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