Understanding risk has always been critical to option traders. Most of the time, we think of risk in terms of volatility, and the impact that has on the value of an option. Options traders even talk about the cost of an option in terms of the volatility being implied by the price. Higher implied volatilities mean higher option prices.

Unfortunately, most options traders have only a basic understanding of the impact volatility can have on strategy selection. Covered call writing is one of the common options strategies, but to be successful, the covered call writer has to consistently sell overpriced calls — calls that are implying a higher volatility than the underlying stock is likely to experience over the life of the option.

Perhaps a better way to view risk is in terms of probability. What risks offer the best odds of success? Think about it in terms of a poker game. Suppose you are trying to draw to a straight. If you have a 3, 4, 5 and 6, you are drawing to an outside straight, which means you complete the straight by drawing either a 2 or a 7. Now, suppose you have a 4, 5, 7 and 8 in your hand. In this case, you would be drawing to an inside straight. The only
card that can help you is the 6.

Here’s what I mean when I talk about risk within the context of probabilities. The player drawing to the outside straight has twice the odds of success as the player drawing to the inside straight. Yet the reward for both hands is the same, suggesting some rewards are simply not worth the risk.

The poker analogy is an interesting reference to the benefits of linking risk to probability. When you apply the poker logic to the stock market, most investors hold poker hands with a 3, 6, 9 and 10, and are still trying to draw to a straight.

The same thinking applies to the options market. All too often, we buy calls on a whim. Or sell covered calls or write naked options because these are chances to pick up some extra cash. And we never consider the risk involved with the position.

That leads us to another point. When we talk about probabilities, we can apply the analysis to any option strategy, both from the long and short side of the market. If you leave this discussion thinking that probability analysis favours covered call writing because “time is on my side,” you have missed the point.

If you buy XYZ at $30 and write an XYZ 35 call for $2 a share, your maximum return is capped at the $35 strike price. What if, at expiration, the stock closes at $50? The covered call writer earned the maximum profit, and the odds favoured the covered call writer relative to the call buyer. But was the covered call writer the ultimate winner? Not necessarily. In this case, the call buyer could have purchased the call for $2 a share and sold it for $15 a share at expiration. A much better return, although the probability of
earning that return was much lower.

But here’s the thing: If call buyers can earn three to four times their initial investment 20% of the time, are they worse off than the investor who earns 20% on his investment 50% of the time? A lot depends on the psychological makeup of the investor, which speaks to what flow of investment return one would like to have. But from a purely statistical position, both positions may end up with the same risk-adjusted returns over time.

So perhaps there is a case for buying options. If so, it goes against all you hear in the marketplace. There are just so many questionable statistics stacked up against the options buyer. How many times, for example, have you heard that 80%-90% of all option contracts expire worthless? How many times have you heard that time is your enemy so you should always sell options?

In truth, there is little evidence supporting the notion that 80% or 90% of all options contracts expire worthless. I’m not sure what number is reasonable, but these percentages seem high. Moreover, the notion that even the majority of options contracts expire worthless does not, in itself, make the case that one should never buy options. It doesn’t take into account how often options are bought and sold prior to expiry.

@page_break@The reality may be that options buyers do better than you think. Especially if they have done some due diligence before making the purchase. The trick is buying the right strike, selecting the right time period and, more importantly, knowing when to sell.

Here is an example of how one can bring probability into the discussion. XYZ closed at $90. The XYZ October 95 calls are trading at $5. Some simple math tells us XYZ has to be above $100 at expiration for this option to be profitable. To calculate that, we simply add the premium paid to the strike price of the call ($5 + $95 = $100).

If we apply a probability distribution to XYZ shares, there is about a 35% chance that XYZ will be above $100 over the next four months. Not the formidable odds one might get when looking at the percent of option contracts that expire worthless but, still, the odds are stacked against the call buyer. Or are they?

Here is where statistics can be misleading. Just because XYZ has only a 35% chance of being more than $100 at expiration, doesn’t mean XYZ cannot reach $100 at some point before the October expiration.

If you looked at the historical price patterns of XYZ, there may be a better than 80% chance that the stock will touch $100 at some point prior to the October expiration. How do we know that? We begin by calculating the percentage move that XYZ must make in order to reach $100 at the October expiration. The percentage move is +11.1%, which is simply the $100 target price divided by the current price ($90) minus 1.


The next step is to look at how often XYZ’s share price advanced more than 11.1% over any 127-day period.


That speaks directly to how options are traded in the real world. The call buyer does not have to wait until expiration to turn a profit. In fact, most options are sold prior to their expiration, and they sometimes are purchased and sold many times before they expire.

Historical price patterns are always 20/20. In reality, they never tie perfectly to the future.
However, looking at historical patterns does give us some perspective of the odds of meeting expectations in the future. And successful option-buying strategies are based on this kind of information.

Traders who want to utilize this type of analysis should seek positions in which the underlying stock has historically moved the required distance at least 80% of the time. IE