Math Problem Statement

Refer to the stock options on Microsoft in the Figure 2.10. Suppose you buy a November expiration call option on 230 shares with the excise price of $140.

Required: a-1. If the stock price at option expiration is $144, will you exercise your call?

multiple choice 1 Yes_____ answer No

a-2. What is the net profit/loss on your position? (Input the amount as a positive value.)

Net loss of $(304)

a-3. What is the rate of return on your position? (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

FIGURE 2.10 Stock options on Microsoft, September 4, 2019

Expiration Strike Call Put 27-September-2019 130 8.65 1.03 27-September-2019 135 4.82 2.17 27-September-2019 140 1.99 4.35 15-November-2019 130 11.50 3.55 15-November-2019 135 8.12 5.15 15-November-2019 140 5.32 7.40 Note: Microsoft stock price on this day was $137.49. Source: Compiled from data downloaded from Yahoo! Finance.

Solution

Let's break down each part of the question step by step.

a-1. Will you exercise your call if the stock price at expiration is $144?

  • You bought a call option with a strike price of $140.
  • A call option gives you the right (but not the obligation) to buy the stock at the strike price.
  • If the stock price is above the strike price at expiration, it is in your interest to exercise the option, as you can buy the stock for less than its current market value.

Since the stock price at expiration is $144, which is above the strike price of $140, the answer is Yes.

a-2. Net Profit/Loss on the Position

To calculate the profit or loss:

  1. Exercise Value (Intrinsic Value): The value of the option at expiration (if exercised) is: Exercise Value=Stock PriceStrike Price=144140=4 dollars per share\text{Exercise Value} = \text{Stock Price} - \text{Strike Price} = 144 - 140 = 4 \text{ dollars per share} Since you hold 230 shares, the total intrinsic value is: Total Exercise Value=4×230=920 dollars\text{Total Exercise Value} = 4 \times 230 = 920 \text{ dollars}

  2. Cost of the Option: From the table, the cost (premium) of buying a call option with a strike price of $140 and expiration in November is $5.32 per share. Therefore, the total cost is: Total Cost=5.32×230=1223.60 dollars\text{Total Cost} = 5.32 \times 230 = 1223.60 \text{ dollars}

  3. Net Profit/Loss: Net Profit/Loss=Total Exercise ValueTotal Cost=9201223.60=303.60 dollars\text{Net Profit/Loss} = \text{Total Exercise Value} - \text{Total Cost} = 920 - 1223.60 = -303.60 \text{ dollars} So, the net loss is $303.60. Since the question asks for input in positive value format, the answer is approximately $304.

a-3. Rate of Return on Your Position

To calculate the rate of return:

  1. Initial Investment: The initial investment is the cost of the option, which is $1223.60.

  2. Net Loss: As calculated earlier, the net loss is $303.60.

  3. Rate of Return formula: Rate of Return=Net Profit/LossInitial Investment×100\text{Rate of Return} = \frac{\text{Net Profit/Loss}}{\text{Initial Investment}} \times 100 Substituting the values: Rate of Return=303.601223.60×100=24.81%\text{Rate of Return} = \frac{-303.60}{1223.60} \times 100 = -24.81\%

So, the rate of return is -24.81%.

Summary:

  • a-1: Yes, you will exercise the call option.
  • a-2: The net loss is approximately $304.
  • a-3: The rate of return is -24.81%.

Would you like further details on any step?

5 Related Questions:

  1. How does the strike price influence the profit/loss of an option?
  2. What is the significance of the expiration date in options trading?
  3. Can you explain the difference between a call and a put option?
  4. How would a change in stock price before expiration affect your option’s value?
  5. What are some strategies to reduce risk in options trading?

Tip:

Options trading can involve complex risks, especially when time decay (Theta) reduces the value of the option over time, even when the stock price moves in your favor.

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Math Problem Analysis

Mathematical Concepts

Options Pricing
Profit and Loss Calculation
Rate of Return

Formulas

Exercise Value = Stock Price - Strike Price
Net Profit/Loss = Total Exercise Value - Total Cost
Rate of Return = (Net Profit/Loss / Initial Investment) * 100

Theorems

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Suitable Grade Level

College Level (Finance/Investment Studies)