There are countless companies that may not be on your investment radar but would be interesting at the right price. In other cases, there are stocks that you wouldn't want in your portfolio no matter what.

That could be because you simply don't like the brand, or it could be something deeper. The two companies noted here will probably never find their way into my portfolio -- although one of them could (but probably won't) address the issue that keeps me away and the other could, in theory, completely revamp its operations and win me back over (but that's not likely, either).

A pepperoni pizza is seen on a wooden table.

Papa John's pizza does not look this good. Image source: Getty Images.

Don't come to Papa

While Papa John's (NASDAQ:PZZA) stock has been in freefall due to the company's fight with its founder John Schnatter, I would have advised against buying shares before those issues surfaced. The pizza company won't find its way into my portfolio because it does a terrible job executing on its core product.

Put simply, Papa John's may use "better ingredients, better pizza" as a marketing tag line, but it's not true. I'm sure the chain uses better ingredients than some low-end pizza restaurants (maybe all-you-can-eat for $5 chain CiCis?) and it's also probably better than, say, Red Baron frozen pizza, but those are low bars.

Papa John's core product is worse than what's available at most local pizzerias, and it's inferior to the still-bad pies served up by Domino's (NYSE:DPZ) (though some may argue that). The struggling company also lags its chief rival when it comes to technology and execution. Domino's may not be great at pizza, but it's really good at getting attention (for the right reasons) and at getting you your order in a variety of ways.

I can't invest in a company that disappoints me with its core product and celebrates that same product as being great. Domino's at least tried to improve its pizza (it's better than it was) and then recognized its core offering is convenience. Papa John's has never acknowledged that its food needs work -- and that seems unlikely to change.

Death of an icon

I want Sears Holdings (NASDAQ:SHLD) to survive, but that seems unlikely. The company has lost money in every quarter for roughly five years, except the ones when it only made a profit due to a one-time asset sale. It has burned through not only its cash, but also most of the assets that could be sold for cash to buy time.

This is happening because while CEO Edward Lampert talks about turning things around, he doesn't have a credible plan for doing so. Whereas struggling rival J.C. Penney has added new product categories (including appliances, toys, and home services), revamped its salons, and changed its women's apparel assortment, Sears has mostly closed stores.

Being aggressive and trying to turn its stores into destinations has not saved J.C. Penney, but it does give the company a chance at survival. Selling off real estate and name brands including Craftsman while closing stores has not slowed Sears' losses, and some of its moves may be hastening its demise.

Even though Sears Holdings shares sometimes jump on some glimmer of good news, the end of this story isn't in doubt. Sears has very little, if any, hope for survival, and there's no reason to believe that will change.

New levels of misery

Papa John's and Sears are both moving in a bad direction. The pizza chain may fix its management issues, but at the moment, those problems add to the woes created by its subpar food. For Sears, there's seemingly no hope that management will improve, because Lampert isn't getting fired. Money from his hedge fund has, in part, kept the chain afloat in the first place, so he'll likely be there to turn off the lights as the last store closes -- probably right after he delivers a speech about how things are turning around.

Daniel B. Kline has no position in any of the stocks mentioned. The Motley Fool has no position in any of the stocks mentioned. The Motley Fool has a disclosure policy.