TWO Year rate zero is currently trading at $4\mathrm{.}80\%$ yield and ten year zero trading at

$4\mathrm{.}40\%$ rate. Overnight cash yield is $5\mathrm{.}5\%$

a$.$ What is the duration for cash, $2y$ and $10y$ bond respectively?

b$.$ You think the yield curve will steepen as the economy slows down and Fed cuts

short term federal fund rate, AND also due to the massive coupon bond supply

from Treasuries. If you LONG $100$ million of $2Y$ bond, how many dollars of

short position do you need to take in the $10Y$ in order to offset the dollar duration

risk?

c$.2Y$ yield went down by $10bps$ and $10Y$ yield went down by $5bps.$ What is your

profit or loss $(PnL)$ for the above position based on duration?

d$.2Y$ yield went up by $10bps$ and $10Y$ yield went up by $20bps.$ What is your PnL

based on duration?

e$.$ What is your position in cash for the zero$-$cost portfolio? What is your one day

interest carry $($net int pmt$)$ for the zero$-$cost duration neutral position?$($hint: for zero$-$cost position, you net long and short position, including cash, is zero.$)$