Before embarking on any type of comparative analysis regarding the best option spreads to trade, we need to establish some reasonable estimate as to where a stock price is likely
to be on some future date. We can then assess all possible permutations of Buy and Sell Strikes for an option spread using this stock target to find the combination
that offers the highest return.
So what constitutes a reasonable target for a stock price at some arbitrary date in the future; let's say one week from today. A logical starting point would be to ask,
"how much does the stock typically move over the course of one week?". We could determine this my examining historical weekly returns and computing the
Mean Absolute Deviation (MAD) of those returns. This would tell us the average amount a stock moves in a week without regard to the direction of that move (up versus down).
With a long history of weekly returns you will find that the stock has an equal chance of moving either up or down in price over such a short time frame so the Mean return
will come out to zero.
As elegant as this approach may be, it has some serious short comings. For one, the range of movement may change as a company matures or might vary at different times.
This begs the question, "what is the appropriate look back period for calculating historical returns?". Another issue concerns accounting for dividend payouts. It is a
known phenomenon that a stock tends to drop by the amount of its dividend on xDividend Date. Stock volatility also tends to increase around the time earnings are
being reported. Such events will cause distortions in the future volatility of the underlying stock which would not be reflected in a smoothed out set of historical
returns.
Fortunately, there is an alternative approach to estimating the amount of movement one can expect in a given stock. It is based on the notion that
option premiums reflect the anticipated movement in the underlying stock. If an earnings event is on the horizon, option premiums will rise to reflect the
anticipated increase in volatility. If an xDividend date is pending before an option expires, then Put premiums will be higher than Call
premiums in anticipation of the stock dropping by the amount of the dividend. Calculating the volatility of a stock based on the premiums of the underlying options is
referred to as calculating the "Implied Volatility". The following algorithm will serve to illustrate how this can be accomplished using the
Black-Scholes Option Pricing Model.
Using actual option quotes for the S&P 500 ETF (SPY) expirying on July 21, 2017 (at the close of trading on June 5, 2017), we calculated the maximum returns for buying
either a simple Call or Put option at each strike price that was within our projected lower and upper stock target. The maximum returns were calculated based on the assumption
that the stock would close exactly at our projected target on expiry date. For both Calls and Puts, the highest expected returns occur with a strike price that is
close to the current stock price. We found this pattern to be fairly consistent when testing over multiple stock symbols across different expiry dates. The fact that
options close to the current stock price have higher expected returns than options farther in or out of the money should make sense at an intuitive level. For example, buying
a deep in the money option would require a a large cash outlay there by lowering your return. An option that is far out of the money would be expected to expire worthless
so an at the money option is the best compromise between these extremes. If you take a look at a financial website that displays the implied volatility in its option chains
(e.g. Yahoo Finance), you will notice that in general, the implied volatility decreases as the strike price moves closer to the current stock price. this is another way of saying that these
options are the cheapest.
Using actual option quotes we paired all possible spread combinations for the S&P 500 ETF (SPY) Calls expirying on March 17, 2017 where the strike prices were between the
lower and upper projected targets for the stock. These options had about 4 weeks of time remaining when the analysis was conducted. In the left image below we show only
the set of strike prices paired with a buy strike of 230. However, for all combinations tested; the returns increased as the sell strike was pushed out further toward the
stocks projected upper target. The table on the right summarizes the results for each buy strike. As you can see, the highest return is obtained by selecting a sell strike
just inside the stock's upper target and a buy strike exactly one strike interval below it.
For put options the same pattern emerges. The highest return is obtained when the sell strike is equal to the the stock's lower target and the buy strike is one strike
price interval above that.
The above represents the most aggressive strategy since the stock price needs to move past the Buy Strike in order to have any value on expiry date. By moving the Buy Strike
closer to the current stock price, you will increase the chance of having a winning trade while decreasing the potential return. The Expiry Week Option Evaluator and Screener
automatically select the nearest at the money strike as the buy strike and the strike price closest to our projected target as the sell strike. In other words we are
taking the same buy strike we would take if we were only interested in buying a simple option. We then write the option against this position that will net us the highest
return based on our projected target.