Q$1.$ Ten Year zero is currently trading at $4\mathrm{.}50\%$ yield and thirty year zero trading at $5\mathrm{.}00\%$ yield. Overnight cashyield is $4\mathrm{.}25\%$Q$1$a$.$ You think yield curve will steepen due to the massive coupon bond issuance from Treasuries and lack ofdemand for bonds of longer maturity. How do you express your view using a duration$-$neutral position? Which legto long and which leg to short and how much to long and short? $(3$ points$)($Note: keep $30$Y exposure at $100$ million. You can go long or short that $100$ million $30$Y depending on your choice$).$Q$1$b$.10$Y yld went down by $20$ bps and $30$Y yld went down by $15$ bps$.$ What is your profit or loss $($PnL$)$ for theabove position based on duration? $(3$ points$)$Q$1$c$\mathrm{.}10$Y yld went up by $10$ bps and $30$Y yld went up by $15$ bps$.$ What is your PnL based on duration? $(3$ points$)$Q$1$d$.$ What is your position in cash for the zero$-$cost portfolio? What is your one$-$day interest carry $($net int pmt$)$ forthe zero$-$cost duration neutral position $(3$ points$)?($hint: for zero$-$cost position, you net long and short positions,including cash, is zero$)$