Trading yld curve slope

You manage a bond arbitrage fund with AUM at $100M.

5Y zero at 1.65%; 30Y zero at 2.30%. Cash at 1.5%

Construct a long short portfolio in 5Y and 30Y that is duration neutral, ie zero overall dollar duration.

1a. calculate modified duration for 5Y and 30Y.

1b. What is the $dur for 100M long position in 30Y zero? You want to hedge the duration risk in 100M

long position in 30Y zero using 5Y note. What is $ amount to take in 5Y ? Do you want to long or short?

1c If 5Y yld goes up by 15 bps, and 30Y goes up by 10 bps, what is your PnL from duration?

1d. If 5Y yld goes dn by 10 bps, and 30Y goes dn by 5 bps, what is your PnL?

1f. What is the daily interest earned if the entire AUM is put in short term cash?

1g. What is the ONE DAY net interest payment from the long short portfolio? (note: portfolio has THREE

components, 5Y,30Y, and cash. The weights add up to be 100%)