A$.$ John Lemon, a fund manager currently holds $$100$ million par value of Treasury note T$-$A$.$ He is worried that the interest rate might increase in the near future thus thinking of hedging his position using Treasury futures contracts. Suppose the Treasury futures contract is worth of $$20,000$ each. He finds the current cheapest$-$to$-$deliver issue of T$-$notes is T$-$B$.$ The relevant information of T$-$A and T$-$B on his planned settlement date are given below. The conversion factor for the cheapest to deliver issue is $0\mathrm{.}82.$

T$-$ A T$-$ B

Coupon $8\%$ p$.$a$.9\%$ p$.$a$.$

Yield to maturity $8\%$ p$.$a$.8\%$ p$.$a$.$

Maturity $($years$)25$

Par $$100\mathrm{.}00$ $$100\mathrm{.}00$

Price $$100\mathrm{.}00$ $$104\mathrm{.}06$

a$.$ What is the hedge ratio? $(8$ marks$)$

b$.$ How many Treasury bond futures contracts should be sold to hedge the bond? $($Round down to the nearest number$)(3$ marks$)$

c$.$ Besides hedging with futures, explain one other way by which a manager could hedge her long bond positions against an increase in interest rates using derivatives. No calculations are necessary but you should provide some discussion of how the strategy works and whether it provides full or partial protection against rising interest rates. $(2$ marks$)$ how to calculate pvbp for hedge ration?