Trading Options: Deriving the Value of a Derivative

One of the biggest questions that I get asked is: “What’s the point of trading options?” I give the usual spiel:

  1. Reduce your cost-basis (how much you pay for a trade)
  2. Increase your profitability (the chance you have to make money)
  3. Increase the number of trades you can make, putting the law of large numbers in your favor
  4. Place neutral, bullish, or bearish trades on the market
  5. Thus, you can make money when the market goes up, down, or all around
  6. Use math and probability to make money
  7. Take control of your financial future
  8. And have fun! 🙂

But I’ve come to realize that I can say all these things, but I need to prove them for anyone to actually take it seriously. Investing is not something that comes “naturally”. And with the national savings rate at 2.8% for the month of April 2018, a lot of people think that they don’t have the money to do it.

It takes a some effort, and for that reason, a lot of people don’t really don’t want to do it. It takes some capital, and some commitment, and that’s a scary thought.

As someone who can’t decide on what type of sandwich she wants for at least 10 mins (and even after I make the decision, I still question it) I completely understand the fears.

Trading can be intimidating and scary.

But it is all about trading small, and trading often.

So I am going to walk through a numerical analysis of the Poor Man’s Covered Call (discussed here). And by the end of this blog, the “Why Options?” question will be a little bit clearer.

Poor Man’s Covered Call: The SPY

note: the numbers on this post are from 6/15/2018

1a. Trading Options

The SPY is currently trading at $278.19 (6/15/18). The SPY is an ETF that tracks the SP 500 index, and thus has some pretty broad market exposure. As such, it’s a great stock to trade to match that of the actual SP 500 (SPX).

I am using it in this scenario because it is a simple stock to trade, and doesn’t have many binary events to deal with.

When we trade the Poor Man’s Covered Call, we look to buy the far-out ITM call (below the stock price) at the 70 delta point, and look to sell the near OTM call (above the stock price) near the 30 delta point.

ITM —- STOCK —- OTM

111

For the SPY, this results in trading at the $271 Call at the 66 day expiration (far-out-er), and the $282 Call at the 45 day expiration (near-er).

As you can see in the picture above, it costs us $10.08 to buy the ITM call, and $1.80 to sell the OTM call, for a total debit of $8.28.

The intrinsic value of a call option is equal to the Stock Price – Strike Price. Everything that is left over is the extrinsic value. Intrinsic value basically means that there should be value to the option at expiration.

For example, if I own the 95 call on a $100 stock, I would have $5 of intrinsic value. Upon expiration, I would be able to buy the stock for $95, even though it is actually $100. It’s the opposite for puts. Let’s say I own the 40 put on a $35 stock – I would be able to sell the stock at $40 upon expiration, giving me $5 of intrinsic value.

th (2)

Image via Slide Serve

So in our case, for the long call (271), that would calculate to be 278.19 – 271 = $7.19 of intrinsic value.

  • Stock (278.19) – Option (271) = $7.19

However, the option itself is worth $10.08, giving us 2.89 of extrinsic value.

  • Intrinsic = Stock – Strike
  • Extrinsic = Cost of Option – Intrinsic Value

th (3)

Image via Dough

For the short call, it is composed entirely of extrinsic value. Only ITM options have intrinsic value (which for calls, the strike < stock price, and for puts, strike > stock price).

Thus, the short call is composed entirely of $1.8 of extrinsic value, which is a combo of time value and volatility. The breakdown of this is outside the scope of this article (but I will have a piece soon explaining the option jargon, so be on the lookout!)

To put this trade on, it costs us $8.28. We have to pay the debit of the long call ($10.08), but can subtract the premium received from the short call ($1.8) to get our overall payment. So if we bought 100 contracts, to mimic one share, it would cost us $828 to put that trade on.

Trading Options: Total = $828

1b. Trading Shares

But what if we decided to just buy 100 shares?

It would cost us the [stock price x number of shares bought]. So it would be $278.19 x 100, or $27,819.  And that’s all the math we have to do there. Pretty simple.

  • Stock Price ($278.19) x # of Shares (100) = $27,819

So we are dealing with a $828 investment (assuming we buy 100 contracts) on the option side, and a $27,819 investment on the stock side.

That’s a pretty big difference.

Trading Shares: Total = $27,819

2. Shares vs. Options: When the Stock does a Down Move

So what happens when the stock drops down by 1 standard deviation?

That would be a drop to $264, with the SPY currently at $278.19.

A one standard deviation move is represented by 16 delta, with the high end predicted by the 16 delta call, and the low end predicted by the 16 delta put.

111111.png

As seen in this (tiny) picture, a one standard deviation move would encompass the stock from 264 to 286. A two standard deviation move (not pictured), represented by the 2.5 delta point  (95% of the data), would encompass the stock from about 245 to 300 based on deltas.

normal dist

Image via Statistics How To

If the stock drops to 264, that means that we lose all of the intrinsic and extrinsic value in the long call option.

For illustrative purposes, we are going to work within this one standard deviation and assume that the stock price declined to $272.

If the stock declines to $272, we still have $1 intrinsic value left in our long call option (which we traded at $271). We can also add that premium collected from the short option ($1.8) to reduce our loss.

This gives us a total value of $2.8 ($1 intrinsic value + $1.8 premium). We subtract that from the debt we paid, which was $8.28, and realize a $5.48 loss (or $548 on 100 contract).

Trading Options: $548 loss 

Shares

On our stock trade of 100 shares, we would only interact with the stock price and the current stock price to calculate our loss. So we bought the stock at $278.19, and realize a loss of simply the difference between the price we bought it at and the price that it is now. (278.19 – 272) = $619. That would bring our total loss for 100 shares to $619, which is 2.2% on our investment.

Trading Shares: $619 loss

So we actually lose LESS dollar value trading with options, albeit we lose more of our total percentage invested. We have more invested in the shares, so we theoretically don’t lose as much. But both are still losers.

BUT do not worry, dear reader! I’ve saved the best for last. Let’s see what happens when the stock moves up.

3. Shares vs. Options: The Up Move

So what happens if the stock moves up by 1 standard deviation?

This means that the stock price would move to 286. Working within that band again, let’s assume, for ease and simplicity, that the stock goes to $284.

However, we have to be careful with calculating our new intrinsic value.

We can only make more money past the 282 short call strike price in our options trade.

Any point past this (283, 284, etc) we stop experiencing an increase in the intrinsic value of the option that we hold. So at the point of 284, we only have (282 – 271) $11 of intrinsic value. Even if the stock went to $300, $400, or $1,586, we would still have $11 of intrinsic value on this trade.

And this is not necessarily a bad thing. We are reducing our overall risk in order to improve our probability of profit. Risk / reward. Reduce the risk, reduce the reward.

Taking the $11 of intrinsic value, and adding on the premium of $1.80 that we collected from the short call, we get a total of $12.8. Then subracting our the debit paid ($828), we get a total profit of $452.

This represents a $452 gain on investment, or a 55% return on the trade investment of $828.

Let me repeat that. 55% return.

FIFTY FIVE PERCENT. Let me tell you, unless you somehow find the next Apple or Facebook, and pick them right before they shoot up, that kind of return is not going to happen in the world of shares.

And let me prove it to you.

For the stock, we would make (284 – 278.19) a profit of $5.81. Multiplied by the 100 shares, this results in a profit of $581. Which is a pitiful return (2%) compared to 55%.

Takeaways

Overall, investing is kind of just a little bit scary. It’s takes some effort. It takes some capital.

But if you can make 55% return over the course of 40- 60 somewhat days? It is entirely worth it.

And imagine doing that again. And again. And again. Maybe 8 times per year, you invest $800 and make $450. I am sure many people would love to see a 55% return stamped onto their portfolio at the end of the year (myself included!)

With that being said, I am NOT promising that this is going to happen when you begin trading. I’ve been burned by options (Brazilian ETF; horrible memories)

And I am still having trouble dipping my toes completely back in the water.

Also, this is NOT investment advice. I am NOT an advisor, by any means. Please, do not consider this as advice.

This is a finance blog, for learning and education.

This is so you can learn that it is entirely possible to actually mathematically determine the probability that you will make money. It is probable to take your financial future by the reins, even though it is a little scary.

Enjoy doubing, tripling, quadrupling, and octupling your returns.

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