Today is $\frac{5}{5}.$ You are a pension fund manager and will have to make disbursements on $\frac{7}{3}.$ You plan

on selling bonds worth $$2\mathrm{.}6m$ on $\frac{6}{30}$ to fund this disbursement. You are concerned that interest rates

may rise over this period and would like to hedge your portfolio by using futures contracts. The

following information is available to you $($from a Bloomberg terminal and CME$)$:

Modified Duration of your portfolio $=8\mathrm{.}8$ years.

For futures contracts

Correlation between your portfolio and futures contract $=\mathrm{.}94$

a$.$ Which is the appropriate maturity of the contract?

b$.$ Should you go long or short on the futures contract?

c$.$ What are the optimal number of contracts?

d$.$ How effective can you expect your hedge to be$?$

Answer:

a$.$ Since hedge is till $\frac{6}{30}$ the appropriate maturity would be September

b$.$ Since I already own the bonds $($long position$)$ I would short the futures contract since correlation is $>0.$

c$.$ Number of contracts is given by

$N_f=(\frac{M{D}_B}{M{D}_f})(\frac{B}{f})=(\frac{8\mathrm{.}8}{6\mathrm{.}5})(2,600,\frac{000}{97},125)=36\mathrm{.}24=36$ contracts

d$.$ Hedging effectiveness $={0\mathrm{.}94}^2=\mathrm{.}88=88\%$