You would like to be holding a protective put position on the stock of XYZ Company to lock in a guaranteed minimum value of $105 at year-end. XYZ currently sells for $105. Over the next year, the stock price will increase by 9% or decrease by 9%. The T-bill rate is 7%. Unfortunately, no put options are traded on XYZ Company. Required: Suppose the desired put option were traded. How much would it cost to purchase? What would have been the cost of the protective put portfolio? What portfolio position in stock and T-bills will ensure you a payoff equal to the payoff that would be provided by a protective put with X = 105? Show that the payoff to this portfolio and the cost of establishing the portfolio match those of the desired protective put.

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
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You would like to be holding a protective put position on the stock of XYZ Company to lock in a guaranteed minimum value of $105 at year-end. XYZ currently sells for $105. Over the next year, the stock price will increase by 9% or decrease by 9%. The T-bill rate is 7%. Unfortunately, no put options are traded on XYZ Company.

Required:

  1. Suppose the desired put option were traded. How much would it cost to purchase?
  2. What would have been the cost of the protective put portfolio?
  3. What portfolio position in stock and T-bills will ensure you a payoff equal to the payoff that would be provided by a protective put with X = 105? Show that the payoff to this portfolio and the cost of establishing the portfolio match those of the desired protective put.

 

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