Not long ago, Vanessa Woods sold her company for several million dollars $($after taxes$).$ She took some of that

money and put it into the stock market. Today, Vanessa's portfolio of blue$-$chip stocks is worth $$3\mathrm{.}9$ million.

Vanessa wants to keep her portfolio intact, but she's concerned about a developing weakness in the market for

blue chips. She decides, therefore, to hedge her position with six$-$month futures contracts on the E$-$mini Dow

Jones Industrial Average, which are currently trading at $12,170.$

a$.$ Why would she choose to hedge her portfolio with the DJIA rather than the S&P $500?$

b$.$ Given that Vanessa wants to cover the full $$3\mathrm{.}9$ million in her portfolio, describe how she would go about setting

up this hedge.

c$.$ If each contract required a margin deposit of $$5,015,$ how much money would she need to set up this hedge?

d$.$ Assume that over the next $6$ months stock prices do fall, and the value of Vanessa's portfolio drops to $$3\mathrm{.}2$

million. If E$-$mini DJIA futures contracts are trading at $10,850,$ how much will she make $($or lose$)$ on the

futures hedge? Is it enough to offset the loss in her portfolio? That is$,$ what is her net profit or loss on the hedge?

e$.$ Will she now get her margin deposit back, or is that a "sunk cost"$-$gone forever?