Seeking Alpha

At the request of several readers this is a follow-up of my previous article.

Some readers thought the previous article was too complicated while others thought it didn't contain enough information. That is the perfect backdrop. Those who regularly follow my articles have learned that option strategies are never quite as easy as at first glance and look for more information. Those new to my methods may like to think options are easy as one-two-three and are reluctant to do the homework.

So, in this article I’ll “walk the line” between the two and attempt to provide simplification and clarity.

First, let me simplify the previous article:

1. For the investor who wants to own Apple (AAPL), or any other stock, options can provide a very effective hedge. Investors hedging are not looking to make money on the option, itself, but have a larger picture in focus. For instance, if they hedge their AAPL shares and AAPL takes off, they may lose a little on the hedge, but they achieved the result they really wanted.
2. The “trader” has no such luxury. They are looking to make a gain on the option trade, itself, and there is no offsetting larger goal.
3. The “trader” needs to take into account that there is a cost in any option trade. It is not just the cost of fees/commissions, but the chance the trade loses and doesn’t win.
4. The amount of any gain or loss depends on where AAPL lands at expiry. There are many possibilities and each has a different result.
5. Probability and statistical theory can reduce all these possibilities to a simple calculus that represents the “expected result.”
6. For the average trader, the expected result of a bull call vertical spread is likely a loss and typically around 9%.
7. Above-average traders can use skill to tip the odds in their favor. If they use bull call vertical spreads they need to make the right choices 55% of the time to overcome the inherent costs and break even. They need to be right 63% of the time to make modest gains.
8. Careful selection of different option strategies and strike prices (usually narrower) can increase their chances of success, but still must be selected using their own skill.

If you wanted things simple STOP HERE. If you want more explanation keep reading.

I just won’t be able to provide exactly how these “expected results” are calculated. It requires the use of differential calculus or the appropriate software. For those who want to jump in and try, may I suggest they start by reading about Black–Scholes.

What I can do, however, is give a very simplified but somewhat less exact method that could be employed by the reader. In order to do this I will use the option Greek DELTA. DELTA not only tells us how much an option will move relative to the underlying, it also approximates the probability of the underlying hitting that strike price.

Let me apply this method to AAPL, which is currently trading at \$376. Let’s say the option strategy is a January 2012 bull vertical call spread with strikes at \$380 and \$420. That means buying the \$380 call for a debit of \$19.20 and selling the \$420 for a credit of \$5.05. Net debit of \$14.15.

Let’s now look to the DELTA. The \$380 call has a DELTA of 50%. Unless AAPL closes above \$380 the trader will lose his/her entire investment of \$14.15. The DELTA of 50% tells us that this is a 50% probability. Well, if I have a 50% chance to lose \$14.15, my expected loss is \$7.08.

But we need to look at other loss scenarios to round out the picture. Even if AAPL closes above \$380 the trader will lose some money if AAPL doesn’t reach \$394 (\$380 strike plus \$14 debit). Let’s look at the DELTA of AAPL at \$395 to approximate this. The DELTA is 38%. Hold onto your hat, as I “massage” this number. If there is a 38% chance AAPL reaches \$395 there is a 62% chance it doesn’t. Since I’ve already accounted for 50% of these possibilities (AAPL below \$380) there is a 12% chance that AAPL closes between \$380 and \$395.

Instead of differential calculus, let’s just say that there is a 12% chance of losing somewhere between \$14.15 and zero. The average loss is \$7.08 and has a 12% probability, so the “expected loss” if AAPL closes between \$380 and \$395 is 85 cents. Add this to the “expected loss” if AAPL closes below \$380 of \$7.08 and the combined “expected loss” is \$7.93.

Now we turn to the expected gain. The maximum gain is \$25.85 (\$420-\$380-\$14.15). The DELTA of \$420 is 21%. So the strategy has a 21% chance of making \$25.85. As before, if you have a 21% chance of making \$25.85 you have an expected result of \$5.42.

So far we have covered AAPL below \$380 (50%), AAPL between \$380 and \$395 (12%) and AAPL above \$420 (21%). That leaves the \$395-\$420 corridor and it would be the remaining probability of 17% (100%-50%-12%-21%).

Once again, simplified to making between zero and \$25.85 for an average of around \$13. Expected gain is \$13 times a 17% probability or \$2.21.

Adding all this together, the expected gains are \$5.42 plus \$2.21, which equals \$7.63. Compared with expected losses of \$7.93 it results in a net expectation of a loss of \$.30.

This loss is smaller than my previous article. Let me explain why. Probabilities are expressed by the "Bell Curve." Distributions are clustered around the middle and less likely at the extremities. In order to calculate points on a curve you need differential calculus. So, I said let's just "average" certain results. This gave more weight to the likelihood that AAPL closes higher than it really warranted. That resulted in an overstatement of the potential gains.