Question

You are evaluating a stock that is currently selling for $30 per share. Over the investment
period you think that the stock price might get as low as $25 or as high as $40. There is a call
option available on the stock with an exercise price of $35. Answer the following questions
about hedging your position in the stock. Assume that you will hold one share. The interest
rate is 6%.
1) (5 points) What is the hedge ratio? How much would you borrow to purchase the stock?
What is the amount of your net investment in the stock?
2) (5 points) Complete the table below to show the value of your stock portfolio at the end of
the holding period.

Scenario	low stock price	high stock price
value of stock at year end
repayment of loan
total

3) (5 points) How many call options will you combine with the stock to construct the perfect
hedge? Will you buy the calls or sell the calls?

4) (5 points) Show the option values in the table below.

scenario	low stock price	high stock price
value of call position

5) (5 points) Show the net payoff to your portfolio in the table below.

scenario	low stock price	high stock price
value of stock at year end
value of call position
total

6) (5 points) What must the price of one call option be?

Answer 1

Dear student as per the policies, we are only allowed to answer the first 4 sub parts of the question unless otherwise specifically asked. You can ask Part (5) & (6) as separate one.
# Information given- = boten CMP & $30 per share & Over the investment period - High price (S1) = $40 Dit slots low price (S2) - $25 Exercise price of option = $35 Interest rate = 6% (1) Hedge ratio B(A) = Dal C-C2 si-S2 0.333 z na 5-0 so 40=25 where C, is fair op of call as on expiry at high price Die Max. of Comp on expiry - E.P.;o) 2 2 Max. of ( 40-3JoAna = $5. 0 2 _1 101 C is fair op of call as on expriey at low price - i.e. Max. of (LMP on expiey - E-P., O - max. of (25-35,0) Borrowings = L ito [ AXS₂ - Cz] or L [axs, -C,] Itr [0.333 X 25 –0] 1+0.06 B = $7.851

Net Investment in Stous = CM PXA-B. = $ 30 X 0.333 = $7.85 = $2.14 High Stock price $40 40.333 (2) Scenario low stockprice value of stock at $25*0.333 year end Repayment of loan (WNI) ($8.32 ) Total (Stock portfolio _ at end of holding d.) L$8-32) $5 NI Note: Repayment of Loan = = B(ltr) $7.85 Ult0.06) e $8.32 13 required to To construct the perfect hedge , we are combine One call option with the stock We will sell one call option Value of call position : At low Stock price (S.2) . Max. of ((MPasen Expiry - ELD = max. of (25-35,0) At High stock price (Si) - max. of (a 40 35,0)