A Chipotle Mexican Grill in New York City. Image source: Chipotle Mexican Grill (Photographer: David Sundberg).

As a shareholder in Chipotle Mexican Grill (CMG -0.43%), I was happy to learn yesterday that billionaire hedge fund manager Bill Ackman has taken a nearly 10% stake in the burrito chain, sending its shares as much as 7% higher in Tuesday's after-hours trading session.

The impact filtered through to today, with Chipotle's shares up more than 5% halfway through Wednesday's trading session.

I couldn't agree more with Ackman's belief that Chipotle's stock is "undervalued" and an "attractive investment." And while I'm skeptical that Ackman will succeed at introducing substantive changes to the way Chipotle operates -- after all, aside from the food safety incidents that cropped up last year, it's hard to criticize, in Ackman's terms, Chipotle's "visionary leadership" -- his past success as a hedge fund manager is encouraging for investors who may have begun to lose faith in the restaurant chain.

At the same time, what matters more for ordinary investors in Chipotle is not the fact that someone with as high of a profile as Ackman has taken an interest in its stock. The underlying issue is instead about one simple thing: same-restaurant sales.

This is the metric that investors should be tracking right now in order to divine Chipotle's success at moving past the food safety issues that cropped up at the chain last year, causing customers to flee its stores and investors to dump its stock.

Data source: Chipotle Mexican Grill. Chart by author.

The low point came in January of this year, when same-restaurant sales were down 36% compared to the same month last year. For the entire quarter, which spanned from the beginning of January through the end of March, same-restaurant sales were off by 29.7%.

The situation remained dire in the second quarter. For the three months ended June 30, 2016, comparable sales were down 23.6%. It may go without saying, but until Chipotle can turn this around, there's little reason to think that its shares will reclaim the ground they've lost over the past 11 months -- they're still down 42% from last year's high.

But all is not lost. Even though Chipotle's same-restaurant sales are negative, they're gradually improving.

On its second-quarter conference call, the chain's executives noted that comps were down 21% in the first three weeks of July. That's abysmal, but it's meaningfully better than the larger declines in the first and second quarters. And it's much better than January, when sales were lower by 36%.

This will undoubtedly improve, both as a result of Chipotle's own actions, such as its recently rolled-out customer loyalty program, Chiptopia, as well as from the fact that it will soon be comping against much lower numbers. Consider this: By the first quarter of next year, its comparable sales will be measured against its worst quarterly performance on record -- the first quarter of this year.

That's the inflection point investors should keep their eyes on. After crossing it, the psychological impact from falling same-restaurant sales should no longer act as a drag on Chipotle's stock. It will be then, according to my thesis and probably Ackman's, too, that investors are likely to begin seeing sustainable growth in its share price.