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My question is Please discuss about the following statement

“ the advantages and disadvantages of writing a call option on an existing portfolio of stocks”

Note that

I read an article nearly about that, and I think such a question, but I could not generate a sound idea about that.

Thanks a lot!

—- My answer

The long stock profit equation is $\pi = N_s (S_F - S_ 0)$

The short call profit equation is $ \pi = - N_c [max(0, S_F -X) - C]$

Consider the bullish market expectation, that’s, the stock price is increasing.

If we have only long stock, then the maximum profit from this long stock is infinite. It generates positive infinite profit.

But if we have only short calls, then since the higher stock price is increasing, the final stock price will exceeds the exercise price, so the call fill finish in the money. And thus, the counter party will exercise it, but we generate a loss. And the maximum loss is negative infinity in theory.

As a result, for the bullish market expectation, short call has a disadvantage, but long stock has a advantage.

Next, consider the bearish market expectation, that’s, the stock price is decreasing.

If we have only long stock, then it generates an infinite negative cash flow. We have a big loss.

If we have only short call, then since the stock price is decreasing, the call will finish out of the money, so the counter party won’t exercise it, so we generate a positive profit. We have a constant positive profit.

As a result, for the bearish market expectation, short call has an advantage, but long stock has a disadvantage.

If I put the profit diagrams of short call and long stock together, which one is true? (I cannot decide it at this point)

enter image description here

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  • $\begingroup$ No I don’t know anything about the volatility. I think we should evaluate all conditions about the volatility and anything else related to stock. Please can you expand your answer. @noob2 $\endgroup$
    – 1190
    Commented Apr 12, 2020 at 9:47
  • $\begingroup$ There are 2 questions. (1) Cost and benefits of writing a call on pfolio vs not writing it (just do nothing). (2) Differences between writing call on a portfolio and writing a call on a single stock. IT IS NOT CLEAR TO ME WHICH QUESTION YOU ARE ASKING. $\endgroup$
    – nbbo2
    Commented Apr 12, 2020 at 10:00
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    $\begingroup$ Well that is easy. You receive some revenue from the sale of the Call, but you give up some returns if the portfolio price rises a lot (you do not make as much as if you had not written the call). People say "you make some money now in return for giving up some future price appreciation". Analyze different outcomes (portfolio down, portfolio unchanged, portfolio up a lot) to see what this means. $\endgroup$
    – nbbo2
    Commented Apr 12, 2020 at 10:13
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    $\begingroup$ The 3 diagrams you drew are different only in the strike price X. The diagrams show a high X, a medium X and a low X respectively. $\endgroup$
    – dm63
    Commented Apr 12, 2020 at 13:18
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    $\begingroup$ The 3 diagrams are fine, they are 3 different cases that can happen depending on the Exercise price you choose. $\endgroup$
    – nbbo2
    Commented Apr 12, 2020 at 13:53

1 Answer 1

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Adding a short option position to a long stock position is a risk management strategy to reduce expected loss due to a downward movement in your long position.

You get paid the premium for the cost of forgoing the theoretical unlimited upward movement in your long position.

Don't forget that a bullish or a bearish market doesn't guarantee a similar movement in a single stock.

So, neither of your charts are correct. Selling option will move your profit region upward, and it's a straight line for any price higher than the strike of the option you sold. It's still a linear line for any price lower than the price you paid as you still lose money if it goes lower than the sum of the price you paid and the premium you received.

Profit function is a piecewise function,

Profit = Spot - (P0 - Premium) for Prices lower than strike

Profit = Strike-P0+Premium for prices higher than strike

enter image description here

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  • $\begingroup$ What you said is the covered call strategy. Right? $\endgroup$
    – 1190
    Commented Apr 12, 2020 at 14:03
  • $\begingroup$ @B11b, going long stock and short call option is covered call. $\endgroup$
    – Mehdi Zare
    Commented Apr 12, 2020 at 16:18
  • $\begingroup$ Hmm, then What you Said is different from The Covered call? Can you explain more please? How is its graph? Can you explain your strategy in more detail please? $\endgroup$
    – 1190
    Commented Apr 12, 2020 at 16:21
  • $\begingroup$ How can I write the profit equation and what is the profit diagram? $\endgroup$
    – 1190
    Commented Apr 12, 2020 at 16:24
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    $\begingroup$ You're right, I edited both. $\endgroup$
    – Mehdi Zare
    Commented Apr 12, 2020 at 20:06

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