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 $104 at year-end. XYZ currently sells for $104. Over the next year the stock price will increase by 7% or decrease by 7%. The T-bill rate is 5%. Unfortunately, no put options are traded on XYZ Co. a. Suppose the desired put option were traded. How much would it cost to purchase?(Do not round intermediate calculations and round your final answer to 2 decimal places. Omit the "" sign in your response.) Purchase cost b. What would have been the cost of the protective put portfolio? (Do not round intermediate calculations and round your final answer to 2 decimal places. Omit the"$" sign in your response.) c. What portfolio position in stock and bills will ensure you a payoff equal to the payoff that would be provided by a protective put with X= 104? Show that the payoff to this portfolio and the cost of establishing the portfolio matches that of the desired protective put. S = 96.72 S= 111.28 Portfolio Buy 0.5 shares Invest in T-bills Total

Explanation / Answer

a)

UpPrice = 104*(1+7%) = 111.28

Payoff = max(0, 104 -111.28) = 0

DownPrice = 104*(1 - 7%) = 96.72

Payoff = max(0, 104 -96.72) = 7.28

p = (Rf - d) / (u-d) = (5% - (-7%)) / (7% - (-7%)) = 0.86

put = (0.86*0 + (1-0.86)*7.28) / (1+5%) = 0.99

b)

Protective put = Stock + put = 104 + 0.99 = 104.99

c)

S = 96.72,

0.5 shares = 96.72/2 - 52 = -3.64

T-bills = 52*(0.05) = 2.6

total = -3.64 + 2.6 = -1.04

S = 111.28,

0.5 shares = 111.28/2 - 52 = 3.64

T-bills = 52*(0.05) = 2.6

total = -3.64 + 2.6 = -1.04

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