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 150 at year-end. XYZ currently sells for 150. Over the next year, the stock price will either increase by 10% or decrease by 10%. The T-bill rate is 5%. Unfortunately, no put options are traded on XYZ Co.
a. 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.)
Cost to purchase $
b. What would be the cost of the protective put portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Cost of the protective put portfolio $

Answer 1

Answer:

a. $3.38

b=$153.38

a. Calculation for how much would it cost to purchase if the desired put option were traded

Calculation for Pd=10/100×150=15

Calculation for uS0=10/100×150=15+150=165

Calculation for dS0=150-15=135

Hence

X=150; uS0= 165; Pu= 0; dS0= 135; Pd= 15

Using this formula to find the Hedge ratio

Hedge ratio :Pu- Pd / uSo-dSo

Let plug in the formula

Hedge ratio=0.15/165-135

=-15/30

=-0.5or -1/2

The portfolio comprised of one share and as well as a two puts which provides a guaranteed payoff of $165

Let find the present value:

-0.5S-P= -0.5*165=-82.5

-0.5*150-P=-82.5/1.05= -78.57

P=78.38-75

P=3.38

Therefore how much that it would cost to purchase if the desired put option were traded will be$3.38

b. Calculation for what would be the cost of the protective put portfolio

The Cost of protective put portfolio with a $150 guaranteed payoff will be

$150 + $3.38 = $153.38

Therefore what would be the cost of the protective put portfolio will be $153.38