Ask Question
BusinessBusiness
15 July, 10:19

A stock is selling for $41.60. The strike price on a call, maturing in 6 months, is $45. The possible stock prices at the end of 6 months are $35.00 and $49.00. Interest rates are 5.0%. Given an underpriced option, what are the short sale proceeds in an arbitrage strategy

+4
Answers (2)
  1. 15 July, 11:14
    0
    The short sale proceeds in an arbitrage strategy is 1.2277

    Explanation:

    From the question given,

    The Possible outcome of stock price at end of 6 months (0.5 years)

    The Outcome is:

    The Stock price = 35

    The Strike price = 45

    The Payoff call = max (ST - K, 0) = max (35-45,0) = 0

    The Present value = PV = 0 / (1+5%) ^0.5 = 0

    The possible Outcome 2:

    The Stock price = 49

    The Strike price = 45

    The Payoff call = max{ST - K, 0} = max{49-45,0} = 4

    The Present value =

    PV = 4 / (1+5%) ^0.5 = 3.903

    Then,

    The Probability of both outcomes = 0.5

    Value of call option = 0.5*0 + 0.5 x 3.903 = 1.95

    Therefore, the Short sale arbitrage opportunity is:

    The Short the stock and buy a call option.

    Invest the proceeds at 5% for 6 months:

    Short stock = + 41.6

    long call = - 1.95

    Proceeds = 41.6 - 1.95 = 39.65

    Amount after 6 months = 39.65 * (1+5%) ^0.5 = 40.629

    The Case 1:

    Stock price = 35

    Payoff from long call = 0

    Buy the stock at market price and close the short stock position = - 35

    The Total payoff = 40.629 - 35 = 5.629

    For Case 2:

    Stock price = 49

    Payoff from long call = 49 - 45 = 4

    Buy the stock from market price and close the short stock position = - 49

    Total payoff = 40.629 + 4 - 49 = - 4.3708

    The Present value of payoff from both cases = (0.5*5.629 + 0.5 * (-4.3708)) / (1+5%) ^0.5

    = 1.2581/1.0246 = 1.2277

    Then the Arbitrage payoff = 1.2277
  2. 15 July, 11:41
    0
    Possible outcome of stock price at end of 6 months (0.5 years)

    Outcome 1:

    Stock price = 35

    Strike price = 45

    Payoff call = max{ST - K, 0} = max{35-45,0} = 0

    Present value =

    PV = 0 / (1+5%) ^0.5 = 0

    Outcome 2:

    Stock price = 49

    Strike price = 45

    Payoff call = max{ST - K, 0} = max{49-45,0} = 4

    Present value =

    PV = 4 / (1+5%) ^0.5 = 3.903

    Probability of both outcomes = 0.5

    Value of call option = 0.5*0 + 0.5*3.903 = 1.95

    Short sale arbitrage opportunity:

    Short the stock and buy a call option. Invest the proceeds at 5% for 6 months:

    Short stock = + 41.6

    long call = - 1.95

    Proceeds = 41.6 - 1.95 = 39.65

    Amount after 6 months = 39.65 * (1+5%) ^0.5 = 40.629

    Case 1:

    Stock price = 35

    Payoff from long call = 0

    Buy the stock at market price and close the short stock position = - 35

    Total payoff = 40.629 - 35 = 5.629

    Case 2:

    Stock price = 49

    Payoff from long call = 49 - 45 = 4

    Buy the stock from market price and close the short stock position = - 49

    Total payoff = 40.629 + 4 - 49 = - 4.3708

    Present value of payoff from both cases = (0.5*5.629 + 0.5 * (-4.3708)) / (1+5%) ^0.5

    = 1.2581/1.0246 = 1.2277

    Arbitrage payoff = 1.2277
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “A stock is selling for $41.60. The strike price on a call, maturing in 6 months, is $45. The possible stock prices at the end of 6 months ...” in 📘 Business if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers
You Might be Interested in
The sustainable growth rate is based on the premise that:
Answers (1)
Panther Pacific uses the net method of accounting for purchases and sales. The net method assumes that discounts are taken when a purchase or sale of inventory is made on account.
Answers (1)
The principle prescribing that financial statements reflect the assumption that the business will continue operating instead of being closed or sold, unless evidence shows that it will not continue is the: A. Going-concern principle B.
Answers (1)
One common advantage of a long-term investment is
Answers (1)
Franklin Manufacturing manufactures two models of windows, bay windows and casement windows. Franklin uses an activity-based costing system. The following information about the activities used to produce the company's products has been provided.
Answers (1)
New Questions in Business
Corporate shareholders: A. are proportionately liable for the firm's debts. B. are protected from all losses. C. have the ability to change the corporation's bylaws. D.
Answers (1)
Cash $ 14,000 Accounts payable $ 42,000 Receivables 70,000 Other current liabilities 28,000 Inventories 210,000 Total CL $ 70,000 Total CA $294,000 Long-term debt 70,000 Net fixed assets 126,000 Common equity 280,000 Total assets $420,000 Total liab.
Answers (1)
An employment test for men is used by a police department to find successful candidates. A woman who was denied employment with the police department based on her test scores sues the police chief.
Answers (1)
What is a great marketing strategy
Answers (2)
Ralph owns a small pizza restaurant, where he works full-time in the kitchen. his total revenue last year was $100,000, and his rent was $3,000 per month.
Answers (1)
Home » Business » A stock is selling for $41.60. The strike price on a call, maturing in 6 months, is $45. The possible stock prices at the end of 6 months are $35.00 and $49.00. Interest rates are 5.0%.
Sign Up Forgot Password?