Lloyds Banking Group (LSE: LLOY) is quite an enigma these days.

The bank quickly outstripped its fellow bailed-out casualty Royal Bank of Scotland in the recovery stakes. It returned to a modest profit as early as 2013, paid its first post-crash dividend in 2014 after profits recovered strongly, and in 2015 paid a dividend yield of 3.1%.

Forecasts suggest that dividend yields will rise as far as 6.6% this year and 7.7% next, and Lloyds shares are on a forward P/E of 8.8 for 2016, dropping as low as 8.6 based on 2017 forecasts. And the City’s tipsters are putting out a pretty serious strong buy rating.

Mixed quarter

On top of that, a first-quarter update in April announced a “robust financial performance with stable underlying profit and strong underlying returns“. Statutory pre-tax profit was a modest £0.7bn for the quarter, and that disappointed the market a little. But the bank also reported an underlying profit of £2.1bn, and an impressive 13.8% return on equity. All the usual liquidity ratios look fine, tangible net assets are rising, and operating costs are falling.

Yet Lloyds shares have been in a slump. The price was recovering reasonably well up until last May, but in a little less than a year we’ve seen a fall of 25%, to just 67p. So why do investors apparently not want Lloyds shares when all the signs are looking so good?

It must be in part due to the lingering fears surrounding the whole banking sector, with still-unknown levels of financial penalties for past misdeeds weighing heavily on the minds of institutional investors who just can’t handle uncertainty. Lloyds was, after all, the biggest culprit in the PPI mis-selling scandal.

Cracking fundamentals

But when you compare the bank’s fundamentals with the others in the sector, Lloyds shares really do look oversold. RBS is on a much higher forward P/E of 12.7 with no substantial dividend expected before 2017, and Barclays shares command a multiple of 10.8 despite that bank’s recent 50% dividend cut (and expected yields of less than 2%). Even HSBC Holdings, with its worrying exposure to the impenetrable Chinese financial sector, is on a multiple of 10.4.

But Lloyds looks the strongest in the sector right now, with the greatest potential to reward shareholders long-term. Provisions already made for PPI penalties should hopefully now be sufficient, and the bank’s recent record of dumping poorer-performing assets and strengthening its balance sheet, and improving its capital efficiency ahead of its rivals, really makes Lloyds shares look attractive – even ahead of Barclays shares.

A double?

Could Lloyds shares double in the next 12 months? If they did, we’d be looking at a forward 2017 P/E of a little over 17, and a dividend yield of 3.9%. That might be a little overpriced, but not by very much. And within the next couple of years, a doubling looks very possible.

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Alan Oscroft owns shares of Lloyds Banking Group. The Motley Fool UK has recommended Barclays and HSBC Holdings. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.