Shares in Barclays (LSE: BARC) have fallen by 31% since the start of the year, with the bank cutting its dividend in half and announcing yet another fall in annual profits.

But, here are 3 reasons to stay bullish:

1. Valuations

With Barclays trading at 0.46 times its book value (or 0.55x tangible book value), the bank’s shares are selling for well below its liquidation value. By comparison, HSBC is worth 0.68 times book value, while Lloyds Banking Group is valued at 1.17 times. Low profitability and worsening expectations of global growth could explain for some of its discount, but Barclays’ shares seem massively oversold in the light of recent restructuring efforts and the bank’s strong underlying profitability.

On a forward price-to-earnings basis, valuations are attractive too. Its forward P/E is 8.6, on city analysts’ forecast that adjusted EPS will rise 5% this year to 17.5p. In 2017, they expect adjusted earnings will soar 30% to 22.8p, its forward P/E will fall to a mere 6.6 by 2017.

2. Barclaycard

Most banks offer credit cards, but none have a credit card franchise quite like Barclays’. Barclaycard is not only the market leader in the UK, but it is also unique in the way it operates across the entire payment flow – serving both consumers and businesses to make and receive payments. This helps Barclaycard to build scale, which in turn leads to cross-selling opportunities, lower costs and continued product innovation.

Barclaycard’s profitability ratios demonstrate the growing competitive advantage that it has over rivals – in 2015, the division’s return on average allocated equity rose 1.7 percentage points17.7%, with the business accounting 30% of the group’s total adjusted pre-tax profits. What’s more, underlying pre-tax profits have been growing at double-digit rates – with a 22% rise in 2015 alone.

Benefiting from its industry-leading international credit card experience, Barclaycard is not restricted to the UK economy. It has great organic growth opportunities across the world, with an expanding presence in both consumer lending and merchant services across Europe and the US.

If Barclaycard could be a standalone business, it could easily be worth at least 1.5x book value, or £9.5bn. That’s because the franchise is not simply worth  the value of its outstanding credit card balances, but also its brand name and its future growth potential. At that valuation, Barclaycard would account for 38% of the bank’s market cap, leaving the rest of the bank valued at around a third of its book value.

3. Recovery coming soon?

Legacy misconduct issues, particularly PPI, continue to hold back the bank’s recovery in profitability. Barclays announced a further £1.45bn provision for PPI in 2015, bringing its total misconduct costs to more than £4bn in the year, a 70% increase on last year. This more than offset the continued improvement in the bank’s core businesses, which saw adjusted profits rise 9% in the year.

The volume of PPI claims cannot continue to rise indefinitely, at least, not at anywhere near the pace it has been growing in recent years. Under proposals put forward by the Financial Conduct Authority (FCA), banks may soon be able draw a line under the PPI compensation saga, with a possible deadline for PPI claims in mid-2018. When these legacy misconduct costs eventually begin to taper off, Barclays may finally be able to reach its return on equity target of 11%.

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Jack Tang has a position in Barclays PLC. The Motley Fool UK has recommended Barclays. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.