A portfolio manager currently manages a number of stock portfolios. One portfolio is

scheduled to be liquidated and so the portfolio manager is concerned about market

movements between now and then. It is January $3$ and the portfolio will be liquidated on

March $30.$

a$.$ The manager decides to hedge the portfolio over the next $3$ months with the S&P

$500$ index contract. The next closest contract matures in June. Given the

circumstances, should they take a short or long position in June futures?

b$.$ On January $3,$ the portfolio value is $$2,369,650.$ The June futures index price is

$167\mathrm{.}95.$ The contracts have a $$250$ multiplier. Portfolio beta is $1\mathrm{.}065.$ Compute

the optimal number of contracts to use to hedge the spot position.

c$.$ On March $30,$ the following conditions exist: The portfolio's value is

$$2,148,812.$ The futures index price is $161\mathrm{.}05.$ Compute the change in the spot

position and the change in the futures position. What was the net change in spot

plus futures?