You would like to be holding a protective put position on the stock of XYZ Co. t

Question

You would like to be holding a protective put position on the stock of XYZ Co. to lock in a guaranteed minimum value of 50 at year-end. XYZ currently sells for 50. Over the next year, the stock price will either increase by 10% or decrease by 10%. The T-bill rate is 4%. Unfortunately, no put options are traded on XYZ Co.

How much would it cost to purchase if the desired put option were traded? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

What would be the cost of the protective put portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

You would like to be holding a protective put position on the stock of XYZ Co. to lock in a guaranteed minimum value of 50 at year-end. XYZ currently sells for 50. Over the next year, the stock price will either increase by 10% or decrease by 10%. The T-bill rate is 4%. Unfortunately, no put options are traded on XYZ Co.

Explanation / Answer

H = (C - C )/(S - S) = -5/10 = -0.5 The hedge ratio is -0.5.

The hedge ratio is -0.5. A portfolio comprised of one share and two puts would provide a guaranteed payoff of 55, with present value of 55/1.04 = 52.88. Therefore,

S + 2P = 52.88

50 + 2P = 52.88

P = 1.44

The hedge ratio is -0.5. A portfolio comprised of one share and two puts would provide a guaranteed payoff of 55, with present value of 55/1.04 = 52.88. Therefore,

S + 2P = 52.88

50 + 2P = 52.88

P = 1.44

The protective put strategy = 1 share + 1 put = 50 + 1.44 = 51.44

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