John Reese's bullish view on the oil majors on these pages Monday caught me by surprise because I gave up on this group when it failed to match broad market performance in the post-bear-market recovery. In light of his wakeup call, let's look at these sleeping giants from a technical perspective.

I'll focus on just two stocks,

ExxonMobil

(XOM) - Get Report

and

Chevron

(CVX) - Get Report

, because they're members of the

Dow Industrials

and homegrown oil behemoths. Any conclusions we can reach about these mega-caps might also point to bottom-picking opportunities in the smaller refiners that have been nearly obliterated by several years of selling pressure.

First off, let's note that Chevron pays a higher dividend than Exxon -- 3.4% vs. 2.7% -- which might tip the scales if you decide that just one of these issues deserves a place in your portfolio. But that's begging the question; are these stocks worth buying at current levels?.

Exxon was a fabulous investment for more than 20 years, rising more than 200% in an historic uptrend that finally topped out at $95.64 in May 2008. The six-year run to its all-time high was especially strong, unfolding in strong alignment with crude oil's parabolic rise over $140.

The stock carved a triple-top pattern (red lines) with slightly higher highs between July 2007 and May 2008, finally breaking down in October of that year and dropping to a two year low at $56. It bounced quickly into the mid-$80s in December 2008 and then entered a steady downtrend that remains in place nearly two years later.

It's interesting that Exxon outperformed the broad averages during the bear market, holding well above five- to 10-year lows, and then failed to recover at the same pace. Of course, profit margins have been the devil in the works, with the refining side of the oil and gas equation failing to keep up with recovering crude oil prices.

The decline that started in December 2008 returned to the bear-market low in July of this year, when the stock bounced in a two-legged rally that's now reached the mid-$60s. Sadly, accumulation measured by on-balance volume (OBV) has hardly budged off deep lows, pointing to a dead-cat bounce as opposed to the start of a new bull-market advance.

However, there are a few technical bright spots in the three-month bounce. For starters, the stock has remounted the 200-day moving average for the first time since late 2009. You can see that price spent a few days trying to push over this resistance level back in April (red circle) and failed, yielding the decline that tested the two-year low.

It has also ended the unbroken string of lower highs and lower lows (green lines) set into motion after the November 2009 swing high near $76. This suggests the recovery effort will continue, at least until rising price nears stronger resistance in the lower $70s. A break through that level, along with a strong volume uptick, will signal the start of a new uptrend.

The verdict: Exxon has made progress in the last few months but still lacks the buying power needed to enter a sustained bull market. That might change in the next three to six months.

Like Exxon, Chevron was an exceptionally strong performer from the start of the bull market during the Reagan administration all the way to its May 2008 peak at $104. It also broke topping support (red lines) in October of that year, but that's where the easy comparisons end -- this issue took a much steeper plunge than its competition during the crash.

The stock bottomed out near $55 a few weeks later and popped up to $81 in December 2008. It tested the deep low three months later and posted a double-bottom pattern (red circle) that has yielded a stronger recovery than its energy peer Exxon. In fact, Chevron never looked back after turning the corner in March 2009 and is now trading at a two-year high.

However, the stock has barely extended the 27-point trading range printed in the two months following the October 2008 plunge. No, this isn't a problem if all you care about is the higher-paying dividend, but consider its limp performance compared to mid-cap oil & gas plays that are now running up to all-time highs.

The stock has also carved out an unstable broadening formation (red lines), posting a series of higher highs and lower lows. It's currently trading near resistance at the 62% retracement of the bear-market decline. This level also marks pattern resistance, with a buying spike over that level opening the door to a rally that should reach the high at $104.

The verdict: This stock is better positioned technically than Exxon, but investors should wait for a high-volume rally through the $85-to-$87 resistance zone before taking on risk.

Alan Farley provides daily stock picks and commentary with his "Daily Swing Trade" newsletter.

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At the time of publication, Farley had no positions in the stocks mentioned, although holdings can change at any time.

Alan Farley is a private trader and publisher of

Hard Right Edge

, a comprehensive resource for trader education, technical analysis, and short-term trading techniques. He is also the author of

The Daily Swing Trade

, a premium product from TheStreet.com that outlines his charts and analysis. Farley has also been featured in

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,

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,

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,

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,

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,

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,

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and

Online Investor

. He has written two books:

The Master Swing Trader

and

The Master Swing Trader Toolkit: The Market Survival Guide

, due out in April. Under no circumstances does the information in this column represent a recommendation to buy or sell stocks.

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