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 S105 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 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.) Cost to purchase 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.) Cost of the protective put portfolio c. 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. Do not round intermediate calculations and round your final answer to 2 decimal places) Portfolio S-9555 - 114.45 Invest in Tbilis

Answer 1

Solution

Current Price = $ 105

Increased Price = $ 114.45

Decreased Price = $ 95.55

Change in Price = $ 9.45 ($ 114.45 - $ 105)

Change in new prices = $ 18.90 ($ 114.45 - $ 95.55)

To measure the exposure to change in prices we need to calculate Delta

Delta = - (Change in Price/ Difference in new prices)

= - $ 9.45/ $ 18.90

= - 0.5

Calculate Beta to measure risk from the exposure to change in prices

Beta = (Change in Prices - decreased price * Delta)/ 1.07

= ($ 9.45 - $ 95.55)*-0.5/ 1.07

= $ 40.23

a. Cost of purchase = Current Price * Delta + Beta

= $ 105 * -0.5 + $ 40.23

= - $ 12.27

b. Cost of Put Portfolio = Cost of stock + Cost of Purchase

= $ 105 - $ 12.27

= $ 92.73

c.