Consider the following three bonds:

Bond 1: 2-year maturity, YTM 4.5%, bond price $100.936, $ Duration 188.6

Bond 2: 5-year maturity, YTM 5.5%, bond price $97.865, $ Duration 421.17 Bond 3: 10-year maturity, YTM 6%, bond price $92.64, $ Duration 701.14

Suppose we construct the body of the butterfly by selling 10,000 5- year maturity bonds. In the butterfly, on the wings, we buy qs 2-year maturity bonds and ql 10-year maturity bonds

(a) What are the qs and ql if we build up a cash- and $duration- neutral weighting butterfly.

(b) Build up a butterfly that is $duration-neutral and quasi-curve- neutral to the following flattening scenario (3x/0/-x) and steep- ening scenario (-3x/0/x). (-3x/0/x) means the short wing YTM decreases by 3x bps, the body YTM does not move and the long wing YTM increases by a bps, where x is a positive and relatively small value. What are the qs and ql in your butterfly?