Ask Question
BusinessBusiness
26 November, 08:46

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

+5
Answers (2)
  1. 26 November, 10:21
    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
  2. 26 November, 11:09
    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
Know the Answer?
Not Sure About the Answer?
Get 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 there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers
You Might be Interested in
Jane contracts Tom, a home developer, to build her a new house. In the contract it states that all necessary parts of the home must be complete before the contract is to be considered finished.
Answers (1)
On Jan 5, a customer returned merchandise that had been purchased earlier on credit. The original sale was for $500, and the cost to the seller was $150.
Answers (1)
A nation's capital stock was valued at $300 billion at the start of the year and $350 billion at the end. Consumption of private fixed capital in the year was $25 billion. Assuming stable prices, gross investment was?
Answers (1)
Margaret, a 35-year-old client who earns $70,000 a year, pays 7.65% of her gross pay in Social Security payroll taxes, spends14% on a 30-year mortgage, and saves 8% of her annual gross income.
Answers (1)
The monthly income of 5,000 workers at the Microsoft plant are distributed normally. Suppose the mean monthly income is $1,250 and the standard deviation is $250.
Answers (1)
New Questions in Business
Match the following definitions with the correct term 1. Delocalization of food production and consumption connections 2. The process of learning culturally specific preferences passed from generation to generation 3.
Answers (1)
Adobe Systems Incorporated reported the following accounts and amounts (in millions) in its financial statements for the year ended November 30, 2013.
Answers (1)
A Trek Cycles manufactures and sells bicycles to retailers. The X-1 model sells for $500 and has per-unit variable costs of $300 associated with its production. The company has fixed expenses of $30,000 per month.
Answers (1)
A firm supplies aircraft engines to the government and to private firms. It must decide between two mutually exclusive contracts. If it contracts with a private firm, its profit will be $2 million, $1 million, or - $1 million with probabilities. 25,.
Answers (1)
Important business data that is not known to the public is considered what type of information?
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?