Let a 2 -year bond with a semiannual coupon rate of \(2.25 \%\) p.a. have a semiannual yield of \(2 \%\) p.a., and a 10 -year bond with a semiannual coupon rate of \(2.5 \%\) p.a. have a semiannual yield of \(3 \%\) p.a.

(a) Calculate the PV01 of each bond.

(b) Assume you own \(N_{1}=\$ 10 M\) face value of the 2 -year bond, and want to protect (hedge) yourself against parallel shifts in the yield curve by shorting the 10 -year bond. How much face value of the 10 -year bond do you need to sell short?

(c) What is the Profit and Loss (PnL) of your combined (long+short) position due to a \(10 \mathrm{bp}\) parallel shift: the 2 -year and 10 -year bond yields both increase by \(10 \mathrm{bps}(10 \times 0.0001)\) ?

(d) What is your PnL due to a 10 bp steepening: the 10 -year yield change is 10 bps more than 2-year yield's change? (Assume the 2-year yield change is 0 .)