An investor shorts 100 shares of XYZ at $40 and …

Business Questions

An investor shorts 100 shares of XYZ at $40 and sells a 1 XYZ Oct 40 put for $5. If the put is exercised when the stock price is $35 and the stock received is used to cover the short position, what is the investor’s profit or loss? a) $500 loss b) $500 profit c) $0 profit d) $1000 profit

Short Answer

The investor’s initial revenue from short selling 100 shares at $40 each and selling a put option for $5 per share totals $4,500. After covering the short position by purchasing shares at $35 each for $3,500, the final profit is calculated to be $500 after adjusting for the put option premium.

Step-by-Step Solution

Step 1: Calculate Initial Revenue from Short Sale

The first calculation involves the proceeds from the short sale. The investor short sells 100 shares of XYZ at $40 each. This results in an initial revenue of:

  • $40 (price per share) x 100 (number of shares) = $4000

In addition to the short sale, the investor sells one put option contract for $5 per share, equating to:

  • $5 (premium per share) x 100 (shares represented by the contract) = $500

Thus, the total initial revenue from both transactions is:

  • $4000 (short sale) + $500 (put option) = $4500

Step 2: Determine the Cost to Cover the Short Position

The next step is to calculate how much it costs to cover the short position once the put option is exercised. The investor must purchase 100 shares at the current market price of $35:

  • $35 (market price per share) x 100 (number of shares) = $3500

This amount, $3500, represents the cost to buy back the shares in order to cover the short sale. Now we update our profit calculation with this cost consideration.

Step 3: Calculate Final Profit or Loss

The final profit or loss is determined by subtracting the cost to cover the short position from the total initial revenue. We calculate this as follows:

  • Profit or Loss = Total Revenue – Cost to Cover
  • Profit or Loss = $4500 (total initial revenue) – $3500 (cost to cover) = $1000

However, we remember to adjust for the premium received from the put option to avoid double-counting:

  • Final Profit = $1000 – $500 (put option premium) = $500

Thus, the investor’s realized profit is $500.

Related Concepts

Short Sale

A trading strategy where an investor borrows shares and sells them at the current market price, hoping to buy them back later at a lower price to profit from the difference

Put Option

A financial contract that gives the buyer the right, but not the obligation, to sell an asset at a specified price within a certain timeframe

Profit Calculation

The process of determining the financial gain or loss by subtracting costs from total revenues, often incorporating various factors like premiums or expenses.

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