Determine the appropriate number of puts and shares to hold

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On July 5 a market index is at 492.54. You hold a portfolio that duplicates the index and is worth 20,500 times the index. You wish to insure the portfolio at a particular value over the period until September 20. You can buy risk-free debt maturing on September 20 with a face value of \$100 for \$98.78.

a. You plan to use puts, which are selling for \$23.72 and have an exercise price of 510. Determine the appropriate number of puts and shares to hold. What is the insured value of the portfolio?

b. Determine the value of the portfolio if the index on September 20 is at 507.35.

c. Determine the value of the portfolio if the index on September 20 is at 515.75. Compute the upside capture and the cost of the insurance.

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