Betty and Bob buy 2 October 60 Calls @$7 and sell3 October 65Calls @$4.  At October expiration the stock is $80 per share. Algebraically find their profit /loss, i.e. their P&L.
 
Y = __________per share quoted price. Profit or loss? _____________

This is an options trading problem where Betty and Bob engage in a spread strategy involving buying calls and selling calls. Let's break down the problem algebraically to determine their profit or loss.

### Given:
- Buy 2 October 60 Calls at $7 each.
- Sell 3 October 65 Calls at $4 each.
- The stock price at expiration is $80.

### Step 1: Define Variables
Let $ Y $ be the stock price at expiration. The given stock price at expiration is $ Y = 80 $.

### Step 2: Determine the Payoff for Each Option
1. **Payoff from the October 60 Calls:**
   - Strike Price = $60
   - Stock Price at Expiration = $80
   - Call Option Payoff = $ \max(Y - 60, 0) = \max(80 - 60, 0) = 20 $ per option.
   - Since they bought 2 contracts, total payoff = $ 2 \times 20 = 40 $.

2. **Payoff from the October 65 Calls:**
   - Strike Price = $65
   - Stock Price at Expiration = $80
   - Call Option Payoff = $ \max(Y - 65, 0) = \max(80 - 65, 0) = 15 $ per option.
   - Since they sold 3 contracts, total payoff = $ -3 \times 15 = -45 $.

### Step 3: Calculate the Net Payoff
The total payoff is the sum of the payoffs from the options:

\[
\text{Total Payoff} = (2 \times 20) - (3 \times 15) = 40 - 45 = -5
\]

### Step 4: Calculate the Cost of the Options
1. **Cost for Buying the October 60 Calls:**
   - Cost per option = $7
   - Total cost = $ 2 \times 7 = 14 $

2. **Premium Received for Selling the October 65 Calls:**
   - Premium received per option = $4
   - Total premium received = $ 3 \times 4 = 12 $

### Step 5: Calculate the Net Cost
\[
\text{Net Cost} = 14 - 12 = 2
\]

### Step 6: Calculate the Total Profit/Loss
\[
\text{P&L} = \text{Total Payoff} - \text{Net Cost} = -5 - 2 = -7
\]

So, the profit/loss per share is:

\[
Y = -7 \text{ per share}
\]

**Conclusion:**

- **Profit or Loss?** Loss
- **Loss Amount:** $7 per share.

Would you like to know more details or have any questions?

### Relative Questions:
1. What is a bull call spread, and how does it relate to this problem?
2. How would the profit/loss change if the stock price at expiration was $70 instead?
3. What is the maximum profit possible in this trade?
4. What is the maximum loss possible in this trade?
5. How would different strike prices affect the strategy?

**Tip:** In options trading, understanding the breakeven points can help you assess whether a strategy is worth the risk.

Learn how to calculate profit or loss in options trading using Betty and Bob's spread strategy involving buying and selling call options. Understand the algebraic approach to determining P&L with detailed examples and calculations.

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