Understanding risk has always been critical to options traders. Most of the time, risk is thought of in terms of volatility — and the impact that has on the value of the options. Options traders even talk about the cost of an option in terms of the volatility being implied by the price, because higher implied volatility means higher options prices.

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

Perhaps a better way to view risk is in terms of probability. What type of risk offers 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 three, a four, a five and a six, you are drawing to an outside straight, which means you complete the straight by drawing either a two or a seven.

Now, suppose you have a four, a five, a seven and an eight in your hand. In this scenario, you would be drawing to an inside straight — the only card that can help you is a six.

So, 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. This suggests that 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 three, a six, a nine and a 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 it is a chance to pick up some extra cash without ever considering the risk involved with the position.

That leads to another point. When we talk about probabilities, we can apply the analysis to any options strategy, both from the long and short sides 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. But what if the stock closes at $50 at expiration? 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. That’s a much better return, although the probability of earning it was much lower.

But here’s the thing: if call buyers earn three to four times their initial investment 20% of the time, are they worse off than inves-tors who earn 20% on their investment 50% of the time?

A lot depends on the psychological makeup of the investor, which speaks to what flow of investment return he or she would like to have.

However, from a purely statistical position, both positions may end up with the same risk-adjusted returns over time.

So, maybe there is a case for buying options. If so, it goes against all that you hear in the marketplace. There are just so many questionable statistics that are stacked up against the options buyer.

How many times, for example, have you heard that 80% to 90% of all options contracts expire worthless? How many times have you heard that time is your enemy, so always sell options?

In truth, about 20% of options contracts actually expire worthless. But that aside, the notion that even the majority of options contracts expire worthless does not, by itself, make the case that one should never buy options.

@page_break@It doesn’t take into account how often options are bought and sold prior to expiry.

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 important, knowing when to sell.

Here’s an example of how one can bring probability into the discussion: XYZ closed at $90. The XYZ 95 calls expiring in four months are trading at $5. Some simple math tells us that XYZ has to be above $100 at expiration for this options 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 during the next four months. These are not the formidable odds you might get when looking at the percentage of options contracts that expire worthless; but, still, the odds are stacked against the call buyer — or are they?

Here’s where statistics can sometimes be misleading.

Just because XYZ has only a 35% chance of being above $100 at expiration doesn’t mean that XYZ cannot reach $100 at some point over the next four months leading up to 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 expiration. How do we know that?

Begin by calculating the percentage move that XYZ must make in order to reach $100 at expiration. The percentage move is +11.1%, which is simply the $100 target price divided by the current price ($90) minus one.

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

This 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 expiration, and sometimes, are purchased and sold many times prior to expiration.

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

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