All the Intel (Nasdaq: INTC) bulls are going to love this: I was wrong about ARM Holdings (Nasdaq: ARMH).

I now realize that I've been overly bullish on the British chip designer, as I had bought shares personally back in September. My thesis was centered on ARM's unique role in the mobile-chip supply chain as the dominant IP licensor of nearly all mobile processors found in smartphones and tablets today.

On top of that, the company has promising prospects in other markets like smart TVs, servers, and embedded devices.

I've since sold my shares, and here's why.

Tale of the tape
Unfortunately, there is a glaring disconnect between ARM's royalties and the mobile-device market that I can no longer ignore. In fact, it's this same discrepancy that led to an official sell recommendation in Stock Advisor. Our flagship service had recommended buying ARM as early as 2003 near $5, and it was subsequently crossed off the scorecard in June 2009.

It's true that ARM has risen substantially since then and would have greatly benefited the SA scorecard if it had kept its spot, as shares have gained over 350% since that sell recommendation, but that doesn't address the flaws in its royalty model. This is how shares have performed since getting the SA boot.

ARMH Chart

ARMH data by YCharts

The problem then -- and now -- is that ARM has only modestly benefited from the meteoric rise of mobile-device adoption, and shares carry a rather lofty valuation that's increasingly hard to justify, even as it gains traction in new markets.

These numbers don't add up
ARM realizes revenue on chip shipments one quarter after they're shipped. So, for example, chips shipped in the second quarter of any given year will show up in ARM's results in the third quarter.

In ARM's first-quarter report, it saw 1.1 billion chips shipped bound for mobile devices, including phones and tablets, which was actually a decrease compared to the 1.15 billion mobile-bound ARM chips a year ago. Remember, those correspond to fourth-quarter 2011 device shipments.

In contrast, Gartner's fourth-quarter figures show that worldwide mobile-phone sales grew more than 5% to 476.5 million. Within those estimates, smartphone sales soared 47% to 149 million. IDC's tablet figures show even higher growth, jumping 155% to 28.2 million units.

So the broader mobile-device market is growing, driven by incredible gains in smartphone and tablet adoption, yet the number of royalty-bearing ARM chips decreased over the same time.

ARM inside
Smartphones and tablets predominantly carry ARM chips. The first Intel Atom-powered smartphone just launched in the Indian market, and Intel currently has no tablet spots. MIPS Technologies (Nasdaq: MIPS) has a tiny sliver of the market, notably in low-end devices that are ultimately doomed. MIPS has a handful of smartphone wins, but don't expect to be familiar with any of them.

All the gadgets you know and love, notably Apple's (Nasdaq: AAPL) iPhone and iPad, carry ARM-based chips -- anything from NVIDIA Tegras to Qualcomm (Nasdaq: QCOM) Snapdragons to Texas Instruments OMAPs, among many others. So why isn't ARM seeing more upside as its partners pump out processors based on its designs?

Qualcomm's chip business was literally responsible for all of its growth last quarter. Its CDMA technologies segment, which includes ARM-based Snapdragons, jumped 56%, while its licensing segment was flat.

Apple continues to evolve its own ARM-based chip strategy using its A-family of chips in iPod touches and Apple TVs, alongside iPhones and iPads. Good luck getting any detail on ARM and Apple's relationship, though, for Apple's stringent supplier secrecy requirements also apply to ARM.

At Mobile World Congress last month, when asked about the pair's partnership, an ARM strategist simply replied, "We don't comment on Apple." When asked a follow-up question, he responded with British charm, "We don't comment on Apple. Full stop." (That's a British colloquialism for "period," as in, "This conversation is over. Period.")

The best way to play ARM is not ARM
One theory might be that ARM smartphone chips are simply cannibalizing ARM feature-phone (dumb phone) chips, so ARM's results may be more closely tied to the broader market, rather than smartphones and tablets specifically. (The smartphone and tablet figures above add up to only 177.2 million, compared to the 1.1 billion chips ARM reported.)

Still, ARM should have more to show for it, as smartphones carry more ARM chips than feature phones, and tablets are a nascent market that is more of a threat to Intel's PC business than anything else.

Seems like the processor IP licensing business may not be all that attractive, as MIPS doesn't look good, either. This is where the Intel bulls predict that vertically integrated Chipzilla will overtake the mobile market, but that's still a steep hill to climb. It can be done, but I still think the odds are stacked heavily against Intel in mobile.

ARM chips still own the market, but it just seems that ARM isn't the one enjoying most of the benefits from that domination. There are many rungs of the supply chain where companies have a chance to add value, and it looks like most of the value-adding takes place after ARM's role and is being enjoyed primarily by its partners. In fact, licensees like Qualcomm and Apple are doing just fine.

Another one of ARM's partners has significant upside potential as it begins to gain traction in "The Next Trillion-Dollar Revolution." This company continues to score processor design wins and will be cashing in thanks to ARM's designs. Get the free report now.