-year
zero-coupon bond with a face value of $10,000. The Macaulay
Duration of the portfolio is 7.89, the Modified Duration of the
portfolio is 7.3015. If the price of the 10-year bond is $3,999,
what is the answer that is closest to the yield to maturity of the
5-year bond

10.
Assume you have a portfolio comprising 5 zero-coupon bonds that
have 2 years to maturity and 6 zero-coupon bond with a maturity of
20 years. Assuming semi-annual compounding and that all bonds have
a face value of 100 and that the yield curve is flat at 5% pa, what
is the modified duration of this portfolio?
Group of answer choices
None of the answers provided are correct
7.752
13.711
10.732
7.609

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?

A bond portfolio is made up of $14 million in zero-coupon bonds
maturing in 2 years, and $9 million in zero-coupon bonds maturing
in 24 years. The yield curve is flat at 8%. What is the Macaulay
duration of this bond portfolio? Please enter your answer in years
rounded to two decimal places.

Currently, the term structure is as follows: One-year bonds
yield 8.50%, two-year zero-coupon bonds yield 9.50%, three-year and
longer maturity zero-coupon bonds all yield 10.50%. You are
choosing between one, two, and three-year maturity bonds all paying
annual coupons of 9.50%. You strongly believe that at year-end the
yield curve will be flat at 10.50%.
a. Calculate the one year total rate of return for the three
bonds. (Do not round intermediate calculations. Round your answers
to 2 decimal places.)...

Suppose you would like to create a two-year synthetic
zero-coupon bond. Assume the
following is true: One-year zero-coupon bonds are trading for
$0.93 per dollar of face value
and two-year 7% coupon bonds (with annual payments) are selling
at $983.30 (face =
$1,000).
a) What are the cash flows from the two-year coupon bond?
b) What is the one-year spot rate?
c) What must be the two-year spot rate?
d) Assume you can purchase the two-year coupon bond and unbundle...

For two bonds with equal coupons, duration would be higher for
the bond with the shortest maturity.
A. True
B. False
For bonds of the same maturity and yield to maturity, the lower
the coupon rate, the greater the duration.
A. True
B. False
Convexity is a measure of how much a bond's price-yield curve
deviates from the linear approximation of that curve.
A. True
B. False

Suppose you own following bond portfolio
Face Value
Bond Type
Maturity
yield to maturity
Portfolio I
$88 million
Zero Coupon
5 years
4%
You expect interest rate to rise in near future(hence decrease
the value of bond portfolio). You decided to sell some of 5-year
bond and use that proceed to buy 1.5-year zero coupon bonds with
yield to maturity 3%. If you want new duration of the portfolio to
be 3 years (that mean after selling 5-year bond and...

Sun Bank has six-year zero coupon bonds with a total face value
of $20 million. The current market yield on the bonds us 10%.
A) what is the modified duration of these bonds?
B) what is the price volatility if the max potential adverse move
in yields is estimated at 20 basis points?
C) what is the daily earnings at risk of this bond portfolio?
d) what is the 10-day VAR assuming the daily returns are
independently distributed?

You plan to form a portfolio by investing in a 6-year
zero-coupon bond and a 3-year 6% annual coupon bond with a yield to
maturity of 10%. The target duration of this portfolio is 4 years.
Therefore, ________ of the portfolio value should be allocated to
the zero-coupon bond. A) 37.1% B) 62.9% C) 83.33% D) 24%

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