The flagship XOI oil-stock index has been a wonderland for options speculators this year. A combination of factors including strong energy prices, outstanding oil-stock fundamentals, fairly moderate and predictable volatility, and bullish technicals has created dazzling opportunities in oil-stock options.

In our Zeal Speculator alert service we started layering into oil-stock calls back in late November when oil-stock sentiment was pretty rotten. At the time prevailing market wisdom assumed that the high oil prices were a hurricane anomaly rather than a new fundamental reality. Few investors were willing to bet that oil prices would remain strong even in the absence of hurricanes and geopolitical scares.

Yet with oil stocks trading around 7x to 10x earnings, dirt cheap in fundamental terms, it was a very compelling play to get on their long side. But the problem with oil stocks is they don't rally very rapidly. A typical XOI upleg might run 25% higher or so. This is pretty anemic compared to the average HUI gold-stock index upleg of 104% in its bull to date. But thankfully oil stocks' modest expected gains can be leveraged tremendously with options.

Because oil stocks are so large, stable, and low-priced relative to the earnings and cashflows they are spinning off, they are ideal for call options. Even relatively conservative call options strategies in oil stocks can lead to enormous realized gains. In Zeal Speculator, for example, our average realized gain in oil-stock calls this year is running 164%. And we currently have another dozen or so open trades expiring later this year and early next with average unrealized gains running 72% as of this week.

While oil-stock calls are very lucrative today, timing options trades is always a paramount concern. When you buy a normal call option, it will cease to exist no more than 6 or 7 months from the date of purchase. If the stock underlying it hasn't moved far enough up in that period of time, you are guaranteed a 100% loss. Options are a highly risky side game only appropriate for those with nerves of steel and plenty of risk capital.

Since oil stocks are not very volatile compared to most other commodities producers, I have been concentrating on swing trading for our oil-stock calls. Our swing trading is technically focused and tries to catch and ride the major uplegs so it generally has a time horizon of 6 months or so. For years now I have been developing tools such as Relativity that help time trade entry and exit points within the context of the major swings.

While these broader tools work well, with options any increase in the precision of timing can yield dramatic increases in profits. For example, this week we exited a call trade on an up-and-coming oil refiner at a 343% realized gain. Just one week before this sale though, this very trade was only up 186%. And two weeks before this sale it was just up 77%. Thus developing better tools for more precise options timing is well worth the effort.

This perpetual quest is always in the back of my mind as I try to better my understanding of the probabilities underlying the markets. It was with this mindset, and heavy personal exposure in oil-stock calls, that I watched the amazing run in the XOI over the last couple weeks. As of this Wednesday, the data cutoff for this essay, the XOI was up an unbelievable 10 consecutive trading days in a row!

While I was certainly thankful to watch my options explode higher, I was wondering how rare a 10-day winning streak is in the XOI. And even more importantly, how has the XOI tended to behave in the past after long winning streaks. Is it best to buy additional positions after a long winning streak to game the momentum or best to remain neutral like a contrarian and wait for weakness to buy again? I needed to know.

In order to explore the likelihood of XOI streaks as well as the expected XOI behavior after them, I examined the entire history of the index, which runs back to 1983. I also took a liberty with the concept of a streak. Technically a winning streak only exists when the XOI closes up a number of days in a row without interruption, and of course the opposite for a losing streak. But sometimes a streak has a minor interruption.

For example, say the XOI closed higher 7 days in a row. Then on the 8th day it fell modestly, just a small fraction of a percent. Then on days 9 and 10 it rose again strongly. Is this a 7-day streak or a 10-day streak? Technically it is a 7-day, but as a speculator I think it is more realistically a 10-day streak since the index had been rising strongly on balance for 10 days. The small contrary day did not end the uptrend that we want to trade, it was essentially a 10-day winning streak with excellent potential to spawn big gains in oil-stock options.

In order to account for these small contrary days, I used a modified definition of a streak. After a streak started, if it had a contrary day that moved less than 0.1% against it on a closing basis and then the streak resumed, I considered the entire duration a single streak. While not as strictly academic, this focus is much more closely aligned with my interest in streak odds as an active options speculator.

I also counted each streak only once. A 7-day streak was only counted as a 7-day streak even though it contained a 4, 5, and 6-day streak within it. So each streak in this analysis is considered just a single time at its maximum duration, not as a Russian-matryoshka-nesting-doll-type thing with each large streak containing all the sequentially smaller ones.

To start, I wondered if long streaks tended to cluster around certain tradable events, like major interim highs or lows in the XOI. I plotted every streak of 4 days and over on this chart since this oil-stock bull began back in early 2003. The minor streaks running 4 to 6 days are kind of a control group, because streaks really don't get interesting and rare until they hit 7 days or greater. Their relative rarity is quite apparent in this chart.

As you can see, 4-day streaks, both winning and losing, are all over the place. They happen during uplegs, corrections, and consolidations. These 4-day streaks, since they are so common, are essentially market noise. This explains why not many traders get very excited when the XOI is up or down just 4 days in a row. As we should expect during a bull market though, there are more 4-day winning streaks than losing streaks.

5-day winning streaks are naturally a little rarer than the 4-day ones. If you look carefully at all the 5-day winning streaks above, interestingly the vast majority tend to occur in the middle of major uplegs. Conversely the 5-day losing streaks tend to manifest themselves in the middle of major corrections or consolidations. As such, when we see a 5-day streak in the XOI it is likely just a reflection of the ongoing tactical trend and not a reversal signal.

6-day streaks are rarer still, there have only been five 6-day up streaks and three 6-day down streaks in the XOI since this bull market launched. Unfortunately these 6-day streaks don't seem to cluster meaningfully. There is one in early 2005 at the very beginning of a massive upleg but there is another in mid-2004 towards the apex of an earlier upleg. Another in late 2005 is in the middle of a consolidation. So I don't see any exciting tradable likelihoods based off of 6-day winning streaks.

The 6-day losing streaks are another matter though. All three of them in this chart happened just after the XOI hit its highest levels it was going to see for another couple months or so. While our sample size of only three 6-day losing streaks is small, I will definitely favor viewing them in the future as the possible beginning of a correction or consolidation based on their prior clustering in this bull to date, especially if they spawn off a major interim top.

7-day streaks are where things really start getting interesting. There have only been three winning and one losing since this bull launched. The early 2003 7-day winning streak happened early on in a major upleg when the XOI still had much room left to run yet. So did the recent one in 2006. But the 2004 7-day winning streak lead to a major interim top in the XOI that was not to be eclipsed for a couple months or so.

There was only one 8-day streak in late 2003, and that was near the end of the surge phase of a major upleg. No 8-day losing streaks have been witnessed yet in this bull. No 9-day streaks, going either way, have been witnessed yet in this bull market either. And until this week, there were no 10-day streaks. But our recent 10-day winning streak erupted off relatively low levels where the XOI was under its 200-day moving average for the first time in this entire bull to date.

While plotting these XOI streaks in its bull to date was somewhat interesting, it doesn't seem to be particularly helpful for trading. There wasn't a lot of serious clustering. For example, if the vast majority of winning streaks had all occurred off of major interim lows as our recent monster 10-day one did, then they would be a great signal to buy. But alas this did not prove to be the case. Big streaks seem to be able to happen in all stages of a bull, which does not make them very conducive to this method of gaming them.

Undaunted, I forged ahead. There are lots of dry holes in market research, ideas that don't prove particularly fruitful. So to examine XOI streaks from a deeper level, I looked at them purely mathematically rather than relatively on a chart. While I examined the entire XOI history since 1983, I also did a second subset that only included the recent XOI bull since 2003. This additional analysis did prove promising for speculators!

I used the same definition of a streak in this secondary analysis, allowing minor contrary days of less than 0.1% on a closing basis to be included within streaks. In the table below the duration of the streaks in days is found in the yellow rows. The numbers of up streaks and down streaks at those durations are listed in the green and red rows respectively. After counting the streaks, I added some rudimentary statistical analysis.

The first row shows an approximation of the probability of a particular streak happening. Since I am a speculator and not a mathematician, these aren't true probabilities. My methodology is simple though. If I was examining 100 trading days and looking for 5-day streaks, I broke up the 100 days into even increments and assumed twenty were possible. With 100 trading days and 10-day streaks, ten would be possible. If two 10-day steaks happened in this example, they would have a probability of 0.2.

While not true probabilities, these give me a good idea of how often streaks are likely to occur relative to each other. Of course they generally get rarer with duration. The longer a streak runs, the less likely it is to happen. Using this methodology, a 5-day streak is 7x more likely than a 10-day streak in the entire history of the XOI. These probability approximations are interesting, but the expected gains are the really important component.

After each streak, I computed the gains 20 trading days, roughly one calendar month, later. I was interested in what the average expected gains were after winning and losing streaks of particular durations. I averaged these gains over all the streaks of a particular duration to derive an expected one-month gain. Included below these gains are the standard deviations of these averages to help show how tightly or loosely they were clustered. The results were very fascinating, not to mention tradable.

Before I did this research, there were three ways I thought it might turn out. It could be totally meaningless, no apparent relationships at all, and hence useless for speculators. Or it could be momentum-based, a month after a streak the XOI continued to run strongly in the same direction. Or it could be contrarian-based, the XOI was likely to head in the opposite direction in the month following a long streak. This latter thesis proved to be correct.

In the first chart we used 7-day streaks as the starting point for defining long streaks. Note above that in the history of the XOI there have been seventeen 7-day winning streaks. 20 trading days after these streaks, on average, the XOI has been down 0.9%. Conversely there have been ten 7-day losing streaks. And 20 days after these losing streaks, on average, the XOI has been up 4.4%. This is definitely a contrary-type relationship, which makes a great deal of sense.

As speculators, we want to buy when everyone else is selling and sell when everyone else is buying. When a long streak is witnessed in the XOI, odds are it has already sucked in most of the short-term traders who want to trade with that streak. So when the streak ends, sentiment is already tilted too far in the direction of the streak. In order to rebalance sentiment, the XOI tends to drift in the opposite direction of the streak over the following month. This is nearly universally apparent above at almost all streak durations.

If you carefully examine this table, a few very important strategic trends emerge regarding streaks. First, in nearly every case, the expected gains one month after a streak were much higher after a losing streak than after a winning streak. Second, the expected gains one month after a winning streak were usually negative while the expected gains after a losing streak were usually positive.

Third, the longer the duration of a streak, the more pronounced these differences were likely to become. Finally, the larger the sample size of a particular streak duration, the more these key observations held true. Taken together, all of these observations support the contrarian view of streaks and suggest speculators can align themselves with much more favorable probabilities by fading the XOI after long streaks rather than betting on their momentum continuing.

Coming full circle to trading oil-stock options, speculators can use streaks in the XOI to more precisely time their buy and sell decisions within the context of the big swings. After an XOI winning streak of moderate-to-long duration, the index generally trades flat to lower over the coming month. So if traders want to align themselves with probabilities, they should probably not be adding new longs at the end of a winning streak. But they can certainly sell their short-dated call options at the end of a winning streak to realize their profits.

And naturally this logic inverts after a moderate-to-long losing streak in the XOI. After an XOI losing streak probabilities favor the index rallying in the coming month so it makes sense to add longs at that time, at least as long as other indicators continue to favor an ongoing XOI upleg. And since the odds favor the XOI rising in the weeks after a losing streak, it doesn't make a lot of sense to sell right at the end of a losing streak rather than wait for higher prices a few weeks out.

Determining when a particular streak ends is easy too. In the context of this research, a streak is not considered over until the XOI closes against the streak by more than 0.1% in the opposite direction for a single day. Once this degree of contrary day arrives, the streak is officially over and the probabilities governing the expected 20-day gains shown above kick in.

Speculators have much higher odds for success if they perceive long streaks in contrarian terms. After winning streaks the odds favor a minor correction or consolidation and after losing streaks the odds favor a minor rally. While the degree of these expected moves counter to the preceding streak direction is generally modest, even minor moves can spell differences of over 100% in realized gains on oil-stock options.

If trading oil-stock call options intrigues you, you ought to consider a subscription to our high-end Zeal Speculator alert service. We currently have about a dozen oil-stock call trades outstanding with average unrealized gains of 72%. I hope to add more on any XOI weakness. The XOI really ought to be strong in the remainder of 2006 due to its low valuations, persistently high oil prices, and non-exuberant technicals. Any hurricane or geopolitical scares will simply be icing on the cake.

The bottom line is long winning and losing streaks in the XOI, and probably any major stock index, are generally governed by probabilities that can be profitably traded. After a long streak sentiment is unbalanced so a slow fade in the opposite direction is probable in the month immediately after a streak ends. Speculators aware of this tendency can use it to fine-tune options entries and exits around streaks.

While the degree of the differential in expected returns following winning and losing streaks is probably not great enough to excite stock investors, in the highly leveraged world of options even small probability edges can yield fantastic additional profits. In options, it pays big to carefully consider even minor details.