As recovery stories go, FTSE 100 star Rolls-Royce (LSE: RR.) has been incredible.

There was a time — not long after the beginning of the global pandemic — when no one would go near the company. Back then, this felt logical. In addition to drowning in debt, the engineer’s outlook was ominous considering air travel had pretty much ceased in an effort to contain Covid-19.

Of course, hindsight is a wonderful thing. We now know that this was precisely the time to load up on the shares. In a few years, CEO Tufan Erginbilgiç has managed to turn the company around through a combination of cost-cutting and streamlining. The share price has duly responded. And then some!

The question I’ve been asking is what will be the next brilliant turnaround stock in the UK market’s top tier?

FTSE 100 laggard

One potential candidate could be automotive marketplace provider Auto Trader (LSE: AUTO).

Yes, it’s true that this is a completely different entity to Rolls-Royce in many respects. Rolls-Royce earns its money from making engines and maintaining them and has a global reach. Auto Trader links UK buyers with sellers of vehicles and does it all online.

However, the latter is currently hated by the market, just as Rolls-Royce was back in 2020. Indeed, it features high up the list of most shorted shares among traders. In other words, many are betting its price — down nearly 40% in 12 months — has even further to fall.

They could well be right. In recent times, more and more investors have begun to question whether businesses such as this can withstand the onslaught of AI.

Elsewhere, the company has faced backlash from dealerships for new initiatives. Even the British competition regulator is now investigating Auto Trader as part of a crackdown on fake reviews.

It never rains but it pours.

Auto Trader isn’t broken

On a more optimistic note, I think there’s quite a lot to like here.

The £4bn cap still has a virtual monopoly in what it does. It still posts incredible margins that would turn most firms green with envy. Levels of debt are current negligible too thanks to its asset-light business model.

Then there’s the valuation. A forecast price-to-earnings (P/E) ratio of 14 practically screams ‘bargain’ if – and that’s a sizeable ‘if’ — relationships with dealerships can be repaired and the aforementioned AI threat proves overblown (it’s worth noting that the company is already integrating its own AI-infused tools into the site).

Worth a closer look

Notwithstanding this, I’m definitely not expecting a recovery like that of Rolls-Royce (if it comes). The latter’s revival has been epic, supported by a recovery in aviation and a boom in defence spending. It’s hard to see how Auto Trader could ever achieve the same levels of revenue growth.

Even so, I do think it might warrant attention from contrarian-minded long-term investors, particularly with the share price languishing where it is. With expectations so low, any chinks of light in the next set of full-year numbers — due 21 May — could be the catalyst value hunters have been waiting for.

But I would like to see some director buying before too long. Damningly, there’s been none of this for many years (and an awful lot of selling!).