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You have three instruments at your disposal

i. cash yield is 5.5%; ii. 2Y yld 5%; and iii. 10Y zero yld 4.5%.

1.You think Fed is done hiking and cash yield will be stable at 5.5%. However the yield curve will get steeper in the back end. So you want to construct a "steepener" position (long 2Y and short 10Y)

a. what is the duration for all three (hint: cash expires immediately and has a duration of zero);

b. if you have 100M short position in 10Y zero, what is the $dur of that position?

c. how many dollar of 2Y do you need to long to offset the $dur for 10Y short?

d. in order to construct zero-cost portfolio, your total $ position in cash, 2Y, and 10Y will be zero. For the steepener position (long 2Y and short 10Y), what is your position in cash?

e. if 10Y yld goes up by 1 bps and 2Y yld stays the same, what is your duration neutral portfolio?

f. if 2Y yld goes up by 1 bps and 10Y stays the same, what is the duration pnl for the long-short portfolio?

g.what is the one day net interest payment for the portfolio (Note: cash also carries interest payment)