Can you help with the following problem and help me understand some of the jargon? I feel jargon is used interchangeably which makes it difficult for a beginner like myself.

The problem:

An investor writes a call option with X=$40 for a price of $6 and buys a call

with X=$50 at a price of $2. The calls are on the same stock and have the same maturity date.

a) Graph the payoff and profit for this strategy at the maturity date of the options as a function of the value of the stock at maturity (i.e., the graph has ST on the x-axis). Label (with a dollar amount) the breakeven profit point (on the ST axis), the maximum profit level (on the profit axis), and the maximum loss level (on the profit axis).

b) Is the investor bullish or bearish on the stock? On what do you base your conclusion regarding the investor's bearish or bullish sentiment?

For starters, I want to make sure I understand what this means "writes a call option with a X = $40".

• Does it mean the investor already owns the stock and is selling a call option for $6, which would give a buyer the option to purchase the stock at the strike price of $40?

I'm trying to understand the logic behind this strategy. This is what I'm thinking, please tell me if I'm on the right track, because I've gone round and round with this in my head.

• Is the investor writing the call for $40, because he/she anticipates the value will stay below $40 and therefore the call buyer will not exercise their option to buy? And, on the plus side, the call writer gets to keep the stock and retain the $6 premium the call buyer paid?

• On the flip side, why would the same investor buy a call for $2 for the same stock with a strike price of $50? In this case, he/she is hoping the same stock he wrote a call on goes above $50. If the value did rise above $50, the investor would exercise the option and receive stock with a value greater than $50 .

• If the value did exceed $50, then the call buyer on the other side would exercise their right and buy it for $40 as they would make a profit. This isn't a good thing for the call writer.

• I don't understand the motivation behind this strategy. I'm going to assume the value of the stock at expiration is $60. In this case, the investor would exercise his call option that he already paid $2 for and buy the stock for $50, sell it on the market for $60, which is a profit of $10, less the $2 he previously paid for the option, making $8 on this deal. On the other side, the call buyer would exercise their option to buy his share of stock for $40, which means the investor ended up with a total profit of 8+6 = $14. I don't understand how this is a win, because he had to sell a stock valued at $60 for $40.

• Is this strategy a covered call? If so, I don't understand the formula.

I also don't know how to make a graph illustrating all of this. I'm hoping you can help!