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A fund manager wants to hedge the exposure of her US equity portfolio using futures contracts on the S&P 500. Her portfolio has a value

A fund manager wants to hedge the exposure of her US equity portfolio using futures
contracts on the S&P 500. Her portfolio has a value of 10 million USD and a beta of
1.4. The S&P 500 futures is currently trading at 1,250 points and each contract is for
delivery of 250 USD times the index. What should the portfolio manager do in order
to minimize her risk?

Consider the same situation as in the previous question. Now, the portfolio managerĀ 
does not want to hedge her whole position but instead just reduce the beta of theĀ 
portfolio from 1.4 to 0.5. What should she do?

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