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 steepened

1%

I.e., what happens if the 20-year rate increases 100 basis points more than the 2-year rate?

Assume the yield curve started flat at 5.26% (i.e., y=1/19)