Does troubled JCPenney need Sears to go away?

Investors seemed to be thinking that way Tuesday.

JCPenney (JCP) jumped 10% in morning trading as reports swirled that Sears was on the verge of going into bankruptcy court to begin the process of shutting down.

But as the story about Sears changed so did the fortunes of JCPenney's battered stock.

Just after 1 p.m. Tuesday, Sears announced an 11th-hour deal to keep the company alive — at least for now. JCPenney shares plunged and the stock closed down 5% for the day.

Despite the move to save Sears, the company's future is still very much in doubt. An auction of its assets could lead to a decision to start the process of closing down as soon as next week.

Investors assume that JCPenney is well positioned to benefit if Sears stores are forced to close. And there's some justification to that thinking, because there's clear crossover between the shoppers of the two store chains.

An analysis by Cowen and Co. found that 56% of Sears shoppers also shop at JCPenney, the highest overlap of any of the traditional department store chain. For example, the average age of a Sears shopper was nearly 50, according to Coresight. At Penney, it's just over 48.

But not everyone thinks Penney will rise if Sears falls.

"I think it's helpful for Penney if Sears goes away. I don't think it's going to really solve JC Penney's problems," said Neil Saunders, managing director of GlobalData Retail. "I don't think it's a game changer. Penney needs to do more to attract shoppers on its own. It's a very telling story if your path of success relies on someone else's failure. If Sears does die, the spoils of that are going to be widely distributed."

Sears has already closed hundreds of stores in recent years. But Penney hasn't been helped by those closures: Its sales have been flat-to-lower in recent years.

"If Penney were really going to benefit from Sears' departure, we would have seen it already," he said. Saunders said.

Penney reported another 3.5% drop in holiday season sales after the market closed Tuesday, which was actually not as bad as feared.

The company also announced it would close three stores, and that it would have positive cash flow for the full fiscal year that ends this month. So shares jumped 9% -- or about 11 cents -- in midday trading Wednesday.

But Penney's decline in sales came as overall holiday sales rose 5.1%, according to an estimate from Mastercard.

And despite the positive cash flow, Penney is expected to post another net loss for the year. So the company is facing trouble no matter what happens to its longtime rival Sears.

CNN Business' Nathaniel Meyersohn contributed to this report

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