Assume you own the following portfolio:

It is $\frac{2}{15}$ and you want to hedge till $7/31.$ You have the following contracts on the S&P$500$ index

available to you. The correlation between your portfolio and the E$-$minis& P$500$ index is $0\mathrm{.}85$

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 contract has to expire after the hedge date the appropriate contract is September

b$.$ I have a long position and the correlation is positive so I would take a short position in the futures

contract

c$.$ Number of futures contract is given by

$N_f=(\frac{{}_s}{{}_f})(\frac{S}{f})$

Rounding weights to $2$ decimal places:

${}_5=\mathrm{.}22**1\mathrm{.}2+\mathrm{.}37**2\mathrm{.}0+\mathrm{.}12**0\mathrm{.}8+\mathrm{.}28**1\mathrm{.}4=1\mathrm{.}5($rounding to $1$ decimal place$)$

Market value of portfolio $($S$)=12,700,000$

$f=3150**50=157,500$

$N_t={1\mathrm{.}5}^{**}(12,700,\frac{000}{157},500)=120\mathrm{.}9=121$ contracts

d$.$ Hedging effectiveness $={0\mathrm{.}85}^2=\mathrm{.}72=72\%$