Google briefly took Apple’s long-held crown on Tuesday, before Apple wrested it back during trading on Wednesday. But while the title of “most valuable company” may seem like an honor to the average observer, research shows that it’s a designation best avoided.

Research Affiliates Rob Arnott and Lillian Wu published a study back in 2012 that showed that companies that lead their sectors in market capitalization vastly underperform the market. “We find a statistically significant tendency for top companies in each sector to underperform both the overall sector and the stock market as a whole,” they write. “We found that 59% of these Top Dogs underperformed their own sector in the next year, and two-thirds lagged their sector over the next decade. We found a daunting magnitude of average underperformance, averaging between 300 and 400 bps per year, over the next 1 to 10 years.”

So why do valuable companies underperform? One reason is government scrutiny. “Being large puts the company under the scrutinizing lights of regulators,” the authors write. Arnott and Wu cite the recent examples of Goldman Sachs (GS) and Microsoft (MSFT) as sector-leaders that came under tough government scrutiny because, as the largest companies in their respective sectors, they were symbolic targets for government regulators on the hunt for headlines. Google’s recent struggles with foreign regulators is one example of this trend.

Another reason for the struggles of valuable companies: It’s likely that their best days are behind them by the time they’ve achieved “top dog status.” Arnot and Wu write:

Many investors seem to ignore the fact that the forces that drove these companies to dominate their competitive landscape do not guarantee sustained growth in the future, or a sustained position at the top. Said another way, these investors do not appear to expect mean reversion in their growth forecasts; they form biased expectations based on extrapolating past successes that are often not predictive of the future. While it is easy to double market share when 5 a company holds 1% or 2% of the market, it is impossible to double market share once the company has a 51% market share.

Regardless of which of these companies settle into the number one spot, it’s likely that these factors will hold back both Google and Apple in the months and years ahead.